ICML 2024 论文列表

Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question. This paper explores a comparison between deeper neural networks (DeNNs) with a flexible number of layers and wider neural networks (WeNNs) with limited hidden layers, focusing on their optimal generalization error in Sobolev losses. Analytical investigations reveal that the architecture of a neural network can be significantly influenced by various factors, including the number of sample points, parameters within the neural networks, and the regularity of the loss function. Specifically, a higher number of parameters tends to favor WeNNs, while an increased number of sample points and greater regularity in the loss function lean towards the adoption of DeNNs. We ultimately apply this theory to address partial differential equations using deep Ritz and physics-informed neural network (PINN) methods, guiding the design of neural networks.

We tackle the challenge of predicting models' Out-of-Distribution (OOD) performance using in-distribution (ID) measurements without requiring OOD data. Existing evaluations with ``Effective robustness'', which use ID accuracy as an indicator of OOD accuracy, encounter limitations when models are trained with diverse supervision and distributions, such as class labels (*Vision Models, VMs, on ImageNet*) and textual descriptions (*Visual-Language Models, VLMs, on LAION*). VLMs often generalize better to OOD data than VMs despite having similar or lower ID performance. To improve the prediction of models' OOD performance from ID measurements, we introduce the *Lowest Common Ancestor (LCA)-on-the-Line* framework. This approach revisits the established concept of LCA distance, which measures the hierarchical distance between labels and predictions within a predefined class hierarchy, such as WordNet. We assess 75 models using ImageNet as the ID dataset and five significantly shifted OOD variants, uncovering a strong linear correlation between ID LCA distance and OOD top-1 accuracy. Our method provides a compelling alternative for understanding why VLMs tend to generalize better. Additionally, we propose a technique to construct a taxonomic hierarchy on any dataset using $K$-means clustering, demonstrating that LCA distance is robust to the constructed taxonomic hierarchy. Moreover, we demonstrate that aligning model predictions with class taxonomies, through soft labels or prompt engineering, can enhance model generalization. Open source code in our [Project Page](https://elvishelvis.github.io/papers/lca/).

This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks' performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.

The coverage and composition of the pretraining data significantly impacts the generalization ability of Large Language Models (LLMs). Despite its importance, recent LLMs still rely on heuristics and trial and error to increase or reduce the influence of data-domains. We propose DOmain reweighting with Generalization Estimation (DoGE), which optimizes the probability of sampling from each domain (domain weights) in a principled way. Our approach is a two stage process consisting (i) training a proxy model to obtain domain weights using a bi-level optimization algorithm; (ii) training a larger base model by sampling training domains according to the learnt domain weights. In our experiments, we extensively show how DoGE improves the generalization of the base model to any target data mixture. On the SlimPajama dataset, our base model gets a better perplexity and few-shot reasoning accuracies across 6 tasks compared to baseline methods. Moreover, aiming to generalize to out-of-domain target tasks, which is unseen in the pretraining corpus (OOD domain), DoGE can effectively identify inter-domain dependencies, consistently achieves better test perplexity on the target domain.

One of the central problems of statistical learning theory is quantifying the generalization ability of learning algorithms within a probabilistic framework. Algorithmic stability is a powerful tool for deriving generalization bounds, however, it typically builds on a critical assumption that losses are bounded. In this paper, we relax this condition to unbounded loss functions with subweibull diameter. This gives new generalization bounds for algorithmic stability and also includes existing results of subgaussian and subexponential diameters as specific cases. Furthermore, we provide a refined stability analysis by developing generalization bounds which can be $\sqrt{n}$-times faster than the previous results, where $n$ is the sample size. Our main technical contribution is general concentration inequalities for subweibull random variables, which may be of independent interest.

Modern language models can contain billions of parameters, raising the question of whether they can generalize beyond the training data or simply parrot their training corpora. We provide the first non-vacuous generalization bounds for pretrained large language models (LLMs), indicating that language models are capable of discovering regularities that generalize to unseen data. In particular, we derive a compression bound that is valid for the unbounded log-likelihood loss using prediction smoothing, and we extend the bound to handle subsampling, making bound computation 900 times faster on massive datasets. To achieve the extreme level of compression required for non-vacuous bounds, we devise SubLoRA, a simple low-dimensional nonlinear parameterization that leads to non-vacuous generalization bounds for very large models with up to 849 million parameters. Finally, we use our bounds to understand LLM generalization and find that larger models have better generalization bounds and are more compressible than smaller models.

Towards energy-efficient artificial intelligence similar to the human brain, the bio-inspired spiking neural networks (SNNs) have advantages of biological plausibility, event-driven sparsity, and binary activation. Recently, large-scale language models exhibit promising generalization capability, making it a valuable issue to explore more general spike-driven models. However, the binary spikes in existing SNNs fail to encode adequate semantic information, placing technological challenges for generalization. This work proposes the first fully spiking mechanism for general language tasks, including both discriminative and generative ones. Different from previous spikes with 0,1 levels, we propose a more general spike formulation with bi-directional, elastic amplitude, and elastic frequency encoding, while still maintaining the addition nature of SNNs. In a single time step, the spike is enhanced by direction and amplitude information; in spike frequency, a strategy to control spike firing rate is well designed. We plug this elastic bi-spiking mechanism in language modeling, named SpikeLM. It is the first time to handle general language tasks with fully spike-driven models, which achieve much higher accuracy than previously possible. SpikeLM also greatly bridges the performance gap between SNNs and ANNs in language modeling. Our code is available at https://github.com/Xingrun-Xing/SpikeLM.

We provide generalization bounds for matrix completion with Schatten $p$ quasi-norm constraints, which is equivalent to deep matrix factorization with Frobenius constraints. In the uniform sampling regime, the sample complexity scales like $\widetilde{O}\left( rn\right)$ where $n$ is the size of the matrix and $r$ is a constraint of the same order as the ground truth rank in the isotropic case. In the distribution-free setting, the bounds scale as $\widetilde{O}\left(r^{1-\frac{p}{2}}n^{1+\frac{p}{2}}\right)$, which reduces to the familiar $\sqrt{r}n^{\frac{3}{2}}$ for $p=1$. Furthermore, we provide an analogue of the weighted trace norm for this setting which brings the sample complexity down to $\widetilde{O}(nr)$ in all cases. We then present a non-linear model, Functionally Rescaled Matrix Completion (FRMC) which applies a single trainable function from $\mathbb{R}\rightarrow \mathbb{R}$ to each entry of a latent matrix, and prove that this adds only negligible terms of the overall sample complexity, whilst experiments demonstrate that this simple model improvement already leads to significant gains on real data. We also provide extensions of our results to various neural architectures, thereby providing the first comprehensive uniform convergence PAC analysis of neural network matrix completion.

Learning in deep weight spaces (DWS), where neural networks process the weights of other neural networks, is an emerging research direction, with applications to 2D and 3D neural fields (INRs, NeRFs), as well as making inferences about other types of neural networks. Unfortunately, weight space models tend to suffer from substantial overfitting. We empirically analyze the reasons for this overfitting and find that a key reason is the lack of diversity in DWS datasets. While a given object can be represented by many different weight configurations, typical INR training sets fail to capture variability across INRs that represent the same object. To address this, we explore strategies for data augmentation in weight spaces and propose a MixUp method adapted for weight spaces. We demonstrate the effectiveness of these methods in two setups. In classification, they improve performance similarly to having up to 10 times more data. In self-supervised contrastive learning, they yield substantial 5-10% gains in downstream classification.

A main theoretical puzzle is why over-parameterized Neural Networks (NNs) generalize well when trained to zero loss (i.e., so they interpolate the data). Usually, the NN is trained with Stochastic Gradient Descent (SGD) or one of its variants. However, recent empirical work examined the generalization of a random NN that interpolates the data: the NN was sampled from a seemingly uniform prior over the parameters, conditioned on that the NN perfectly classifying the training set. Interestingly, such a NN sample typically generalized as well as SGD-trained NNs. We prove that such a random NN interpolator typically generalizes well if there exists an underlying narrow ``teacher NN" that agrees with the labels. Specifically, we show that such a `flat' prior over the NN parametrization induces a rich prior over the NN functions, due to the redundancy in the NN structure. In particular, this creates a bias towards simpler functions, which require less relevant parameters to represent --- enabling learning with a sample complexity approximately proportional to the complexity of the teacher (roughly, the number of non-redundant parameters), rather than the student's.

Federated Learning is widely employed to tackle distributed sensitive data. Existing methods primarily focus on addressing in-federation data heterogeneity. However, we observed that they suffer from significant performance degradation when applied to unseen clients for out-of-federation (OOF) generalization. The recent attempts to address generalization to unseen clients generally struggle to scale up to large-scale distributed settings due to high communication or computation costs. Moreover, methods that scale well often demonstrate poor generalization capability. To achieve OOF-resiliency in a scalable manner, we propose Topology-aware Federated Learning (TFL) that leverages client topology - a graph representing client relationships - to effectively train robust models against OOF data. We formulate a novel optimization problem for TFL, consisting of two key modules: Client Topology Learning, which infers the client relationships in a privacy-preserving manner, and Learning on Client Topology, which leverages the learned topology to identify influential clients and harness this information into the FL optimization process to efficiently build robust models. Empirical evaluation on a variety of real-world datasets verifies TFL's superior OOF robustness and scalability.

Although most graph neural networks (GNNs) can operate on graphs of any size, their classification performance often declines on graphs larger than those encountered during training. Existing methods insufficiently address the removal of size information from graph representations, resulting in sub-optimal performance and reliance on backbone models. In response, we propose DISGEN, a novel and model-agnostic framework designed to disentangle size factors from graph representations. DISGEN employs size- and task-invariant augmentations and introduces a decoupling loss that minimizes shared information in hidden representations, with theoretical guarantees for its effectiveness. Our empirical results show that DISGEN outperforms the state-of-the-art models by up to 6% on real-world datasets, underscoring its effectiveness in enhancing the size generalizability of GNNs. Our codes are available at: https://github.com/GraphmindDartmouth/DISGEN.