Understanding the mechanisms through which neural networks extract statistics from input-label pairs through feature learning is one of the most important unsolved problems in supervised learning. Prior works demonstrated that the gram matrices of the weights (the neural feature matrices, NFM) and the average gradient outer products (AGOP) become correlated during training, in a statement known as the neural feature ansatz (NFA). Through the NFA, the authors introduce mapping with the AGOP as a general mechanism for neural feature learning. However, these works do not provide a theoretical explanation for this correlation or its origins. In this work, we further clarify the nature of this correlation, and explain its emergence. We show that this correlation is equivalent to alignment between the left singular structure of the weight matrices and the newly defined pre-activation tangent features at each layer. We further establish that the alignment is driven by the interaction of weight changes induced by SGD with the pre-activation features, and analyze the resulting dynamics analytically at early times in terms of simple statistics of the inputs and labels. Finally, motivated by the observation that the NFA is driven by this centered correlation, we introduce a simple optimization rule that dramatically increases the NFA correlations at any given layer and improves the quality of features learned.
相關內容
A central question in deep learning is how deep neural networks (DNNs) learn features. DNN layers progressively collapse data into a regular low-dimensional geometry. This collective effect of non-linearity, noise, learning rate, width, depth, and numerous other parameters, has eluded first-principles theories which are built from microscopic neuronal dynamics. Here we present a noise-non-linearity phase diagram that highlights where shallow or deep layers learn features more effectively. We then propose a macroscopic mechanical theory of feature learning that accurately reproduces this phase diagram, offering a clear intuition for why and how some DNNs are ``lazy'' and some are ``active'', and relating the distribution of feature learning over layers with test accuracy.
Applying differential privacy (DP) by means of the DP-SGD algorithm to protect individual data points during training is becoming increasingly popular in NLP. However, the choice of granularity at which DP is applied is often neglected. For example, neural machine translation (NMT) typically operates on the sentence-level granularity. From the perspective of DP, this setup assumes that each sentence belongs to a single person and any two sentences in the training dataset are independent. This assumption is however violated in many real-world NMT datasets, e.g. those including dialogues. For proper application of DP we thus must shift from sentences to entire documents. In this paper, we investigate NMT at both the sentence and document levels, analyzing the privacy/utility trade-off for both scenarios, and evaluating the risks of not using the appropriate privacy granularity in terms of leaking personally identifiable information (PII). Our findings indicate that the document-level NMT system is more resistant to membership inference attacks, emphasizing the significance of using the appropriate granularity when working with DP.
This study proposes a unified theory and statistical learning approach for traffic conflict detection, addressing the long-existing call for a consistent and comprehensive methodology to evaluate the collision risk emerging in road user interactions. The proposed theory assumes context-dependent probabilistic collision risk and frames conflict detection as assessing this risk by statistical learning of extreme events in daily interactions. Experiments using real-world trajectory data are conducted in this study, where a unified metric of conflict is trained with lane-changing interactions on German highways and applied to near-crash events from the 100-Car Naturalistic Driving Study in the U.S. Results of the experiments demonstrate that the trained metric provides effective collision warnings, generalises across distinct datasets and traffic environments, covers a broad range of conflicts, and delivers a long-tailed distribution of conflict intensity. Reflecting on these results, the unified theory ensures consistent evaluation by a generic formulation that encompasses varying assumptions of traffic conflicts; the statistical learning approach then enables a comprehensive consideration of influencing factors such as motion states of road users, environment conditions, and participant characteristics. Therefore, the theory and learning approach jointly provide an explainable and adaptable methodology for conflict detection among different road users and across various interaction scenarios. This promises to reduce accidents and improve overall traffic safety, by enhanced safety assessment of traffic infrastructures, more effective collision warning systems for autonomous driving, and a deeper understanding of road user behaviour in different traffic conditions.
Humans are capable of solving complex abstract reasoning tests. Whether this ability reflects a learning-independent inference mechanism applicable to any novel unlearned problem or whether it is a manifestation of extensive training throughout life is an open question. Addressing this question in humans is challenging because it is impossible to control their prior training. However, assuming a similarity between the cognitive processing of Artificial Neural Networks (ANNs) and humans, the extent to which training is required for ANNs' abstract reasoning is informative about this question in humans. Previous studies demonstrated that ANNs can solve abstract reasoning tests. However, this success required extensive training. In this study, we examined the learning-independent abstract reasoning of ANNs. Specifically, we evaluated their performance without any pretraining, with the ANNs' weights being randomly-initialized, and only change in the process of problem solving. We found that naive ANN models can solve non-trivial visual reasoning tests, similar to those used to evaluate human learning-independent reasoning. We further studied the mechanisms that support this ability. Our results suggest the possibility of learning-independent abstract reasoning that does not require extensive training.
Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems however, these models tend to be expensive to evaluate, making surrogate models quite valuable. Artificial neural networks approximate systems very well by taking advantage of the inherent information of its given training data. In this context, this paper investigates the improvement of the training process by including sensitivity information, which are partial derivatives w.r.t. inputs, as outlined by Sobolev training. In computational mechanics, sensitivities can be applied to neural networks by expanding the training loss function with additional loss terms, thereby improving training convergence resulting in lower generalisation error. This improvement is shown in two examples of linear and non-linear material behavior. More specifically, the Sobolev designed loss function is expanded with residual weights adjusting the effect of each loss on the training step. Residual weighting is the given scaling to the different training data, which in this case are response and sensitivities. These residual weights are optimized by an adaptive scheme, whereby varying objective functions are explored, with some showing improvements in accuracy and precision of the general training convergence.
Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy for problems spanning low- and high-dimensional domains, integrating a non-probabilistic regression model for the low-fidelity with a Bayesian model for the high-fidelity. The models are trained in a staggered scheme, where the low-fidelity model is transfer-learned to the high-fidelity data and a Bayesian model is trained for the residual. This three-model strategy -- deterministic low-fidelity, transfer learning, and Bayesian residual -- leads to a prediction that includes uncertainty quantification both for noisy and noiseless multi-fidelity data. The strategy is general and unifies the topic, highlighting the expressivity trade-off between the transfer-learning and Bayesian models (a complex transfer-learning model leads to a simpler Bayesian model, and vice versa). We propose modeling choices for two scenarios, and argue in favor of using a linear transfer-learning model that fuses 1) kernel ridge regression for low-fidelity with Gaussian processes for high-fidelity; or 2) deep neural network for low-fidelity with a Bayesian neural network for high-fidelity. We demonstrate the effectiveness and efficiency of the proposed strategies and contrast them with the state-of-the-art based on various numerical examples. The simplicity of these formulations makes them practical for a broad scope of future engineering applications.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the thesis, we will empirically study how training deep networks via stochastic gradient descent implicitly controls the networks' capacity. Subsequently, to show how this leads to better generalization, we will derive {\em data-dependent} {\em uniform-convergence-based} generalization bounds with improved dependencies on the parameter count. Uniform convergence has in fact been the most widely used tool in deep learning literature, thanks to its simplicity and generality. Given its popularity, in this thesis, we will also take a step back to identify the fundamental limits of uniform convergence as a tool to explain generalization. In particular, we will show that in some example overparameterized settings, {\em any} uniform convergence bound will provide only a vacuous generalization bound. With this realization in mind, in the last part of the thesis, we will change course and introduce an {\em empirical} technique to estimate generalization using unlabeled data. Our technique does not rely on any notion of uniform-convergece-based complexity and is remarkably precise. We will theoretically show why our technique enjoys such precision. We will conclude by discussing how future work could explore novel ways to incorporate distributional assumptions in generalization bounds (such as in the form of unlabeled data) and explore other tools to derive bounds, perhaps by modifying uniform convergence or by developing completely new tools altogether.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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