Neural collapse describes the geometry of activation in the final layer of a deep neural network when it is trained beyond performance plateaus. Open questions include whether neural collapse leads to better generalization and, if so, why and how training beyond the plateau helps. We model neural collapse as an information bottleneck (IB) problem in order to investigate whether such a compact representation exists and discover its connection to generalization. We demonstrate that neural collapse leads to good generalization specifically when it approaches an optimal IB solution of the classification problem. Recent research has shown that two deep neural networks independently trained with the same contrastive loss objective are linearly identifiable, meaning that the resulting representations are equivalent up to a matrix transformation. We leverage linear identifiability to approximate an analytical solution of the IB problem. This approximation demonstrates that when class means exhibit $K$-simplex Equiangular Tight Frame (ETF) behavior (e.g., $K$=10 for CIFAR10 and $K$=100 for CIFAR100), they coincide with the critical phase transitions of the corresponding IB problem. The performance plateau occurs once the optimal solution for the IB problem includes all of these phase transitions. We also show that the resulting $K$-simplex ETF can be packed into a $K$-dimensional Gaussian distribution using supervised contrastive learning with a ResNet50 backbone. This geometry suggests that the $K$-simplex ETF learned by supervised contrastive learning approximates the optimal features for source coding. Hence, there is a direct correspondence between optimal IB solutions and generalization in contrastive learning.
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Classical physical modelling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that -- in addition to the always necessary specification of the process conditions -- can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally, and their use in industrial applications (e.g. the interaction of vehicles with sand).
Global contexts in images are quite valuable in image-to-image translation problems. Conventional attention-based and graph-based models capture the global context to a large extent, however, these are computationally expensive. Moreover, the existing approaches are limited to only learning the pairwise semantic relation between any two points on the image. In this paper, we present Latent Graph Attention (LGA) a computationally inexpensive (linear to the number of nodes) and stable, modular framework for incorporating the global context in the existing architectures, especially empowering small-scale architectures to give performance closer to large size architectures, thus making the light-weight architectures more useful for edge devices with lower compute power and lower energy needs. LGA propagates information spatially using a network of locally connected graphs, thereby facilitating to construct a semantically coherent relation between any two spatially distant points that also takes into account the influence of the intermediate pixels. Moreover, the depth of the graph network can be used to adapt the extent of contextual spread to the target dataset, thereby being able to explicitly control the added computational cost. To enhance the learning mechanism of LGA, we also introduce a novel contrastive loss term that helps our LGA module to couple well with the original architecture at the expense of minimal additional computational load. We show that incorporating LGA improves the performance on three challenging applications, namely transparent object segmentation, image restoration for dehazing and optical flow estimation.
The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.
Partially-supervised instance segmentation is a task which requests segmenting objects from novel unseen categories via learning on limited seen categories with annotated masks thus eliminating demands of heavy annotation burden. The key to addressing this task is to build an effective class-agnostic mask segmentation model. Unlike previous methods that learn such models only on seen categories, in this paper, we propose a new method, named ContrastMask, which learns a mask segmentation model on both seen and unseen categories under a unified pixel-level contrastive learning framework. In this framework, annotated masks of seen categories and pseudo masks of unseen categories serve as a prior for contrastive learning, where features from the mask regions (foreground) are pulled together, and are contrasted against those from the background, and vice versa. Through this framework, feature discrimination between foreground and background is largely improved, facilitating learning of the class-agnostic mask segmentation model. Exhaustive experiments on the COCO dataset demonstrate the superiority of our method, which outperforms previous state-of-the-arts.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
Federated learning enables multiple parties to collaboratively train a machine learning model without communicating their local data. A key challenge in federated learning is to handle the heterogeneity of local data distribution across parties. Although many studies have been proposed to address this challenge, we find that they fail to achieve high performance in image datasets with deep learning models. In this paper, we propose MOON: model-contrastive federated learning. MOON is a simple and effective federated learning framework. The key idea of MOON is to utilize the similarity between model representations to correct the local training of individual parties, i.e., conducting contrastive learning in model-level. Our extensive experiments show that MOON significantly outperforms the other state-of-the-art federated learning algorithms on various image classification tasks.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
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