Daily Papers

Stable Diffusion XL (SDXL) has become the best open source text-to-image model (T2I) for its versatility and top-notch image quality. Efficiently addressing the computational demands of SDXL models is crucial for wider reach and applicability. In this work, we introduce two scaled-down variants, Segmind Stable Diffusion (SSD-1B) and Segmind-Vega, with 1.3B and 0.74B parameter UNets, respectively, achieved through progressive removal using layer-level losses focusing on reducing the model size while preserving generative quality. We release these models weights at https://hf.co/Segmind. Our methodology involves the elimination of residual networks and transformer blocks from the U-Net structure of SDXL, resulting in significant reductions in parameters, and latency. Our compact models effectively emulate the original SDXL by capitalizing on transferred knowledge, achieving competitive results against larger multi-billion parameter SDXL. Our work underscores the efficacy of knowledge distillation coupled with layer-level losses in reducing model size while preserving the high-quality generative capabilities of SDXL, thus facilitating more accessible deployment in resource-constrained environments.

Layer dropout (a.k.a. stochastic depth) has been shown to enable faster training, higher accuracy, and robustness to zero-shot layer pruning in both language and vision transformers. However, as models and datasets have scaled, dropout - particularly layer dropout - has largely disappeared from large language models (LLMs) pre-training recipes. While some prior work has reported that dropout can degrade accuracy, no comprehensive study has quantified, let alone mitigated, this effect. In this study, we show that layer dropout should be used in state-of-the-art LLM training, establishing best practices and scaling analysis for both training and post-training benefits. Concretely, with optimal layer distribution, time schedule, and optimizer hyperparameters, we observe that at the same training FLOPs layer dropout leads to lower loss. For a given number of training steps, LLMs can achieve lower or similar validation loss while saving upto 25% of training FLOPs. Moreover, layer dropout enables significant post-training optimizations, such as early exit, intermediate-layer skipping, and self-speculative decoding, yielding up to 1.5x inference speedup with negligible accuracy loss. Across more than 2400 training experiments, spanning models from 271M to 8.2B parameters and datasets up to 160B tokens, we demonstrate that these findings extend reliably to large-scale training regimes. All pre-training experiments were run on Cerebras CS-3 systems.

The machine learning community has recently had increased interest in the climate and disaster damage domain due to a marked increased occurrences of natural hazards (e.g., hurricanes, forest fires, floods, earthquakes). However, not enough attention has been devoted to mitigating probable destruction from impending natural hazards. We explore this crucial space by predicting building-level damages on a before-the-fact basis that would allow state actors and non-governmental organizations to be best equipped with resource distribution to minimize or preempt losses. We introduce PreDisM that employs an ensemble of ResNets and fully connected layers over decision trees to capture image-level and meta-level information to accurately estimate weakness of man-made structures to disaster-occurrences. Our model performs well and is responsive to tuning across types of disasters and highlights the space of preemptive hazard damage modelling.

Neural network training relies on our ability to find "good" minimizers of highly non-convex loss functions. It is well-known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effects on the underlying loss landscape, are not well understood. In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple "filter normalization" method that helps us visualize loss function curvature and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture affects the loss landscape, and how training parameters affect the shape of minimizers.

Deep classifiers are known to be sensitive to data distribution shifts, primarily due to their reliance on spurious correlations in training data. It has been suggested that these classifiers can still find useful features in the network's last layer that hold up under such shifts. In this work, we question the use of last-layer representations for out-of-distribution (OOD) generalisation and explore the utility of intermediate layers. To this end, we introduce Intermediate Layer Classifiers (ILCs). We discover that intermediate layer representations frequently offer substantially better generalisation than those from the penultimate layer. In many cases, zero-shot OOD generalisation using earlier-layer representations approaches the few-shot performance of retraining on penultimate layer representations. This is confirmed across multiple datasets, architectures, and types of distribution shifts. Our analysis suggests that intermediate layers are less sensitive to distribution shifts compared to the penultimate layer. These findings highlight the importance of understanding how information is distributed across network layers and its role in OOD generalisation, while also pointing to the limits of penultimate layer representation utility. Code is available at https://github.com/oshapio/intermediate-layer-generalization

Loss spikes often occur during pre-training of large language models. The spikes degrade the performance of large language models and sometimes ruin the pre-training. Since the pre-training needs a vast computational budget, we should avoid such spikes. To investigate the cause of loss spikes, we focus on gradients of internal layers. Through theoretical analyses, we reveal two causes of the exploding gradients, and provide requirements to prevent the explosion. In addition, we propose a method to satisfy the requirements by combining the initialization method and a simple modification to embeddings. We conduct various experiments to verify our theoretical analyses empirically. Experimental results indicate that the combination is effective in preventing spikes during pre-training.

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose plasticity over the course of training even in relatively simple learning problems, but the mechanisms driving this phenomenon are still poorly understood. This paper conducts a systematic empirical analysis into plasticity loss, with the goal of understanding the phenomenon mechanistically in order to guide the future development of targeted solutions. We find that loss of plasticity is deeply connected to changes in the curvature of the loss landscape, but that it typically occurs in the absence of saturated units or divergent gradient norms. Based on this insight, we identify a number of parameterization and optimization design choices which enable networks to better preserve plasticity over the course of training. We validate the utility of these findings in larger-scale learning problems by applying the best-performing intervention, layer normalization, to a deep RL agent trained on the Arcade Learning Environment.

Although deep models have greatly improved the accuracy and robustness of image segmentation, obtaining segmentation results with highly accurate boundaries and fine structures is still a challenging problem. In this paper, we propose a simple yet powerful Boundary-Aware Segmentation Network (BASNet), which comprises a predict-refine architecture and a hybrid loss, for highly accurate image segmentation. The predict-refine architecture consists of a densely supervised encoder-decoder network and a residual refinement module, which are respectively used to predict and refine a segmentation probability map. The hybrid loss is a combination of the binary cross entropy, structural similarity and intersection-over-union losses, which guide the network to learn three-level (ie, pixel-, patch- and map- level) hierarchy representations. We evaluate our BASNet on two reverse tasks including salient object segmentation, camouflaged object segmentation, showing that it achieves very competitive performance with sharp segmentation boundaries. Importantly, BASNet runs at over 70 fps on a single GPU which benefits many potential real applications. Based on BASNet, we further developed two (close to) commercial applications: AR COPY & PASTE, in which BASNet is integrated with augmented reality for "COPYING" and "PASTING" real-world objects, and OBJECT CUT, which is a web-based tool for automatic object background removal. Both applications have already drawn huge amount of attention and have important real-world impacts. The code and two applications will be publicly available at: https://github.com/NathanUA/BASNet.

Transfer learning is widely used for training deep neural networks (DNN) for building a powerful representation. Even after the pre-trained model is adapted for the target task, the representation performance of the feature extractor is retained to some extent. As the performance of the pre-trained model can be considered the private property of the owner, it is natural to seek the exclusive right of the generalized performance of the pre-trained weight. To address this issue, we suggest a new paradigm of transfer learning called disposable transfer learning (DTL), which disposes of only the source task without degrading the performance of the target task. To achieve knowledge disposal, we propose a novel loss named Gradient Collision loss (GC loss). GC loss selectively unlearns the source knowledge by leading the gradient vectors of mini-batches in different directions. Whether the model successfully unlearns the source task is measured by piggyback learning accuracy (PL accuracy). PL accuracy estimates the vulnerability of knowledge leakage by retraining the scrubbed model on a subset of source data or new downstream data. We demonstrate that GC loss is an effective approach to the DTL problem by showing that the model trained with GC loss retains the performance on the target task with a significantly reduced PL accuracy.

Many approximate machine unlearning methods demonstrate strong logit-level forgetting -- such as near-zero accuracy on the forget set -- yet continue to preserve substantial information within their internal feature representations. We refer to this discrepancy as superficial forgetting. Recent studies indicate that most existing unlearning approaches primarily alter the final classifier, leaving intermediate representations largely unchanged and highly similar to those of the original model. To address this limitation, we introduce the Erase at the Core (EC), a framework designed to enforce forgetting throughout the entire network hierarchy. EC integrates multi-layer contrastive unlearning on the forget set with retain set preservation through deeply supervised learning. Concretely, EC attaches auxiliary modules to intermediate layers and applies both contrastive unlearning and cross-entropy losses at each supervision point, with layer-wise weighted losses. Experimental results show that EC not only achieves effective logit-level forgetting, but also substantially reduces representational similarity to the original model across intermediate layers. Furthermore, EC is model-agnostic and can be incorporated as a plug-in module into existing unlearning methods, improving representation-level forgetting while maintaining performance on the retain set.

The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size increases, a previously unexplored issue. We theoretically analyze the convergence of the loss landscape in a fully connected neural network and derive upper bounds for the difference in loss function values when adding a new object to the sample. Our empirical study confirms these results on various datasets, demonstrating the convergence of the loss function surface for image classification tasks. Our findings provide insights into the local geometry of neural loss landscapes and have implications for the development of sample size determination techniques.

Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are impossible in shallow models, or do they merely spread the same kinds of computation out over more layers? To address these questions, we analyze the residual stream of the Llama 3.1 and Qwen 3 family of models. We find: First, comparing the output of the sublayers to the residual stream reveals that layers in the second half contribute much less than those in the first half, with a clear phase transition between the two halves. Second, skipping layers in the second half has a much smaller effect on future computations and output predictions. Third, for multihop tasks, we are unable to find evidence that models are using increased depth to compose subresults in examples involving many hops. Fourth, we seek to directly address whether deeper models are using their additional layers to perform new kinds of computation. To do this, we train linear maps from the residual stream of a shallow model to a deeper one. We find that layers with the same relative depth map best to each other, suggesting that the larger model simply spreads the same computations out over its many layers. All this evidence suggests that deeper models are not using their depth to learn new kinds of computation, but only using the greater depth to perform more fine-grained adjustments to the residual. This may help explain why increasing scale leads to diminishing returns for stacked Transformer architectures.

Semantic image segmentation, the process of classifying each pixel in an image into a particular class, plays an important role in many visual understanding systems. As the predominant criterion for evaluating the performance of statistical models, loss functions are crucial for shaping the development of deep learning-based segmentation algorithms and improving their overall performance. To aid researchers in identifying the optimal loss function for their particular application, this survey provides a comprehensive and unified review of 25 loss functions utilized in image segmentation. We provide a novel taxonomy and thorough review of how these loss functions are customized and leveraged in image segmentation, with a systematic categorization emphasizing their significant features and applications. Furthermore, to evaluate the efficacy of these methods in real-world scenarios, we propose unbiased evaluations of some distinct and renowned loss functions on established medical and natural image datasets. We conclude this review by identifying current challenges and unveiling future research opportunities. Finally, we have compiled the reviewed studies that have open-source implementations on our GitHub page.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks and comparisons across model architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features. These findings challenge the standard focus on final-layer embeddings and open new directions for model analysis and optimization, including strategic use of mid-layer representations for more robust and accurate AI systems.

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, a_i and a_j, diverge to pminfinity, and their input weight vectors, w_i and w_j, become equal to each other. At convergence, the two neurons implement a gated linear unit: a_iσ(w_i cdot x) + a_jσ(w_j cdot x) rightarrow σ(w cdot x) + (v cdot x) σ'(w cdot x). Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of these quasi-flat regions in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

IoU losses are surrogates that directly optimize the Jaccard index. In semantic segmentation, leveraging IoU losses as part of the loss function is shown to perform better with respect to the Jaccard index measure than optimizing pixel-wise losses such as the cross-entropy loss alone. The most notable IoU losses are the soft Jaccard loss and the Lovasz-Softmax loss. However, these losses are incompatible with soft labels which are ubiquitous in machine learning. In this paper, we propose Jaccard metric losses (JMLs), which are identical to the soft Jaccard loss in a standard setting with hard labels, but are compatible with soft labels. With JMLs, we study two of the most popular use cases of soft labels: label smoothing and knowledge distillation. With a variety of architectures, our experiments show significant improvements over the cross-entropy loss on three semantic segmentation datasets (Cityscapes, PASCAL VOC and DeepGlobe Land), and our simple approach outperforms state-of-the-art knowledge distillation methods by a large margin. Code is available at: https://github.com/zifuwanggg/JDTLosses{https://github.com/zifuwanggg/JDTLosses}.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

This paper studies generalization capabilities of neural networks (NNs) using new and improved PyTorch library Loss Landscape Analysis (LLA). LLA facilitates visualization and analysis of loss landscapes along with the properties of NN Hessian. Different approaches to NN loss landscape plotting are discussed with particular focus on normalization techniques showing that conventional methods cannot always ensure correct visualization when batch normalization layers are present in NN architecture. The use of Hessian axes is shown to be able to mitigate this effect, and methods for choosing Hessian axes are proposed. In addition, spectra of Hessian eigendecomposition are studied and it is shown that typical spectra exist for a wide range of NNs. This allows to propose quantitative criteria for Hessian analysis that can be applied to evaluate NN performance and assess its generalization capabilities. Generalization experiments are conducted using ImageNet-1K pre-trained models along with several models trained as part of this study. The experiment include training models on one dataset and testing on another one to maximize experiment similarity to model performance in the Wild. It is shown that when datasets change, the changes in criteria correlate with the changes in accuracy, making the proposed criteria a computationally efficient estimate of generalization ability, which is especially useful for extremely large datasets.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the input point cloud and to have a unit norm gradient, possesses an implicit geometric regularization property that favors smooth and natural zero level set surfaces, avoiding bad zero-loss solutions. We provide a theoretical analysis of this property for the linear case, and show that, in practice, our method leads to state of the art implicit neural representations with higher level-of-details and fidelity compared to previous methods.

Existing metric learning losses can be categorized into two classes: pair-based and proxy-based losses. The former class can leverage fine-grained semantic relations between data points, but slows convergence in general due to its high training complexity. In contrast, the latter class enables fast and reliable convergence, but cannot consider the rich data-to-data relations. This paper presents a new proxy-based loss that takes advantages of both pair- and proxy-based methods and overcomes their limitations. Thanks to the use of proxies, our loss boosts the speed of convergence and is robust against noisy labels and outliers. At the same time, it allows embedding vectors of data to interact with each other in its gradients to exploit data-to-data relations. Our method is evaluated on four public benchmarks, where a standard network trained with our loss achieves state-of-the-art performance and most quickly converges.

Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width d_S can encode at most d_S cdot g(α) features, where g(α) = 1/((1-α)ln1{1-α}) is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure F approx 28{,}700 features at αapprox 0.992 (critical width d_S^* approx 1{,}065). Distillation into five student widths confirms the predicted monotonic floor ordering. The observed floor decomposes into a geometric component and a width-independent architectural baseline (R^2 = 0.993). Linear probing shows coarse concepts survive even 88% feature loss, revealing the floor arises from aggregate loss of fine-grained features in the importance distribution's long tail. Our results connect representation geometry to distillation limits and provide a practical tool for predicting distillation performance from SAE measurements alone.

Knowledge distillation transfers knowledge from a large model to a small one via task and distillation losses. In this paper, we observe a trade-off between task and distillation losses, i.e., introducing distillation loss limits the convergence of task loss. We believe that the trade-off results from the insufficient optimization of distillation loss. The reason is: The teacher has a lower task loss than the student, and a lower distillation loss drives the student more similar to the teacher, then a better-converged task loss could be obtained. To break the trade-off, we propose the Distillation-Oriented Trainer (DOT). DOT separately considers gradients of task and distillation losses, then applies a larger momentum to distillation loss to accelerate its optimization. We empirically prove that DOT breaks the trade-off, i.e., both losses are sufficiently optimized. Extensive experiments validate the superiority of DOT. Notably, DOT achieves a +2.59% accuracy improvement on ImageNet-1k for the ResNet50-MobileNetV1 pair. Conclusively, DOT greatly benefits the student's optimization properties in terms of loss convergence and model generalization. Code will be made publicly available.

Deep convolutional networks (CNNs) have exhibited their potential in image inpainting for producing plausible results. However, in most existing methods, e.g., context encoder, the missing parts are predicted by propagating the surrounding convolutional features through a fully connected layer, which intends to produce semantically plausible but blurry result. In this paper, we introduce a special shift-connection layer to the U-Net architecture, namely Shift-Net, for filling in missing regions of any shape with sharp structures and fine-detailed textures. To this end, the encoder feature of the known region is shifted to serve as an estimation of the missing parts. A guidance loss is introduced on decoder feature to minimize the distance between the decoder feature after fully connected layer and the ground-truth encoder feature of the missing parts. With such constraint, the decoder feature in missing region can be used to guide the shift of encoder feature in known region. An end-to-end learning algorithm is further developed to train the Shift-Net. Experiments on the Paris StreetView and Places datasets demonstrate the efficiency and effectiveness of our Shift-Net in producing sharper, fine-detailed, and visually plausible results. The codes and pre-trained models are available at https://github.com/Zhaoyi-Yan/Shift-Net.

Albeit with varying degrees of progress in the field of Semi-Supervised Semantic Segmentation, most of its recent successes are involved in unwieldy models and the lightweight solution is still not yet explored. We find that existing knowledge distillation techniques pay more attention to pixel-level concepts from labeled data, which fails to take more informative cues within unlabeled data into account. Consequently, we offer the first attempt to provide lightweight SSSS models via a novel multi-granularity distillation (MGD) scheme, where multi-granularity is captured from three aspects: i) complementary teacher structure; ii) labeled-unlabeled data cooperative distillation; iii) hierarchical and multi-levels loss setting. Specifically, MGD is formulated as a labeled-unlabeled data cooperative distillation scheme, which helps to take full advantage of diverse data characteristics that are essential in the semi-supervised setting. Image-level semantic-sensitive loss, region-level content-aware loss, and pixel-level consistency loss are set up to enrich hierarchical distillation abstraction via structurally complementary teachers. Experimental results on PASCAL VOC2012 and Cityscapes reveal that MGD can outperform the competitive approaches by a large margin under diverse partition protocols. For example, the performance of ResNet-18 and MobileNet-v2 backbone is boosted by 11.5% and 4.6% respectively under 1/16 partition protocol on Cityscapes. Although the FLOPs of the model backbone is compressed by 3.4-5.3x (ResNet-18) and 38.7-59.6x (MobileNetv2), the model manages to achieve satisfactory segmentation results.

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

Video super-resolution aims to enhance low-resolution videos by leveraging both spatial and temporal information. While deep learning has led to impressive progress, it typically requires centralized data, which raises privacy concerns. Federated learning offers a privacy-friendly solution, but general FL frameworks often struggle with low-level vision tasks, resulting in blurry, low-quality outputs. To address this, we introduce FedVSR, the first FL framework specifically designed for VSR. It is model-agnostic and stateless, and introduces a lightweight loss function based on the DWT to better preserve high-frequency details during local training. Additionally, a loss-aware aggregation strategy combines both DWT-based and task-specific losses to guide global updates effectively. Extensive experiments across multiple VSR models and datasets demonstrate that FedVSR consistently outperforms existing FL methods, achieving up to 0.82 dB higher PSNR, 0.0327 higher SSIM, and 0.0251 lower LPIPS. These results underscore FedVSR's ability to bridge the gap between privacy and performance, setting a new benchmark for federated learning in low-level vision tasks. The code is available at: https://github.com/alimd94/FedVSR

Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good performing model if the loss surface of interest is very particular, i.e., the loss in the midpoint between the two models needs to be sufficiently low. This is impossible to guarantee for the non-convex losses of state-of-the-art networks. For averaging models trained on vastly different datasets, it was proposed to average only the parameters of particular layers or combinations of layers, resulting in better performing models. To get a better understanding of the effect of layer-wise averaging, we analyse the performance of the models that result from averaging single layers, or groups of layers. Based on our empirical and theoretical investigation, we introduce a novel notion of the layer-wise linear connectivity, and show that deep networks do not have layer-wise barriers between them.

Deep neural networks are highly performant, but might base their decision on spurious or background features that co-occur with certain classes, which can hurt generalization. To mitigate this issue, the usage of 'model guidance' has gained popularity recently: for this, models are guided to be "right for the right reasons" by regularizing the models' explanations to highlight the right features. Experimental validation of these approaches has thus far however been limited to relatively simple and / or synthetic datasets. To gain a better understanding of which model-guiding approaches actually transfer to more challenging real-world datasets, in this work we conduct an in-depth evaluation across various loss functions, attribution methods, models, and 'guidance depths' on the PASCAL VOC 2007 and MS COCO 2014 datasets, and show that model guidance can sometimes even improve model performance. In this context, we further propose a novel energy loss, show its effectiveness in directing the model to focus on object features. We also show that these gains can be achieved even with a small fraction (e.g. 1%) of bounding box annotations, highlighting the cost effectiveness of this approach. Lastly, we show that this approach can also improve generalization under distribution shifts. Code will be made available.

When training or evaluating deep learning models, two essential parts are picking the proper loss function and deciding on performance metrics. In this paper, we provide a comprehensive overview of the most common loss functions and metrics used across many different types of deep learning tasks, from general tasks such as regression and classification to more specific tasks in Computer Vision and Natural Language Processing. We introduce the formula for each loss and metric, discuss their strengths and limitations, and describe how these methods can be applied to various problems within deep learning. This work can serve as a reference for researchers and practitioners in the field, helping them make informed decisions when selecting the most appropriate loss function and performance metrics for their deep learning projects.

Modern deep-learning systems are specialized to problem settings in which training occurs once and then never again, as opposed to continual-learning settings in which training occurs continually. If deep-learning systems are applied in a continual learning setting, then it is well known that they may fail to remember earlier examples. More fundamental, but less well known, is that they may also lose their ability to learn on new examples, a phenomenon called loss of plasticity. We provide direct demonstrations of loss of plasticity using the MNIST and ImageNet datasets repurposed for continual learning as sequences of tasks. In ImageNet, binary classification performance dropped from 89\% accuracy on an early task down to 77\%, about the level of a linear network, on the 2000th task. Loss of plasticity occurred with a wide range of deep network architectures, optimizers, activation functions, batch normalization, dropout, but was substantially eased by L^2-regularization, particularly when combined with weight perturbation. Further, we introduce a new algorithm -- continual backpropagation -- which slightly modifies conventional backpropagation to reinitialize a small fraction of less-used units after each example and appears to maintain plasticity indefinitely.

Deep embeddings answer one simple question: How similar are two images? Learning these embeddings is the bedrock of verification, zero-shot learning, and visual search. The most prominent approaches optimize a deep convolutional network with a suitable loss function, such as contrastive loss or triplet loss. While a rich line of work focuses solely on the loss functions, we show in this paper that selecting training examples plays an equally important role. We propose distance weighted sampling, which selects more informative and stable examples than traditional approaches. In addition, we show that a simple margin based loss is sufficient to outperform all other loss functions. We evaluate our approach on the Stanford Online Products, CAR196, and the CUB200-2011 datasets for image retrieval and clustering, and on the LFW dataset for face verification. Our method achieves state-of-the-art performance on all of them.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

Contrastive loss is a powerful approach for representation learning, where larger batch sizes enhance performance by providing more negative samples to better distinguish between similar and dissimilar data. However, scaling batch sizes is constrained by the quadratic growth in GPU memory consumption, primarily due to the full instantiation of the similarity matrix. To address this, we propose a tile-based computation strategy that partitions the contrastive loss calculation into arbitrary small blocks, avoiding full materialization of the similarity matrix. Furthermore, we introduce a multi-level tiling strategy to leverage the hierarchical structure of distributed systems, employing ring-based communication at the GPU level to optimize synchronization and fused kernels at the CUDA core level to reduce I/O overhead. Experimental results show that the proposed method scales batch sizes to unprecedented levels. For instance, it enables contrastive training of a CLIP-ViT-L/14 model with a batch size of 4M or 12M using 8 or 32 A800 80GB without sacrificing any accuracy. Compared to SOTA memory-efficient solutions, it achieves a two-order-of-magnitude reduction in memory while maintaining comparable speed. The code will be made publicly available.

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.

We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions. In particular, we derive the exact closed-form expressions for the gradients and test loss after one and two steps of gradient descent, enabling a precise characterization of early training dynamics. We characterize how learning rates should scale under the gradient approximation in the first two steps, and prove that performing updates with this approximation yields a tractable surrogate loss with a tight, small approximation error. This formulation enables the theoretical analysis of layer-wise learning rates and reveals a distinct early-training regime: test loss can be minimized by unequal learning rates at the initial step, while equal learning rates become optimal in subsequent steps. Our numerical experiments validate the theory and demonstrate the importance of balancing layer-wise learning rates early during training. The code is available at: https://github.com/TDCSZ327/Layer-Balancing.

Deep metric learning objectives (e.g., triplet loss) require storing and comparing high-dimensional embeddings, making the per-batch loss buffer scale as O(Scdot D), where S is the number of samples in a batch and D is the feature dimension, thus limiting training on memory-constrained hardware. We propose Shadow Loss, a proxy-free, parameter-free objective that measures similarity via scalar projections onto the anchor direction, reducing the loss-specific buffer from O(Scdot D) to O(S) while preserving the triplet structure. We analyze gradients, provide a Lipschitz continuity bound, and show that Shadow Loss penalizes trivial collapse for stable optimization. Across fine-grained retrieval (CUB-200, CARS196), large-scale product retrieval (Stanford Online Products, In-Shop Clothes), and standard/medical benchmarks (CIFAR-10/100, Tiny-ImageNet, HAM-10K, ODIR-5K), Shadow Loss consistently outperforms recent objectives (Triplet, Soft-Margin Triplet, Angular Triplet, SoftTriple, Multi-Similarity). It also converges in approx 1.5-2times fewer epochs under identical backbones and mining. Furthermore, it improves representation separability as measured by higher silhouette scores. The design is architecture-agnostic and vectorized for efficient implementation. By decoupling discriminative power from embedding dimensionality and reusing batch dot-products, Shadow Loss enables memory-linear training and faster convergence, making deep metric learning practical on both edge and large-scale systems.

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

Deep networks are increasingly being applied to problems involving image synthesis, e.g., generating images from textual descriptions and reconstructing an input image from a compact representation. Supervised training of image-synthesis networks typically uses a pixel-wise loss (PL) to indicate the mismatch between a generated image and its corresponding target image. We propose instead to use a loss function that is better calibrated to human perceptual judgments of image quality: the multiscale structural-similarity score (MS-SSIM). Because MS-SSIM is differentiable, it is easily incorporated into gradient-descent learning. We compare the consequences of using MS-SSIM versus PL loss on training deterministic and stochastic autoencoders. For three different architectures, we collected human judgments of the quality of image reconstructions. Observers reliably prefer images synthesized by MS-SSIM-optimized models over those synthesized by PL-optimized models, for two distinct PL measures (ell_1 and ell_2 distances). We also explore the effect of training objective on image encoding and analyze conditions under which perceptually-optimized representations yield better performance on image classification. Finally, we demonstrate the superiority of perceptually-optimized networks for super-resolution imaging. Just as computer vision has advanced through the use of convolutional architectures that mimic the structure of the mammalian visual system, we argue that significant additional advances can be made in modeling images through the use of training objectives that are well aligned to characteristics of human perception.

Traditional transformer models often allocate a fixed amount of computational resources to every input token, leading to inefficient and unnecessary computation. To address this, the Mixture of Depths (MoD) was introduced to dynamically adjust the computational depth by skipping less important layers. Despite its promise, current MoD approaches remain under-explored and face two main challenges: (1) high training costs due to the need to train the entire model along with the routers that determine which layers to skip, and (2) the risk of performance degradation when important layers are bypassed. In response to the first issue, we propose Router-Tuning, a method that fine-tunes only the router on a small dataset, drastically reducing the computational overhead associated with full model training. For the second challenge, we propose MindSkip, which deploys Attention with Dynamic Depths. This method preserves the model's performance while significantly enhancing computational and memory efficiency. Extensive experiments demonstrate that our approach delivers competitive results while dramatically improving the computation efficiency, e.g., 21\% speedup and only a 0.2\% performance drop. The code is released at https://github.com/CASE-Lab-UMD/Router-Tuning.

Vision--language models (VLMs) often process visual inputs through a pretrained vision encoder, followed by a projection into the language model's embedding space via a connector component. While crucial for modality fusion, the potential information loss induced by this projection step and its direct impact on model capabilities remain understudied. We introduce two complementary approaches to examine and quantify this loss by analyzing the latent representation space. First, we evaluate semantic information preservation by analyzing changes in k-nearest neighbor relationships between image representations, before and after projection. Second, we directly measure information loss by reconstructing visual embeddings from the projected representation, localizing loss at an image patch level. Experiments reveal that connectors substantially distort the local geometry of visual representations, with k-nearest neighbors diverging by 40--60\% post-projection, correlating with degradation in retrieval performance. The patch-level embedding reconstruction provides interpretable insights for model behavior on visually grounded question-answering tasks, finding that areas of high information loss reliably predict instances where models struggle.

Learning rate scheduling is essential in transformer training, where the final annealing plays a crucial role in getting the best performance. However, the mechanisms behind this cooldown phase, with its characteristic drop in loss, remain poorly understood. To address this, we provide a comprehensive analysis focusing solely on the cooldown phase in the Warmup-Stable-Decay (WSD) learning rate scheduler. Our analysis reveals that different cooldown shapes reveal a fundamental bias-variance trade-off in the resulting models, with shapes that balance exploration and exploitation consistently outperforming alternatives. Similarly, we find substantial performance variations x2013 comparable to those from cooldown shape selection x2013 when tuning AdamW hyperparameters. Notably, we observe consistent improvements with higher values of beta_2 during cooldown. From a loss landscape perspective, we provide visualizations of the landscape during cooldown, supporting the river valley loss perspective empirically. These findings offer practical recommendations for configuring the WSD scheduler in transformer training, emphasizing the importance of optimizing the cooldown phase alongside traditional hyperparameter tuning.

Generalized few-shot semantic segmentation was introduced to move beyond only evaluating few-shot segmentation models on novel classes to include testing their ability to remember base classes. While the current state-of-the-art approach is based on meta-learning, it performs poorly and saturates in learning after observing only a few shots. We propose the first fine-tuning solution, and demonstrate that it addresses the saturation problem while achieving state-of-the-art results on two datasets, PASCAL-5i and COCO-20i. We also show that it outperforms existing methods, whether fine-tuning multiple final layers or only the final layer. Finally, we present a triplet loss regularization that shows how to redistribute the balance of performance between novel and base categories so that there is a smaller gap between them.

Recent studies have observed that intermediate layers of foundation models often yield more discriminative representations than the final layer. While initially attributed to autoregressive pretraining, this phenomenon has also been identified in models trained via supervised and discriminative self-supervised objectives. In this paper, we conduct a comprehensive study to analyze the behavior of intermediate layers in pretrained vision transformers. Through extensive linear probing experiments across a diverse set of image classification benchmarks, we find that distribution shift between pretraining and downstream data is the primary cause of performance degradation in deeper layers. Furthermore, we perform a fine-grained analysis at the module level. Our findings reveal that standard probing of transformer block outputs is suboptimal; instead, probing the activation within the feedforward network yields the best performance under significant distribution shift, whereas the normalized output of the multi-head self-attention module is optimal when the shift is weak.

The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon: we show that the combination of stochastic gradient descent (SGD) and over-parameterization makes the landscape of multilayer neural networks approximately connected and thus more favorable to optimization. More specifically, we prove that SGD solutions are connected via a piecewise linear path, and the increase in loss along this path vanishes as the number of neurons grows large. This result is a consequence of the fact that the parameters found by SGD are increasingly dropout stable as the network becomes wider. We show that, if we remove part of the neurons (and suitably rescale the remaining ones), the change in loss is independent of the total number of neurons, and it depends only on how many neurons are left. Our results exhibit a mild dependence on the input dimension: they are dimension-free for two-layer networks and depend linearly on the dimension for multilayer networks. We validate our theoretical findings with numerical experiments for different architectures and classification tasks.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Real-image super-resolution (Real-ISR) seeks to recover HR images from LR inputs with mixed, unknown degradations. While diffusion models surpass GANs in perceptual quality, they under-reconstruct high-frequency (HF) details due to a low-frequency (LF) bias and a depth-wise "low-first, high-later" hierarchy. We introduce FRAMER, a plug-and-play training scheme that exploits diffusion priors without changing the backbone or inference. At each denoising step, the final-layer feature map teaches all intermediate layers. Teacher and student feature maps are decomposed into LF/HF bands via FFT masks to align supervision with the model's internal frequency hierarchy. For LF, an Intra Contrastive Loss (IntraCL) stabilizes globally shared structure. For HF, an Inter Contrastive Loss (InterCL) sharpens instance-specific details using random-layer and in-batch negatives. Two adaptive modulators, Frequency-based Adaptive Weight (FAW) and Frequency-based Alignment Modulation (FAM), reweight per-layer LF/HF signals and gate distillation by current similarity. Across U-Net and DiT backbones (e.g., Stable Diffusion 2, 3), FRAMER consistently improves PSNR/SSIM and perceptual metrics (LPIPS, NIQE, MANIQA, MUSIQ). Ablations validate the final-layer teacher and random-layer negatives.

We present LayerSkip, an end-to-end solution to speed-up inference of large language models (LLMs). First, during training we apply layer dropout, with low dropout rates for earlier layers and higher dropout rates for later layers, and an early exit loss where all transformer layers share the same exit. Second, during inference, we show that this training recipe increases the accuracy of early exit at earlier layers, without adding any auxiliary layers or modules to the model. Third, we present a novel self-speculative decoding solution where we exit at early layers and verify and correct with remaining layers of the model. Our proposed self-speculative decoding approach has less memory footprint than other speculative decoding approaches and benefits from shared compute and activations of the draft and verification stages. We run experiments on different Llama model sizes on different types of training: pretraining from scratch, continual pretraining, finetuning on specific data domain, and finetuning on specific task. We implement our inference solution and show speedups of up to 2.16x on summarization for CNN/DM documents, 1.82x on coding, and 2.0x on TOPv2 semantic parsing task. We open source our code and checkpoints at https://github.com/facebookresearch/LayerSkip.

Deep learning based methods have achieved significant success in the task of single image reflection removal (SIRR). However, the majority of these methods are focused on High-Definition/Standard-Definition (HD/SD) images, while ignoring higher resolution images such as Ultra-High-Definition (UHD) images. With the increasing prevalence of UHD images captured by modern devices, in this paper, we aim to address the problem of UHD SIRR. Specifically, we first synthesize two large-scale UHD datasets, UHDRR4K and UHDRR8K. The UHDRR4K dataset consists of 2,999 and 168 quadruplets of images for training and testing respectively, and the UHDRR8K dataset contains 1,014 and 105 quadruplets. To the best of our knowledge, these two datasets are the first largest-scale UHD datasets for SIRR. Then, we conduct a comprehensive evaluation of six state-of-the-art SIRR methods using the proposed datasets. Based on the results, we provide detailed discussions regarding the strengths and limitations of these methods when applied to UHD images. Finally, we present a transformer-based architecture named RRFormer for reflection removal. RRFormer comprises three modules, namely the Prepossessing Embedding Module, Self-attention Feature Extraction Module, and Multi-scale Spatial Feature Extraction Module. These modules extract hypercolumn features, global and partial attention features, and multi-scale spatial features, respectively. To ensure effective training, we utilize three terms in our loss function: pixel loss, feature loss, and adversarial loss. We demonstrate through experimental results that RRFormer achieves state-of-the-art performance on both the non-UHD dataset and our proposed UHDRR datasets. The code and datasets are publicly available at https://github.com/Liar-zzy/Benchmarking-Ultra-High-Definition-Single-Image-Reflection-Removal.

We propose a simple pairwise sigmoid loss for image-text pre-training. Unlike standard contrastive learning with softmax normalization, the sigmoid loss operates solely on image-text pairs and does not require a global view of the pairwise similarities for normalization. The sigmoid loss simultaneously allows further scaling up the batch size, while also performing better at smaller batch sizes. With only four TPUv4 chips, we can train a Base CLIP model at 4k batch size and a Large LiT model at 20k batch size, the latter achieves 84.5% ImageNet zero-shot accuracy in two days. This disentanglement of the batch size from the loss further allows us to study the impact of examples vs pairs and negative to positive ratio. Finally, we push the batch size to the extreme, up to one million, and find that the benefits of growing batch size quickly diminish, with a more reasonable batch size of 32k being sufficient. We hope our research motivates further explorations in improving the quality and efficiency of language-image pre-training.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Current knowledge distillation approaches in semantic segmentation tend to adopt a holistic approach that treats all spatial locations equally. However, for dense prediction, students' predictions on edge regions are highly uncertain due to contextual information leakage, requiring higher spatial sensitivity knowledge than the body regions. To address this challenge, this paper proposes a novel approach called boundary-privileged knowledge distillation (BPKD). BPKD distills the knowledge of the teacher model's body and edges separately to the compact student model. Specifically, we employ two distinct loss functions: (i) edge loss, which aims to distinguish between ambiguous classes at the pixel level in edge regions; (ii) body loss, which utilizes shape constraints and selectively attends to the inner-semantic regions. Our experiments demonstrate that the proposed BPKD method provides extensive refinements and aggregation for edge and body regions. Additionally, the method achieves state-of-the-art distillation performance for semantic segmentation on three popular benchmark datasets, highlighting its effectiveness and generalization ability. BPKD shows consistent improvements across a diverse array of lightweight segmentation structures, including both CNNs and transformers, underscoring its architecture-agnostic adaptability. The code is available at https://github.com/AkideLiu/BPKD.

In settings such as fine-tuning and reinforcement learning, neural networks are often adapted under distribution shift. Standard adaptation methods typically optimize the target objective directly, inducing an abrupt change from the source training objective. This abrupt transition can distort learned representations, including features that may still be useful for the new task. We investigate whether a more gradual transition can improve adaptation. We propose loss smoothing, a simple approach that interpolates between the source and target training objectives at the start of adaptation. This smooth transition helps to preserve useful features from the source distribution while still enabling the model to specialize to the target distribution. Across controlled supervised shifts, pretrained vision adaptation, offline-to-online and online reinforcement learning, and language model fine-tuning, we find that loss smoothing consistently improves performance, suggesting that smoother objective transitions are a broadly useful tool for model adaptation.

Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

Deep neural networks have a good success record and are thus viewed as the best architecture choice for complex applications. Their main shortcoming has been, for a long time, the vanishing gradient which prevented the numerical optimization algorithms from acceptable convergence. A breakthrough has been achieved by the concept of residual connections -- an identity mapping parallel to a conventional layer. This concept is applicable to stacks of layers of the same dimension and substantially alleviates the vanishing gradient problem. A stack of residual connection layers can be expressed as an expansion of terms similar to the Taylor expansion. This expansion suggests the possibility of truncating the higher-order terms and receiving an architecture consisting of a single broad layer composed of all initially stacked layers in parallel. In other words, a sequential deep architecture is substituted by a parallel shallow one. Prompted by this theory, we investigated the performance capabilities of the parallel architecture in comparison to the sequential one. The computer vision datasets MNIST and CIFAR10 were used to train both architectures for a total of 6912 combinations of varying numbers of convolutional layers, numbers of filters, kernel sizes, and other meta parameters. Our findings demonstrate a surprising equivalence between the deep (sequential) and shallow (parallel) architectures. Both layouts produced similar results in terms of training and validation set loss. This discovery implies that a wide, shallow architecture can potentially replace a deep network without sacrificing performance. Such substitution has the potential to simplify network architectures, improve optimization efficiency, and accelerate the training process.

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The harmonic loss is a distance-based alternative grounded in Euclidean geometry that improves interpretability and mitigates phenomena such as grokking, or delayed generalization on the test set. However, the study of harmonic loss remains narrow: only Euclidean distance is explored, and no systematic evaluation of computational efficiency or sustainability was conducted. We extend harmonic loss by systematically investigating a broad spectrum of distance metrics as replacements for the Euclidean distance. We comprehensively evaluate distance-tailored harmonic losses on both vision backbones and large language models. Our analysis is framed around a three-way evaluation of model performance, interpretability, and sustainability. On vision tasks, cosine distances provide the most favorable trade-off, consistently improving accuracy while lowering carbon emissions, whereas Bray-Curtis and Mahalanobis further enhance interpretability at varying efficiency costs. On language models, cosine-based harmonic losses improve gradient and learning stability, strengthen representation structure, and reduce emissions relative to cross-entropy and Euclidean heads. Our code is available at: https://anonymous.4open.science/r/rethinking-harmonic-loss-5BAB/.

Traditional knowledge distillation focuses on aligning the student's predicted probabilities with both ground-truth labels and the teacher's predicted probabilities. However, the transition to predicted probabilities from logits would obscure certain indispensable information. To address this issue, it is intuitive to additionally introduce a logit-level loss function as a supplement to the widely used probability-level loss function, for exploiting the latent information of logits. Unfortunately, we empirically find that the amalgamation of the newly introduced logit-level loss and the previous probability-level loss will lead to performance degeneration, even trailing behind the performance of employing either loss in isolation. We attribute this phenomenon to the collapse of the classification head, which is verified by our theoretical analysis based on the neural collapse theory. Specifically, the gradients of the two loss functions exhibit contradictions in the linear classifier yet display no such conflict within the backbone. Drawing from the theoretical analysis, we propose a novel method called dual-head knowledge distillation, which partitions the linear classifier into two classification heads responsible for different losses, thereby preserving the beneficial effects of both losses on the backbone while eliminating adverse influences on the classification head. Extensive experiments validate that our method can effectively exploit the information inside the logits and achieve superior performance against state-of-the-art counterparts.

Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

Image reconstruction and synthesis have witnessed remarkable progress thanks to the development of generative models. Nonetheless, gaps could still exist between the real and generated images, especially in the frequency domain. In this study, we show that narrowing gaps in the frequency domain can ameliorate image reconstruction and synthesis quality further. We propose a novel focal frequency loss, which allows a model to adaptively focus on frequency components that are hard to synthesize by down-weighting the easy ones. This objective function is complementary to existing spatial losses, offering great impedance against the loss of important frequency information due to the inherent bias of neural networks. We demonstrate the versatility and effectiveness of focal frequency loss to improve popular models, such as VAE, pix2pix, and SPADE, in both perceptual quality and quantitative performance. We further show its potential on StyleGAN2.

We introduce a novel and general loss function, called Symmetric Contrastive (Sy-CON) loss, for effective continual self-supervised learning (CSSL). We first argue that the conventional loss form of continual learning which consists of single task-specific loss (for plasticity) and a regularizer (for stability) may not be ideal for contrastive loss based CSSL that focus on representation learning. Our reasoning is that, in contrastive learning based methods, the task-specific loss would suffer from decreasing diversity of negative samples and the regularizer may hinder learning new distinctive representations. To that end, we propose Sy-CON that consists of two losses (one for plasticity and the other for stability) with symmetric dependence on current and past models' negative sample embeddings. We argue our model can naturally find good trade-off between the plasticity and stability without any explicit hyperparameter tuning. We validate the effectiveness of our approach through extensive experiments, demonstrating that MoCo-based implementation of Sy-CON loss achieves superior performance compared to other state-of-the-art CSSL methods.

Deep-learning has proved in recent years to be a powerful tool for image analysis and is now widely used to segment both 2D and 3D medical images. Deep-learning segmentation frameworks rely not only on the choice of network architecture but also on the choice of loss function. When the segmentation process targets rare observations, a severe class imbalance is likely to occur between candidate labels, thus resulting in sub-optimal performance. In order to mitigate this issue, strategies such as the weighted cross-entropy function, the sensitivity function or the Dice loss function, have been proposed. In this work, we investigate the behavior of these loss functions and their sensitivity to learning rate tuning in the presence of different rates of label imbalance across 2D and 3D segmentation tasks. We also propose to use the class re-balancing properties of the Generalized Dice overlap, a known metric for segmentation assessment, as a robust and accurate deep-learning loss function for unbalanced tasks.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

In-context learning (ICL) has shown impressive results in few-shot learning tasks, yet its underlying mechanism is still not fully understood. A recent line of work suggests that ICL performs gradient descent (GD)-based optimization implicitly. While appealing, much of the research focuses on simplified settings, where the parameters of a shallow model are optimized. In this work, we revisit evidence for ICL-GD correspondence on realistic NLP tasks and models. We find gaps in evaluation, both in terms of problematic metrics and insufficient baselines. We show that surprisingly, even untrained models achieve comparable ICL-GD similarity scores despite not exhibiting ICL. Next, we explore a major discrepancy in the flow of information throughout the model between ICL and GD, which we term Layer Causality. We propose a simple GD-based optimization procedure that respects layer causality, and show it improves similarity scores significantly.

Vision Transformers (ViTs) lack the hierarchical inductive biases inherent to Convolutional Neural Networks (CNNs), theoretically allowing them to maintain high-dimensional representations throughout all layers. However, recent observations suggest ViTs often spontaneously manifest a "U-shaped" entropy profile-compressing information in middle layers before expanding it for the final classification. In this work, we demonstrate that this "Inductive Bottleneck" is not an architectural artifact, but a data-dependent adaptation. By analyzing the layer-wise Effective Encoding Dimension (EED) of DINO-trained ViTs across datasets of varying compositional complexity (UC Merced, Tiny ImageNet, and CIFAR-100), we show that the depth of the bottleneck correlates strongly with the semantic abstraction required by the task. We find that while texture-heavy datasets preserve high-rank representations throughout, object-centric datasets drive the network to dampen high-frequency information in middle layers, effectively "learning" a bottleneck to isolate semantic features.

We propose a generalized focal loss function based on the Tversky index to address the issue of data imbalance in medical image segmentation. Compared to the commonly used Dice loss, our loss function achieves a better trade off between precision and recall when training on small structures such as lesions. To evaluate our loss function, we improve the attention U-Net model by incorporating an image pyramid to preserve contextual features. We experiment on the BUS 2017 dataset and ISIC 2018 dataset where lesions occupy 4.84% and 21.4% of the images area and improve segmentation accuracy when compared to the standard U-Net by 25.7% and 3.6%, respectively.

In order to train networks for verified adversarial robustness, it is common to over-approximate the worst-case loss over perturbation regions, resulting in networks that attain verifiability at the expense of standard performance. As shown in recent work, better trade-offs between accuracy and robustness can be obtained by carefully coupling adversarial training with over-approximations. We hypothesize that the expressivity of a loss function, which we formalize as the ability to span a range of trade-offs between lower and upper bounds to the worst-case loss through a single parameter (the over-approximation coefficient), is key to attaining state-of-the-art performance. To support our hypothesis, we show that trivial expressive losses, obtained via convex combinations between adversarial attacks and IBP bounds, yield state-of-the-art results across a variety of settings in spite of their conceptual simplicity. We provide a detailed analysis of the relationship between the over-approximation coefficient and performance profiles across different expressive losses, showing that, while expressivity is essential, better approximations of the worst-case loss are not necessarily linked to superior robustness-accuracy trade-offs.

The purpose of image inpainting is to recover scratches and damaged areas using context information from remaining parts. In recent years, thanks to the resurgence of convolutional neural networks (CNNs), image inpainting task has made great breakthroughs. However, most of the work consider insufficient types of mask, and their performance will drop dramatically when encountering unseen masks. To combat these challenges, we propose a simple yet general method to solve this problem based on the LaMa image inpainting framework, dubbed GLaMa. Our proposed GLaMa can better capture different types of missing information by using more types of masks. By incorporating more degraded images in the training phase, we can expect to enhance the robustness of the model with respect to various masks. In order to yield more reasonable results, we further introduce a frequency-based loss in addition to the traditional spatial reconstruction loss and adversarial loss. In particular, we introduce an effective reconstruction loss both in the spatial and frequency domain to reduce the chessboard effect and ripples in the reconstructed image. Extensive experiments demonstrate that our method can boost the performance over the original LaMa method for each type of mask on FFHQ, ImageNet, Places2 and WikiArt dataset. The proposed GLaMa was ranked first in terms of PSNR, LPIPS and SSIM in the NTIRE 2022 Image Inpainting Challenge Track 1 Unsupervised.

Outliers introduce significant training challenges in neural networks by propagating erroneous gradients, which can degrade model performance and generalization. We propose the Z-Error Loss, a statistically principled approach that minimizes outlier influence during training by masking the contribution of data points identified as out-of-distribution within each batch. This method leverages batch-level statistics to automatically detect and exclude anomalous samples, allowing the model to focus its learning on the true underlying data structure. Our approach is robust, adaptive to data quality, and provides valuable diagnostics for data curation and cleaning.

Due to the rise of privacy concerns, in many practical applications the training data is aggregated before being shared with the learner, in order to protect privacy of users' sensitive responses. In an aggregate learning framework, the dataset is grouped into bags of samples, where each bag is available only with an aggregate response, providing a summary of individuals' responses in that bag. In this paper, we study two natural loss functions for learning from aggregate responses: bag-level loss and the instance-level loss. In the former, the model is learnt by minimizing a loss between aggregate responses and aggregate model predictions, while in the latter the model aims to fit individual predictions to the aggregate responses. In this work, we show that the instance-level loss can be perceived as a regularized form of the bag-level loss. This observation lets us compare the two approaches with respect to bias and variance of the resulting estimators, and introduce a novel interpolating estimator which combines the two approaches. For linear regression tasks, we provide a precise characterization of the risk of the interpolating estimator in an asymptotic regime where the size of the training set grows in proportion to the features dimension. Our analysis allows us to theoretically understand the effect of different factors, such as bag size on the model prediction risk. In addition, we propose a mechanism for differentially private learning from aggregate responses and derive the optimal bag size in terms of prediction risk-privacy trade-off. We also carry out thorough experiments to corroborate our theory and show the efficacy of the interpolating estimator.

In this paper, we propose a feature affinity (FA) assisted knowledge distillation (KD) method to improve quantization-aware training of deep neural networks (DNN). The FA loss on intermediate feature maps of DNNs plays the role of teaching middle steps of a solution to a student instead of only giving final answers in the conventional KD where the loss acts on the network logits at the output level. Combining logit loss and FA loss, we found that the quantized student network receives stronger supervision than from the labeled ground-truth data. The resulting FAQD is capable of compressing model on label-free data, which brings immediate practical benefits as pre-trained teacher models are readily available and unlabeled data are abundant. In contrast, data labeling is often laborious and expensive. Finally, we propose a fast feature affinity (FFA) loss that accurately approximates FA loss with a lower order of computational complexity, which helps speed up training for high resolution image input.

Enabling large language models (LLMs) to unlearn knowledge and capabilities acquired during training has proven vital for ensuring compliance with data regulations and promoting ethical practices in generative AI. Although there are growing interests in developing various unlearning algorithms, it remains unclear how to best formulate the unlearning problem. The most popular formulation uses a weighted sum of forget and retain loss, but it often leads to performance degradation due to the inherent trade-off between forget and retain losses. In this work, we argue that it is important to model the hierarchical structure of the unlearning problem, where the forget problem (which unlearns certain knowledge and/or capabilities) takes priority over the retain problem (which preserves model utility). This hierarchical structure naturally leads to a bi-level optimization formulation where the lower-level objective focuses on minimizing the forget loss, while the upper-level objective aims to maintain the model's utility. Based on this new formulation, we propose a novel algorithm, termed Bi-Level UnleaRning (BLUR), which not only possesses strong theoretical guarantees but more importantly, delivers superior performance. In particular, our extensive experiments demonstrate that BLUR consistently outperforms all the state-of-the-art algorithms across various unlearning tasks, models, and metrics. Codes are available at https://github.com/OptimAI-Lab/BLURLLMUnlearning.

Multimodal Large Language Models (MLLMs) suffer from high computational costs due to their massive size and the large number of visual tokens. In this paper, we investigate layer-wise redundancy in MLLMs by introducing a novel metric, Layer Contribution (LC), which quantifies the impact of a layer's transformations on visual and text tokens, respectively. The calculation of LC involves measuring the divergence in model output that results from removing the layer's transformations on the specified tokens. Our pilot experiment reveals that many layers of MLLMs exhibit minimal contribution during the processing of visual tokens. Motivated by this observation, we propose ShortV, a training-free method that leverages LC to identify ineffective layers, and freezes visual token updates in these layers. Experiments show that ShortV can freeze visual token in approximately 60\% of the MLLM layers, thereby dramatically reducing computational costs related to updating visual tokens. For example, it achieves a 50\% reduction in FLOPs on LLaVA-NeXT-13B while maintaining superior performance. The code will be publicly available at https://github.com/icip-cas/ShortV

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the Information Plane; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on {\emph compression} of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

Although recent diffusion-based single-step super-resolution methods achieve better performance as compared to SinSR, they are computationally complex. To improve the performance of SinSR, we investigate preserving the high-frequency detail features during super-resolution (SR) because the downgraded images lack detailed information. For this purpose, we introduce a high-frequency perceptual loss by utilizing an invertible neural network (INN) pretrained on the ImageNet dataset. Different feature maps of pretrained INN produce different high-frequency aspects of an image. During the training phase, we impose to preserve the high-frequency features of super-resolved and ground truth (GT) images that improve the SR image quality during inference. Furthermore, we also utilize the Jenson-Shannon divergence between GT and SR images in the pretrained DINO-v2 embedding space to match their distribution. By introducing the high- frequency preserving loss and distribution matching constraint in the single-step diffusion-based SR (HF-Diff), we achieve a state-of-the-art CLIPIQA score in the benchmark RealSR, RealSet65, DIV2K-Val, and ImageNet datasets. Furthermore, the experimental results in several datasets demonstrate that our high-frequency perceptual loss yields better SR image quality than LPIPS and VGG-based perceptual losses. Our code will be released at https://github.com/shoaib-sami/HF-Diff.

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (muP and its depth extension), then some hyperparameters - such as the learning rate - exhibit transfer from small to very large models, thus reducing the cost of hyperparameter tuning. From an optimization perspective, this phenomenon is puzzling, as it implies that the loss landscape is remarkably consistent across very different model sizes. In this work, we find empirical evidence that learning rate transfer can be attributed to the fact that under muP and its depth extension, the largest eigenvalue of the training loss Hessian (i.e. the sharpness) is largely independent of the width and depth of the network for a sustained period of training time. On the other hand, we show that under the neural tangent kernel (NTK) regime, the sharpness exhibits very different dynamics at different scales, thus preventing learning rate transfer. But what causes these differences in the sharpness dynamics? Through a connection between the spectra of the Hessian and the NTK matrix, we argue that the cause lies in the presence (for muP) or progressive absence (for the NTK regime) of feature learning, which results in a different evolution of the NTK, and thus of the sharpness. We corroborate our claims with a substantial suite of experiments, covering a wide range of datasets and architectures: from ResNets and Vision Transformers trained on benchmark vision datasets to Transformers-based language models trained on WikiText

We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT). The computational cost of VAT is relatively low. For neural networks, the approximated gradient of virtual adversarial loss can be computed with no more than two pairs of forward- and back-propagations. In our experiments, we applied VAT to supervised and semi-supervised learning tasks on multiple benchmark datasets. With a simple enhancement of the algorithm based on the entropy minimization principle, our VAT achieves state-of-the-art performance for semi-supervised learning tasks on SVHN and CIFAR-10.

Deep Learning is often depicted as a trio of data-architecture-loss. Yet, recent Self Supervised Learning (SSL) solutions have introduced numerous additional design choices, e.g., a projector network, positive views, or teacher-student networks. These additions pose two challenges. First, they limit the impact of theoretical studies that often fail to incorporate all those intertwined designs. Second, they slow-down the deployment of SSL methods to new domains as numerous hyper-parameters need to be carefully tuned. In this study, we bring forward the surprising observation that--at least for pretraining datasets of up to a few hundred thousands samples--the additional designs introduced by SSL do not contribute to the quality of the learned representations. That finding not only provides legitimacy to existing theoretical studies, but also simplifies the practitioner's path to SSL deployment in numerous small and medium scale settings. Our finding answers a long-lasting question: the often-experienced sensitivity to training settings and hyper-parameters encountered in SSL come from their design, rather than the absence of supervised guidance.

Recent advances in distilling expensive diffusion models into efficient few-step generators show significant promise. However, these methods typically demand substantial computational resources and extended training periods, limiting accessibility for resource-constrained researchers, and existing supplementary loss functions have notable limitations. Regression loss requires pre-generating large datasets before training and limits the student model to the teacher's performance, while GAN-based losses suffer from training instability and require careful tuning. In this paper, we propose Embedding Loss (EL), a novel supplementary loss function that complements existing diffusion distillation methods to enhance generation quality and accelerate training with smaller batch sizes. Leveraging feature embeddings from a diverse set of randomly initialized networks, EL effectively aligns the feature distributions between the distilled few-step generator and the original data. By computing Maximum Mean Discrepancy (MMD) in the embedded feature space, EL ensures robust distribution matching, thereby preserving sample fidelity and diversity during distillation. Within distribution matching distillation frameworks, EL demonstrates strong empirical performance for one-step generators. On the CIFAR-10 dataset, our approach achieves state-of-the-art FID values of 1.475 for unconditional generation and 1.380 for conditional generation. Beyond CIFAR-10, we further validate EL across multiple benchmarks and distillation methods, including ImageNet, AFHQ-v2, and FFHQ datasets, using DMD, DI, and CM distillation frameworks, demonstrating consistent improvements over existing one-step distillation methods. Our method also reduces training iterations by up to 80%, offering a more practical and scalable solution for deploying diffusion-based generative models in resource-constrained environments.

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely EnsLoss, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, EnsLoss enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of EnsLoss compared to fixed loss methods is demonstrated through experiments on a broad range of 14 OpenML tabular datasets and 46 image datasets with various deep learning architectures. Python repository and source code are available on GitHub at https://github.com/statmlben/ensloss.

Federated Learning (FL) is a rising approach towards collaborative and privacy-preserving machine learning where large-scale medical datasets remain localized to each client. However, the issue of data heterogeneity among clients often compels local models to diverge, leading to suboptimal global models. To mitigate the impact of data heterogeneity on FL performance, we start with analyzing how FL training influence FL performance by decomposing the global loss into three terms: local loss, distribution shift loss and aggregation loss. Remarkably, our loss decomposition reveals that existing local training-based FL methods attempt to reduce the distribution shift loss, while the global aggregation-based FL methods propose better aggregation strategies to reduce the aggregation loss. Nevertheless, a comprehensive joint effort to minimize all three terms is currently limited in the literature, leading to subpar performance when dealing with data heterogeneity challenges. To fill this gap, we propose a novel FL method based on global loss decomposition, called FedLD, to jointly reduce these three loss terms. Our FedLD involves a margin control regularization in local training to reduce the distribution shift loss, and a principal gradient-based server aggregation strategy to reduce the aggregation loss. Notably, under different levels of data heterogeneity, our strategies achieve better and more robust performance on retinal and chest X-ray classification compared to other FL algorithms. Our code is available at https://github.com/Zeng-Shuang/FedLD.

We consider image transformation problems, where an input image is transformed into an output image. Recent methods for such problems typically train feed-forward convolutional neural networks using a per-pixel loss between the output and ground-truth images. Parallel work has shown that high-quality images can be generated by defining and optimizing perceptual loss functions based on high-level features extracted from pretrained networks. We combine the benefits of both approaches, and propose the use of perceptual loss functions for training feed-forward networks for image transformation tasks. We show results on image style transfer, where a feed-forward network is trained to solve the optimization problem proposed by Gatys et al in real-time. Compared to the optimization-based method, our network gives similar qualitative results but is three orders of magnitude faster. We also experiment with single-image super-resolution, where replacing a per-pixel loss with a perceptual loss gives visually pleasing results.

Data imbalance is a well-known issue in the field of machine learning, attributable to the cost of data collection, the difficulty of labeling, and the geographical distribution of the data. In computer vision, bias in data distribution caused by image appearance remains highly unexplored. Compared to categorical distributions using class labels, image appearance reveals complex relationships between objects beyond what class labels provide. Clustering deep perceptual features extracted from raw pixels gives a richer representation of the data. This paper presents a novel method for addressing data imbalance in machine learning. The method computes sample likelihoods based on image appearance using deep perceptual embeddings and clustering. It then uses these likelihoods to weigh samples differently during training with a proposed Generalized Focal Loss function. This loss can be easily integrated with deep learning algorithms. Experiments validate the method's effectiveness across autonomous driving vision datasets including KITTI and nuScenes. The loss function improves state-of-the-art 3D object detection methods, achieving over 200% AP gains on under-represented classes (Cyclist) in the KITTI dataset. The results demonstrate the method is generalizable, complements existing techniques, and is particularly beneficial for smaller datasets and rare classes. Code is available at: https://github.com/towardsautonomy/DatasetEquity

Contrastive learning applied to self-supervised representation learning has seen a resurgence in recent years, leading to state of the art performance in the unsupervised training of deep image models. Modern batch contrastive approaches subsume or significantly outperform traditional contrastive losses such as triplet, max-margin and the N-pairs loss. In this work, we extend the self-supervised batch contrastive approach to the fully-supervised setting, allowing us to effectively leverage label information. Clusters of points belonging to the same class are pulled together in embedding space, while simultaneously pushing apart clusters of samples from different classes. We analyze two possible versions of the supervised contrastive (SupCon) loss, identifying the best-performing formulation of the loss. On ResNet-200, we achieve top-1 accuracy of 81.4% on the ImageNet dataset, which is 0.8% above the best number reported for this architecture. We show consistent outperformance over cross-entropy on other datasets and two ResNet variants. The loss shows benefits for robustness to natural corruptions and is more stable to hyperparameter settings such as optimizers and data augmentations. Our loss function is simple to implement, and reference TensorFlow code is released at https://t.ly/supcon.

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction.

Image inpainting is an important task in computer vision. As admirable methods are presented, the inpainted image is getting closer to reality. However, the result is still not good enough in the reconstructed texture and structure based on human vision. Although recent advances in computer hardware have enabled the development of larger and more complex models, there is still a need for lightweight models that can be used by individuals and small-sized institutions. Therefore, we propose a lightweight model that combines a specialized transformer with a traditional convolutional neural network (CNN). Furthermore, we have noticed most researchers only consider three primary colors (RGB) in inpainted images, but we think this is not enough. So we propose a new loss function to intensify color details. Extensive experiments on commonly seen datasets (Places2 and CelebA) validate the efficacy of our proposed model compared with other state-of-the-art methods. Index Terms: HSV color space, image inpainting, joint attention, stripe window, transformer

The design of modern neural architectures has converged through incremental empirical choices, yet the mechanisms governing their training dynamics remain only partially understood. We identify and analyze a negative weight drift induced by the interaction between standard losses and positively biased activation functions. We prove that under MSE or cross-entropy loss, the gradient with respect to positive pre-activations is non-negative in expectation at initialization, driving downstream weights toward negative values during early training. The drift is intrinsic to optimization rather than data, and persists across architectures (MLP, ResNet, ViT, GPT-nano, MP-SENe) and asymmetric activation functions (ReLU, GELU, SiLU). Coupled with ReLU, weight drift produces activation sparsity reaching up to 90\% in GPT-nano. We characterize the sparsity-accuracy tradeoff across 79 configurations and identify a sharp accuracy cliff above sim70\% activation sparsity. While ReLU^2 achieves a good sparsity--accuracy ratio in GPT-nano, it pathologically amplifies identified activation spikes in intermediate transformer layers. Clipping resolves this while preserving the representational benefits of squaring: clipped ReLU^2 outperforms its unclipped version, and GELU^2 achieves the lowest validation loss on GPT-nano. Code is available at https://github.com/On-Point-RND/BugOrFeature.

This paper proposes an explicit way to optimize the super-resolution network for generating visually pleasing images. The previous approaches use several loss functions which is hard to interpret and has the implicit relationships to improve the perceptual score. We show how to exploit the machine learning based model which is directly trained to provide the perceptual score on generated images. It is believed that these models can be used to optimizes the super-resolution network which is easier to interpret. We further analyze the characteristic of the existing loss and our proposed explicit perceptual loss for better interpretation. The experimental results show the explicit approach has a higher perceptual score than other approaches. Finally, we demonstrate the relation of explicit perceptual loss and visually pleasing images using subjective evaluation.

Deep learning algorithms can fare poorly when the training dataset suffers from heavy class-imbalance but the testing criterion requires good generalization on less frequent classes. We design two novel methods to improve performance in such scenarios. First, we propose a theoretically-principled label-distribution-aware margin (LDAM) loss motivated by minimizing a margin-based generalization bound. This loss replaces the standard cross-entropy objective during training and can be applied with prior strategies for training with class-imbalance such as re-weighting or re-sampling. Second, we propose a simple, yet effective, training schedule that defers re-weighting until after the initial stage, allowing the model to learn an initial representation while avoiding some of the complications associated with re-weighting or re-sampling. We test our methods on several benchmark vision tasks including the real-world imbalanced dataset iNaturalist 2018. Our experiments show that either of these methods alone can already improve over existing techniques and their combination achieves even better performance gains.

Shortcut models represent a promising, non-adversarial paradigm for generative modeling, uniquely supporting one-step, few-step, and multi-step sampling from a single trained network. However, their widespread adoption has been stymied by critical performance bottlenecks. This paper tackles the five core issues that held shortcut models back: (1) the hidden flaw of compounding guidance, which we are the first to formalize, causing severe image artifacts; (2) inflexible fixed guidance that restricts inference-time control; (3) a pervasive frequency bias driven by a reliance on low-level distances in the direct domain, which biases reconstructions toward low frequencies; (4) divergent self-consistency arising from a conflict with EMA training; and (5) curvy flow trajectories that impede convergence. To address these challenges, we introduce iSM, a unified training framework that systematically resolves each limitation. Our framework is built on four key improvements: Intrinsic Guidance provides explicit, dynamic control over guidance strength, resolving both compounding guidance and inflexibility. A Multi-Level Wavelet Loss mitigates frequency bias to restore high-frequency details. Scaling Optimal Transport (sOT) reduces training variance and learns straighter, more stable generative paths. Finally, a Twin EMA strategy reconciles training stability with self-consistency. Extensive experiments on ImageNet 256 x 256 demonstrate that our approach yields substantial FID improvements over baseline shortcut models across one-step, few-step, and multi-step generation, making shortcut models a viable and competitive class of generative models.

Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting overestimation bias. However, normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. This becomes problematic in continual learning settings, where the resulting effective learning rate schedule may decay to near zero too quickly relative to the timescale of the learning problem. We propose to make the learning rate schedule explicit with a simple re-parameterization which we call Normalize-and-Project (NaP), which couples the insertion of normalization layers with weight projection, ensuring that the effective learning rate remains constant throughout training. This technique reveals itself as a powerful analytical tool to better understand learning rate schedules in deep reinforcement learning, and as a means of improving robustness to nonstationarity in synthetic plasticity loss benchmarks along with both the single-task and sequential variants of the Arcade Learning Environment. We also show that our approach can be easily applied to popular architectures such as ResNets and transformers while recovering and in some cases even slightly improving the performance of the base model in common stationary benchmarks.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

We show that introducing a weighting factor to reduce the influence of identity shortcuts in residual networks significantly enhances semantic feature learning in generative representation learning frameworks, such as masked autoencoders (MAEs) and diffusion models. Our modification notably improves feature quality, raising ImageNet-1K K-Nearest Neighbor accuracy from 27.4% to 63.9% and linear probing accuracy from 67.8% to 72.7% for MAEs with a ViT-B/16 backbone, while also enhancing generation quality in diffusion models. This significant gap suggests that, while residual connection structure serves an essential role in facilitating gradient propagation, it may have a harmful side effect of reducing capacity for abstract learning by virtue of injecting an echo of shallower representations into deeper layers. We ameliorate this downside via a fixed formula for monotonically decreasing the contribution of identity connections as layer depth increases. Our design promotes the gradual development of feature abstractions, without impacting network trainability. Analyzing the representations learned by our modified residual networks, we find correlation between low effective feature rank and downstream task performance.

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational expense challenging to predict. In this manuscript, we increase the "implicitness" of the DEQ by redefining the method in terms of an infinite time neural ODE, which paradoxically decreases the training cost over a standard neural ODE by 2-4x. Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer? To solve this, we develop Skip and Skip Reg. DEQ, an implicit-explicit (IMEX) layer that simultaneously trains an explicit prediction followed by an implicit correction. We show that training this explicit predictor is free and even decreases the training time by 1.11-3.19x. Together, this manuscript shows how bridging the dichotomy of implicit and explicit deep learning can combine the advantages of both techniques.

Class-incremental learning (CIL) has achieved remarkable successes in learning new classes consecutively while overcoming catastrophic forgetting on old categories. However, most existing CIL methods unreasonably assume that all old categories have the same forgetting pace, and neglect negative influence of forgetting heterogeneity among different old classes on forgetting compensation. To surmount the above challenges, we develop a novel Heterogeneous Forgetting Compensation (HFC) model, which can resolve heterogeneous forgetting of easy-to-forget and hard-to-forget old categories from both representation and gradient aspects. Specifically, we design a task-semantic aggregation block to alleviate heterogeneous forgetting from representation aspect. It aggregates local category information within each task to learn task-shared global representations. Moreover, we develop two novel plug-and-play losses: a gradient-balanced forgetting compensation loss and a gradient-balanced relation distillation loss to alleviate forgetting from gradient aspect. They consider gradient-balanced compensation to rectify forgetting heterogeneity of old categories and heterogeneous relation consistency. Experiments on several representative datasets illustrate effectiveness of our HFC model. The code is available at https://github.com/JiahuaDong/HFC.

Dual-encoder retrievers depend on the principle that relevant documents should score higher than irrelevant ones for a given query. Yet the dominant Noise Contrastive Estimation (NCE) objective, which underpins Contrastive Loss, optimizes a softened ranking surrogate that we rigorously prove is fundamentally oblivious to score separation quality and unrelated to AUC. This mismatch leads to poor calibration and suboptimal performance in downstream tasks like retrieval-augmented generation (RAG). To address this fundamental limitation, we introduce the MW loss, a new training objective that maximizes the Mann-Whitney U statistic, which is mathematically equivalent to the Area under the ROC Curve (AUC). MW loss encourages each positive-negative pair to be correctly ranked by minimizing binary cross entropy over score differences. We provide theoretical guarantees that MW loss directly upper-bounds the AoC, better aligning optimization with retrieval goals. We further promote ROC curves and AUC as natural threshold free diagnostics for evaluating retriever calibration and ranking quality. Empirically, retrievers trained with MW loss consistently outperform contrastive counterparts in AUC and standard retrieval metrics. Our experiments show that MW loss is an empirically superior alternative to Contrastive Loss, yielding better-calibrated and more discriminative retrievers for high-stakes applications like RAG.

Dual-encoder (DE) models are widely used in retrieval tasks, most commonly studied on open QA benchmarks that are often characterized by multi-class and limited training data. In contrast, their performance in multi-label and data-rich retrieval settings like extreme multi-label classification (XMC), remains under-explored. Current empirical evidence indicates that DE models fall significantly short on XMC benchmarks, where SOTA methods linearly scale the number of learnable parameters with the total number of classes (documents in the corpus) by employing per-class classification head. To this end, we first study and highlight that existing multi-label contrastive training losses are not appropriate for training DE models on XMC tasks. We propose decoupled softmax loss - a simple modification to the InfoNCE loss - that overcomes the limitations of existing contrastive losses. We further extend our loss design to a soft top-k operator-based loss which is tailored to optimize top-k prediction performance. When trained with our proposed loss functions, standard DE models alone can match or outperform SOTA methods by up to 2% at Precision@1 even on the largest XMC datasets while being 20x smaller in terms of the number of trainable parameters. This leads to more parameter-efficient and universally applicable solutions for retrieval tasks. Our code and models are publicly available at https://github.com/nilesh2797/dexml.

Masked image modeling (MIM) has attracted much research attention due to its promising potential for learning scalable visual representations. In typical approaches, models usually focus on predicting specific contents of masked patches, and their performances are highly related to pre-defined mask strategies. Intuitively, this procedure can be considered as training a student (the model) on solving given problems (predict masked patches). However, we argue that the model should not only focus on solving given problems, but also stand in the shoes of a teacher to produce a more challenging problem by itself. To this end, we propose Hard Patches Mining (HPM), a brand-new framework for MIM pre-training. We observe that the reconstruction loss can naturally be the metric of the difficulty of the pre-training task. Therefore, we introduce an auxiliary loss predictor, predicting patch-wise losses first and deciding where to mask next. It adopts a relative relationship learning strategy to prevent overfitting to exact reconstruction loss values. Experiments under various settings demonstrate the effectiveness of HPM in constructing masked images. Furthermore, we empirically find that solely introducing the loss prediction objective leads to powerful representations, verifying the efficacy of the ability to be aware of where is hard to reconstruct.

We propose a scalable Forward-Forward (FF) algorithm that eliminates the need for backpropagation by training each layer separately. Unlike backpropagation, FF avoids backward gradients and can be more modular and memory efficient, making it appealing for large networks. We extend FF to modern convolutional architectures, such as MobileNetV3 and ResNet18, by introducing a new way to compute losses for convolutional layers. Experiments show that our method achieves performance comparable to standard backpropagation. Furthermore, when we divide the network into blocks, such as the residual blocks in ResNet, and apply backpropagation only within each block, but not across blocks, our hybrid design tends to outperform backpropagation baselines while maintaining a similar training speed. Finally, we present experiments on small datasets and transfer learning that confirm the adaptability of our method.

Low-bit weight-only quantization significantly reduces the memory footprint of large language models (LLMs), but disproportionately affects certain examples. We analyze diverse 3-4 bit methods on LLMs ranging from 7B-70B in size and find that the quantization errors of 50 pairs of methods are strongly correlated (avg. 0.82) on FineWeb examples. Moreover, the residual stream magnitudes of full-precision models are indicative of future quantization errors. We further establish a hypothesis that relates the residual stream magnitudes to error amplification and accumulation over layers. Using LLM localization techniques, early exiting, and activation patching, we show that examples with large errors rely on precise residual activations in the late layers, and that the outputs of MLP gates play a crucial role in maintaining the perplexity. Our work reveals why certain examples result in large quantization errors and which model components are most critical for performance preservation.

Modern deep neural networks (DNNs) have achieved state-of-the-art performances but are typically over-parameterized. The over-parameterization may result in undesirably large generalization error in the absence of other customized training strategies. Recently, a line of research under the name of Sharpness-Aware Minimization (SAM) has shown that minimizing a sharpness measure, which reflects the geometry of the loss landscape, can significantly reduce the generalization error. However, SAM-like methods incur a two-fold computational overhead of the given base optimizer (e.g. SGD) for approximating the sharpness measure. In this paper, we propose Sharpness-Aware Training for Free, or SAF, which mitigates the sharp landscape at almost zero additional computational cost over the base optimizer. Intuitively, SAF achieves this by avoiding sudden drops in the loss in the sharp local minima throughout the trajectory of the updates of the weights. Specifically, we suggest a novel trajectory loss, based on the KL-divergence between the outputs of DNNs with the current weights and past weights, as a replacement of the SAM's sharpness measure. This loss captures the rate of change of the training loss along the model's update trajectory. By minimizing it, SAF ensures the convergence to a flat minimum with improved generalization capabilities. Extensive empirical results show that SAF minimizes the sharpness in the same way that SAM does, yielding better results on the ImageNet dataset with essentially the same computational cost as the base optimizer.

In this work, we study how well the learned weights of a neural network utilize the space available to them. This notion is related to capacity, but additionally incorporates the interaction of the network architecture with the dataset. Most learned weights appear to be full rank, and are therefore not amenable to low rank decomposition. This deceptively implies that the weights are utilizing the entire space available to them. We propose a simple data-driven transformation that projects the weights onto the subspace where the data and the weight interact. This preserves the functional mapping of the layer and reveals its low rank structure. In our findings, we conclude that most models utilize a fraction of the available space. For instance, for ViTB-16 and ViTL-16 trained on ImageNet, the mean layer utilization is 35% and 20% respectively. Our transformation results in reducing the parameters to 50% and 25% respectively, while resulting in less than 0.2% accuracy drop after fine-tuning. We also show that self-supervised pre-training drives this utilization up to 70%, justifying its suitability for downstream tasks.

In this work, we have worked towards two major goals. Firstly, we have investigated the importance of Batch Normalisation (BN) layers in a non-contrastive representation learning framework called Bootstrap Your Own Latent (BYOL). We conducted several experiments to conclude that BN layers are not necessary for representation learning in BYOL. Moreover, BYOL only learns from the positive pairs of images but ignores other semantically similar images in the same input batch. For the second goal, we have introduced two new loss functions to determine the semantically similar pairs in the same input batch of images and reduce the distance between their representations. These loss functions are Cross-Cosine Similarity Loss (CCSL) and Cross-Sigmoid Similarity Loss (CSSL). Using the proposed loss functions, we are able to surpass the performance of Vanilla BYOL (71.04%) by training the BYOL framework using CCSL loss (76.87%) on the STL10 dataset. BYOL trained using CSSL loss performs comparably with Vanilla BYOL.

Monocular 3D detectors achieve remarkable performance on cars and smaller objects. However, their performance drops on larger objects, leading to fatal accidents. Some attribute the failures to training data scarcity or their receptive field requirements of large objects. In this paper, we highlight this understudied problem of generalization to large objects. We find that modern frontal detectors struggle to generalize to large objects even on nearly balanced datasets. We argue that the cause of failure is the sensitivity of depth regression losses to noise of larger objects. To bridge this gap, we comprehensively investigate regression and dice losses, examining their robustness under varying error levels and object sizes. We mathematically prove that the dice loss leads to superior noise-robustness and model convergence for large objects compared to regression losses for a simplified case. Leveraging our theoretical insights, we propose SeaBird (Segmentation in Bird's View) as the first step towards generalizing to large objects. SeaBird effectively integrates BEV segmentation on foreground objects for 3D detection, with the segmentation head trained with the dice loss. SeaBird achieves SoTA results on the KITTI-360 leaderboard and improves existing detectors on the nuScenes leaderboard, particularly for large objects. Code and models at https://github.com/abhi1kumar/SeaBird

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model size compression. However, these studies often approach various lossy and lossless compression methods in isolation, leading to challenges in achieving high compression ratios efficiently. This work proposes a post-training model size compression method that combines lossy and lossless compression in a unified way. We first propose a unified parametric weight transformation, which ensures different lossy compression methods can be performed jointly in a post-training manner. Then, a dedicated differentiable counter is introduced to guide the optimization of lossy compression to arrive at a more suitable point for later lossless compression. Additionally, our method can easily control a desired global compression ratio and allocate adaptive ratios for different layers. Finally, our method can achieve a stable 10times compression ratio without sacrificing accuracy and a 20times compression ratio with minor accuracy loss in a short time. Our code is available at https://github.com/ModelTC/L2_Compression .

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

The high computational costs of large language models (LLMs) have led to a flurry of research on LLM compression, via methods such as quantization, sparsification, or structured pruning. A new frontier in this area is given by dynamic, non-uniform compression methods, which adjust the compression levels (e.g., sparsity) per-block or even per-layer in order to minimize accuracy loss, while guaranteeing a global compression threshold. Yet, current methods rely on heuristics for identifying the "importance" of a given layer towards the loss, based on assumptions such as error monotonicity, i.e. that the end-to-end model compression error is proportional to the sum of layer-wise errors. In this paper, we revisit this area, and propose a new and general approach for dynamic compression that is provably optimal in a given input range. We begin from the motivating observation that, in general, error monotonicity does not hold for LLMs: compressed models with lower sum of per-layer errors can perform worse than models with higher error sums. To address this, we propose a new general evolutionary framework for dynamic LLM compression called EvoPress, which has provable convergence, and low sample and evaluation complexity. We show that these theoretical guarantees lead to highly competitive practical performance for dynamic compression of Llama, Mistral and Phi models. Via EvoPress, we set new state-of-the-art results across all compression approaches: structural pruning (block/layer dropping), unstructured sparsity, as well as quantization with dynamic bitwidths. Our code is available at https://github.com/IST-DASLab/EvoPress.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on items' ranks), their derivatives are either undefined or zero everywhere. This makes them unsuitable for gradient-based optimisation, which is the usual method of learning appropriate scoring functions. Commonly used LTR loss functions are only loosely related to the evaluation metrics, causing a mismatch between the optimisation objective and the evaluation criterion. In this paper, we address this mismatch by proposing NeuralNDCG, a novel differentiable approximation to NDCG. Since NDCG relies on the non-differentiable sorting operator, we obtain NeuralNDCG by relaxing that operator using NeuralSort, a differentiable approximation of sorting. As a result, we obtain a new ranking loss function which is an arbitrarily accurate approximation to the evaluation metric, thus closing the gap between the training and the evaluation of LTR models. We introduce two variants of the proposed loss function. Finally, the empirical evaluation shows that our proposed method outperforms previous work aimed at direct optimisation of NDCG and is competitive with the state-of-the-art methods.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

We present new insights and a novel paradigm (StEik) for learning implicit neural representations (INR) of shapes. In particular, we shed light on the popular eikonal loss used for imposing a signed distance function constraint in INR. We show analytically that as the representation power of the network increases, the optimization approaches a partial differential equation (PDE) in the continuum limit that is unstable. We show that this instability can manifest in existing network optimization, leading to irregularities in the reconstructed surface and/or convergence to sub-optimal local minima, and thus fails to capture fine geometric and topological structure. We show analytically how other terms added to the loss, currently used in the literature for other purposes, can actually eliminate these instabilities. However, such terms can over-regularize the surface, preventing the representation of fine shape detail. Based on a similar PDE theory for the continuum limit, we introduce a new regularization term that still counteracts the eikonal instability but without over-regularizing. Furthermore, since stability is now guaranteed in the continuum limit, this stabilization also allows for considering new network structures that are able to represent finer shape detail. We introduce such a structure based on quadratic layers. Experiments on multiple benchmark data sets show that our new regularization and network are able to capture more precise shape details and more accurate topology than existing state-of-the-art.

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

Recent work has shown that directly fine-tuning large language models (LLMs) for dense retrieval yields strong performance, but their substantial parameter counts make them computationally inefficient. While prior studies have revealed significant layer redundancy in LLMs for generative tasks, it remains unclear whether similar redundancy exists when these models are adapted for retrieval tasks, which require encoding entire sequences into fixed representations rather than generating tokens iteratively. To this end, we conduct a comprehensive analysis of layer redundancy in LLM-based dense retrievers. We find that, in contrast to generative settings, MLP layers are substantially more prunable, while attention layers remain critical for semantic aggregation. Building on this insight, we propose EffiR, a framework for developing efficient retrievers that performs large-scale MLP compression through a coarse-to-fine strategy (coarse-grained depth reduction followed by fine-grained width reduction), combined with retrieval-specific fine-tuning. Across diverse BEIR datasets and LLM backbones, EffiR achieves substantial reductions in model size and inference cost while preserving the performance of full-size models.