General ML · generalization

Can we modify the training data distribution to encourage the underlying optimization method toward finding solutions with superior generalization performance on in-distribution data? In this work, we approach this question for the first time by comparing the inductive bias of gradient descent (GD) with that of sharpness-aware minimization (SAM). By studying a two-layer CNN, we rigorously prove that SAM learns different features more uniformly, particularly in early epochs. That is, SAM is less susceptible to simplicity bias compared to GD. We also show that examples constraining features that are learned early are separable from the rest based on the model’s output. Based on this observation, we propose a method that (i) clusters examples based on the network output early in training, (ii) identifies a cluster of examples with similar network output, and (iii) upsamples the rest of examples only once to alleviate the simplicity bias. We show empirically that USEFUL effectively improves the generalization performance on the original data distribution when training with various gradient methods, including (S)GD and SAM. Notably, we demonstrate that our method can be combined with SAM variants and existing data augmentation strategies to achieve, to the best of our knowledge, state-of-the-art performance for training ResNet18 on CIFAR10, STL10, CINIC10, Tiny-ImageNet; ResNet34 on CIFAR100; and VGG19 and DenseNet121 on CIFAR10.

While the expected calibration error (ECE), which employs binning, is widely adopted to evaluate the calibration performance of machine learning models, theoretical understanding of its estimation bias is limited. In this paper, we present the first comprehensive analysis of the estimation bias in the two common binning strategies, uniform mass and uniform width binning. Our analysis establishes upper bounds on the bias, achieving an improved convergence rate. Moreover, our bounds reveal, for the first time, the optimal number of bins to minimize the estimation bias. We further extend our bias analysis to generalization error analysis based on the information-theoretic approach, deriving upper bounds that enable the numerical evaluation of how small the ECE is for unknown data. Experiments using deep learning models show that our bounds are nonvacuous thanks to this information-theoretic generalization analysis approach.

A primary challenge for visual-based Reinforcement Learning (RL) is to generalize effectively across unseen environments. Although previous studies have explored different auxiliary tasks to enhance generalization, few adopt image reconstruction due to concerns about exacerbating overfitting to task-irrelevant features during training. Perceiving the pre-eminence of image reconstruction in representation learning, we propose SMG (\blue{S}eparated \blue{M}odels for \blue{G}eneralization), a novel approach that exploits image reconstruction for generalization. SMG introduces two model branches to extract task-relevant and task-irrelevant representations separately from visual observations via cooperatively reconstruction. Built upon this architecture, we further emphasize the importance of task-relevant features for generalization. Specifically, SMG incorporates two additional consistency losses to guide the agent's focus toward task-relevant areas across different scenarios, thereby achieving free from overfitting. Extensive experiments in DMC demonstrate the SOTA performance of SMG in generalization, particularly excelling in video-background settings. Evaluations on robotic manipulation tasks further confirm the robustness of SMG in real-world applications. Source code is available at \url{https://anonymous.4open.science/r/SMG/}.

The spurious correlation between the background features of the image and its label arises due to that the samples labeled with the same class in the training set often co-occurs with a specific background, which will cause the encoder to extract non-semantic features for classification, resulting in poor out-of-distribution generalization performance. Although many studies have been proposed to address this challenge, the semantic and spurious features are still difficult to accurately decouple from the original image and fail to achieve high performance with deep learning models. This paper proposes a novel perspective inspired by neural collapse to solve the spurious correlation problem through the alternate execution of environment partitioning and learning semantic masks. Specifically, we propose to assign an environment to each sample by learning a local model for each environment and using maximum likelihood probability. At the same time, we require that the learned semantic mask neurally collapses to the same simplex equiangular tight frame (ETF) in each environment after being applied to the original input. We conduct extensive experiments on four datasets, and the results demonstrate that our method significantly improves out-of-distribution performance.

The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using overparameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic. Since using i.i.d. training data is a necessary condition for a learning algorithm to be generalizable, memorization and its generalization theory for i.i.d. datasets are developed under mild conditions on the data distribution. First, algorithms are given to construct memorization networks for an i.i.d. dataset, which have the smallest number of parameters and even a constant number of parameters. Second, we show that, in order for the memorization networks to be generalizable, the width of the network must be at least equal to the dimension of the data, which implies that the existing memorization networks with an optimal number of parameters are not generalizable. Third, a lower bound for the sample complexity of general memorization algorithms and the exact sample complexity for memorization algorithms with constant number of parameters are given. As a consequence, it is shown that there exist data distributions such that, to be generalizable for them, the memorization network must have an exponential number of parameters in the data dimension. Finally, an efficient and generalizable memorization algorithm is given when the number of training samples is greater than the efficient memorization sample complexity of the data distribution.

Although humans inherently have diverse values, current large language model (LLM) alignment methods often assume that aligning LLMs with the general public’s preferences is optimal. A major challenge in adopting a more individualized approach to LLM alignment is its lack of scalability, as it involves repeatedly acquiring preference data and training new reward models and LLMs for each individual’s preferences. To address these challenges, we propose a new paradigm where users specify what they value most within the system message, steering the LLM’s generation behavior to better align with the user’s intentions. However, a naive application of such an approach is non-trivial since LLMs are typically trained on a uniform system message (e.g., “You are a helpful assistant”), which limits their ability to generalize to diverse, unseen system messages. To improve this generalization, we create Multifaceted Collection, augmenting 66k user instructions into 197k system messages through hierarchical user value combinations. Using this dataset, we train a 7B LLM called Janus and test it on 921 prompts from 5 benchmarks (AlpacaEval 2.0, FLASK, Koala, MT-Bench, and Self-Instruct) by adding system messages that reflect unseen user values. JANUS achieves tie+win rate of 75.2%, 72.4%, and 66.4% against Mistral 7B Instruct v0.2, GPT-3.5 Turbo, and GPT-4, respectively. Unexpectedly, on three benchmarks focused on response helpfulness (AlpacaEval 2.0, MT-Bench, Arena Hard Auto v0.1), JANUS also outperforms LLaMA 3 8B Instruct by a +4.0%p, +0.1%p, +3.0%p margin, underscoring that training with a vast array of system messages could also enhance alignment to the general public’s preference as well. Our code, dataset, benchmark, and models are available at https://lklab.kaist.ac.kr/Janus/.

The efficacy of deep learning techniques is contingent upon access to large volumes of data (labeled or unlabeled). However, in practical domains such as medical applications, data availability is often limited. This presents a significant challenge: How can we effectively train deep neural networks on relatively small datasets while improving generalization? Recent works have explored evolutionary or iterative training paradigms, which reinitialize a subset of parameters to enhance generalization performance for small datasets. However, these methods typically rely on randomly selected parameter subsets and maintain fixed masks throughout training, potentially leading to suboptimal outcomes. Inspired by neurogenesis in the brain, we propose a novel iterative training framework, Dynamic Neural Regeneration (DNR), that employs a data-aware dynamic masking scheme to eliminate redundant connections by estimating their significance. This approach increases the model's capacity for further learning through random weight reinitialization. Experimental results demonstrate that our approach outperforms existing methods in accuracy and robustness, highlighting its potential for real-world applications where data collection is challenging.

Embeddings produced by pre-trained deep neural networks (DNNs) are widely used; however, their efficacy for downstream tasks can vary widely. We study the factors influencing transferability and out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which is closely related to intermediate neural collapse. This hypothesis suggests that deeper DNN layers compress representations and hinder OOD generalization. Contrary to earlier work, our experiments show this is not a universal phenomenon. We comprehensively investigate the impact of DNN architecture, training data, image resolution, and augmentations on transferability. We identify that training with high-resolution datasets containing many classes greatly reduces representation compression and improves transferability. Our results emphasize the danger of generalizing findings from toy datasets to broader contexts.

In this work, we introduce novel information-theoretic generalization bounds using the conditional $f$-information framework, an extension of the traditional conditional mutual information (MI) framework. We provide a generic approach to derive generalization bounds via $f$-information in the supersample setting, applicable to both bounded and unbounded loss functions. Unlike previous MI-based bounds, our proof strategy does not rely on upper bounding the cumulant-generating function (CGF) in the variational formula of MI. Instead, we set the CGF or its upper bound to zero by carefully selecting the measurable function invoked in the variational formula. Although some of our techniques are partially inspired by recent advances in the coin-betting framework (e.g., Jang et al. (2023)), our results are independent of any previous findings from regret guarantees of online gambling algorithms. Additionally, our newly derived MI-based bound recovers many previous results and improves our understanding of their potential limitations. Finally, we empirically compare various $f$-information measures for generalization, demonstrating the improvement of our new bounds over the previous bounds.

This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional robust regression problems. The number of features is comparable to the sample size and errors may be heavy-tailed. We introduce estimators that precisely track the generalization error of the iterates along the trajectory of the iterative algorithm. These estimators are provably consistent under suitable conditions. The results are illustrated through several examples, including Huber regression, pseudo-Huber regression, and their penalized variants with non-smooth regularizer. We provide explicit generalization error estimates for iterates generated from GD and SGD, or from proximal SGD in the presence of a non-smooth regularizer. The proposed risk estimates serve as effective proxies for the actual generalization error, allowing us to determine the optimal stopping iteration that minimizes the generalization error. Extensive simulations confirm the effectiveness of the proposed generalization error estimates.

We characterized the generalization capabilities of deep neural network encoding models when predicting neuronal responses from the visual cortex to flashed images. We collected MacaqueITBench, a large-scale dataset of neuronal population responses from the macaque inferior temporal (IT) cortex to over $300,000$ images, comprising $8,233$ unique natural images presented to seven monkeys over $109$ sessions. Using MacaqueITBench, we investigated the impact of distribution shifts on models predicting neuronal activity by dividing the images into Out-Of-Distribution (OOD) train and test splits. The OOD splits included variations in image contrast, hue, intensity, temperature, and saturation. Compared to the performance on in-distribution test images---the conventional way in which these models have been evaluated---models performed worse at predicting neuronal responses to out-of-distribution images, retaining as little as $20\\%$ of the performance on in-distribution test images. Additionally, the relative ranking of different models in terms of their ability to predict neuronal responses changed drastically across OOD shifts. The generalization performance under OOD shifts can be well accounted by a simple image similarity metric---the cosine distance between image representations extracted from a pre-trained object recognition model is a strong predictor of neuronal predictivity under different distribution shifts. The dataset of images, neuronal firing rate recordings, and computational benchmarks are hosted publicly at: https://github.com/Spandan-Madan/benchmarking_ood_generalization_visual_cortex.

This paper presents a comprehensive analysis of the growth rate of $H$-consistency bounds (and excess error bounds) for various surrogate losses used in classification. We prove a square-root growth rate near zero for smooth margin-based surrogate losses in binary classification, providing both upper and lower bounds under mild assumptions. This result also translates to excess error bounds. Our lower bound requires weaker conditions than those in previous work for excess error bounds, and our upper bound is entirely novel. Moreover, we extend this analysis to multi-class classification with a series of novel results, demonstrating a universal square-root growth rate for smooth *comp-sum* and *constrained losses*, covering common choices for training neural networks in multi-class classification. Given this universal rate, we turn to the question of choosing among different surrogate losses. We first examine how $H$-consistency bounds vary across surrogates based on the number of classes. Next, ignoring constants and focusing on behavior near zero, we identify *minimizability gaps* as the key differentiating factor in these bounds. Thus, we thoroughly analyze these gaps, to guide surrogate loss selection, covering: comparisons across different comp-sum losses, conditions where gaps become zero, and general conditions leading to small gaps. Additionally, we demonstrate the key role of minimizability gaps in comparing excess error bounds and $H$-consistency bounds.

In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored, particularly whether transformers can be trained to generalize to unseen examples in a prompt, which will require the model to acquire contextual knowledge of the prompt for generalization. This paper investigates the training dynamics of transformers by gradient descent through the lens of non-linear regression tasks. The contextual generalization here can be attained via learning the template function for each task in-context, where all template functions lie in a linear space with $m$ basis functions. We analyze the training dynamics of one-layer multi-head transformers to {in-contextly} predict unlabeled inputs given partially labeled prompts, where the labels contain Gaussian noise and the number of examples in each prompt are not sufficient to determine the template. Under mild assumptions, we show that the training loss for a one-layer multi-head transformer converges linearly to a global minimum. Moreover, the transformer effectively learns to perform ridge regression over the basis functions. To our knowledge, this study is the first provable demonstration that transformers can learn contextual (i.e., template) information to generalize to both unseen examples and tasks when prompts contain only a small number of query-answer pairs.

We study the implicit bias of optimization in robust empirical risk minimization (robust ERM) and its connection with robust generalization. In classification settings under adversarial perturbations with linear models, we study what type of regularization should ideally be applied for a given perturbation set to improve (robust) generalization. We then show that the implicit bias of optimization in robust ERM can significantly affect the robustness of the model and identify two ways this can happen; either through the optimization algorithm or the architecture. We verify our predictions in simulations with synthetic data and experimentally study the importance of implicit bias in robust ERM with deep neural networks.

This paper investigates the 3D domain generalization (3DDG) ability of large 3D models based on prevalent prompt learning. Recent works demonstrate the performances of 3D point cloud recognition can be boosted remarkably by parameter-efficient prompt tuning. However, we observe that the improvement on downstream tasks comes at the expense of a severe drop in 3D domain generalization. To resolve this challenge, we present a comprehensive regulation framework that allows the learnable prompts to actively interact with the well-learned general knowledge in large 3D models to maintain good generalization. Specifically, the proposed framework imposes multiple explicit constraints on the prompt learning trajectory by maximizing the mutual agreement between task-specific predictions and task-agnostic knowledge. We design the regulation framework as a plug-and-play module to embed into existing representative large 3D models. Surprisingly, our method not only realizes consistently increasing generalization ability but also enhances task-specific 3D recognition performances across various 3DDG benchmarks by a clear margin. Considering the lack of study and evaluation on 3DDG, we also create three new benchmarks, namely base-to-new, cross-dataset and few-shot generalization benchmarks, to enrich the field and inspire future research. Code and benchmarks are available at \url{https://github.com/auniquesun/Point-PRC}.

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurally stable forms. Although their asymptotic behaviors to maintain memory are categorically distinct, their finite-time behaviors are similar. We build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the existence of a persistent slow manifold that survives the seemingly destructive bifurcation, relating the flow within the manifold to the size of the perturbation. Moreover, this allows the bounding of the memory error of these approximations of continuous attractors. Finally, we train recurrent neural networks on analog memory tasks to support the appearance of these systems as solutions and their generalization capabilities. Therefore, we conclude that continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory.

Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional generalization is $\textit{hybrid}$ neurosymbolic techniques. However, these techniques run into the core issues that plague symbolic approaches to AI: scalability and flexibility. The reason for this failure is that at their core, hybrid neurosymbolic models perform symbolic computation and relegate the scalable and flexible neural computation to parameterizing a symbolic system. We investigate a $\textit{unified}$ neurosymbolic system where transformations in the network can be interpreted simultaneously as both symbolic and neural computation. We extend a unified neurosymbolic architecture called the Differentiable Tree Machine in two central ways. First, we significantly increase the model’s efficiency through the use of sparse vector representations of symbolic structures. Second, we enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems. The improved model retains its prior generalization capabilities and, since there is a fully neural path through the network, avoids the pitfalls of other neurosymbolic techniques that elevate symbolic computation over neural computation.

Label-specific representation learning (LSRL), i.e., constructing the representation with specific discriminative properties for each class label, is an effective strategy to improve the performance of multi-label learning. However, the generalization analysis of LSRL is still in its infancy. The existing theory bounds for multi-label learning, which preserve the coupling among different components, are invalid for LSRL. In an attempt to overcome this challenge and make up for the gap in the generalization theory of LSRL, we develop a novel vector-contraction inequality and derive the generalization bound for general function class of LSRL with a weaker dependency on the number of labels than the state of the art. In addition, we derive generalization bounds for typical LSRL methods, and these theoretical results reveal the impact of different label-specific representations on generalization analysis. The mild bounds without strong assumptions explain the good generalization ability of LSRL.

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number. In addition to the boost these embeddings provide on their own, we show that this fix enables architectural modifications such as input injection and recurrent layers to improve performance even further. With positions resolved, we can study the logical extrapolation ability of transformers. Can they solve arithmetic problems that are larger and more complex than those in their training data? We find that training on only 20 digit numbers with a single GPU for one day, we can reach state-of-the-art performance, achieving up to 99% accuracy on 100 digit addition problems. Finally, we show that these gains in numeracy also unlock improvements on other multi-step reasoning tasks including sorting and multiplication.

Out-of-Distribution (OOD) generalization in machine learning is a burgeoning area of study. Its primary goal is to enhance the adaptability and resilience of machine learning models when faced with new, unseen, and potentially adversarial data that significantly diverges from their original training datasets. In this paper, we investigate time series OOD generalization via pre-trained Large Language Models (LLMs). We first propose a novel \textbf{T}ri-level learning framework for \textbf{T}ime \textbf{S}eries \textbf{O}OD generalization, termed TTSO, which considers both sample-level and group-level uncertainties. This formula offers a fresh theoretic perspective for formulating and analyzing OOD generalization problem. In addition, we provide a theoretical analysis to justify this method is well motivated. We then develop a stratified localization algorithm tailored for this tri-level optimization problem, theoretically demonstrating the guaranteed convergence of the proposed algorithm. Our analysis also reveals that the iteration complexity to obtain an $\epsilon$-stationary point is bounded by O($\frac{1}{\epsilon^{2}}$). Extensive experiments on real-world datasets have been conducted to elucidate the effectiveness of the proposed method.