Understanding Simplicity Bias towards Compositional Mappings via Learning Dynamics

Obtaining compositional mappings is important for the model to generalize well compositionally. To better understand when and how to encourage the model to learn such mappings, we study their uniqueness through different perspectives. Specifically, we first show that the compositional mappings are the simplest bijections through the lens of coding length (i.e., an upper bound of their Kolmogorov complexity). This property explains why models having such mappings can generalize well. We further show that the simplicity bias is usually an intrinsic property of neural network training via gradient descent. That partially explains why some models spontaneously generalize well when they are trained appropriately.

Learning Deep Kernels for Non-Parametric Independence Testing

The Hilbert-Schmidt Independence Criterion (HSIC) is a powerful tool for nonparametric detection of dependence between random variables. It crucially depends, however, on the selection of reasonable kernels; commonly-used choices like the Gaussian kernel, or the kernel that yields the distance covariance, are sufficient only for amply sized samples from data distributions with relatively simple forms of dependence. We propose a scheme for selecting the kernels used in an HSIC-based independence test, based on maximizing an estimate of the asymptotic test power. We prove that maximizing this estimate indeed approximately maximizes the true power of the test, and demonstrate that our learned kernels can identify forms of structured dependence between random variables in various experiments.

Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel regime'' approximately holds, no permutation-equivariant model can achieve small population error on modular addition unless it sees at least a constant fraction of all possible data points. Eventually, however, models escape the kernel regime. We show that two-layer quadratic networks that achieve zero training loss with bounded $\ell_{\infty}$ norm generalize well with substantially fewer training points, and further show such networks exist and can be found by gradient descent with small $\ell_{\infty}$ regularization. We further provide empirical evidence that these networks as well as simple Transformers, leave the kernel regime only after initially overfitting. Taken together, our results strongly support the case for grokking as a consequence of the transition from kernel-like behavior to limiting behavior of gradient descent on deep networks.

Generalized Coverage for More Robust Low-Budget Active Learning

The ProbCover method of Yehuda et al. is a well-motivated algorithm for active learning in low-budget regimes, which attempts to "cover" the data distribution with balls of a given radius at selected data points. We demonstrate, however, that the performance of this algorithm is extremely sensitive to the choice of this radius hyper-parameter, and that tuning it is quite difficult, with the original heuristic frequently failing. We thus introduce (and theoretically motivate) a generalized notion of "coverage," including ProbCover's objective as a special case, but also allowing smoother notions that are far more robust to hyper-parameter choice. We propose an efficient greedy method to optimize this coverage, generalizing ProbCover's algorithm; due to its close connection to kernel herding, we call it "MaxHerding." The objective can also be optimized non-greedily through a variant of $k$-medoids, clarifying the relationship to other low-budget active learning methods. In comprehensive experiments, MaxHerding surpasses existing active learning methods across multiple low-budget image classification benchmarks, and does so with less computational cost than most competitive methods.

Learning Dynamics of LLM Finetuning

Learning dynamics, which describes how the learning of specific training examples influences the model's prediction of other examples, give us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during finetuning, by analyzing the step-wise decomposition and accumulated influence among different responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. The analysis not only explains where the benefits of these methods come from but also inspires a simple, effective method to further improve the alignment performance. Code for experiments is available at https://github.com/Joshua-Ren/Learning_dynamics_LLM.

Language Model Evolution: An Iterated Learning Perspective

With the widespread adoption of Large Language Models (LLMs), the prevalence of iterative interactions among these models is anticipated to increase. Notably, recent advancements in multi-round self-improving methods allow LLMs to generate new examples for training subsequent models. At the same time, multi-agent LLM systems, involving automated interactions among agents, are also increasing in prominence. Thus, in both short and long terms, LLMs may actively engage in an evolutionary process. We draw parallels between the behavior of LLMs and the evolution of human culture, as the latter has been extensively studied by cognitive scientists for decades. Our approach involves leveraging Iterated Learning (IL), a Bayesian framework that elucidates how subtle biases are magnified during human cultural evolution, to explain some behaviors of LLMs. This paper outlines key characteristics of agents' behavior in the Bayesian-IL framework, including predictions that are supported by experimental verification with various LLMs. This theoretical framework could help to more effectively predict and guide the evolution of LLMs in desired directions.

Practical Kernel Tests of Conditional Independence

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing, absent in tests of unconditional independence, is to obtain the correct test level (the specified upper bound on the rate of false positives), while still attaining competitive test power. Excess false positives arise due to bias in the test statistic, which is obtained using nonparametric kernel ridge regression. We propose three methods for bias control to correct the test level, based on data splitting, auxiliary data, and (where possible) simpler function classes. We show these combined strategies are effective both for synthetic and real-world data.

AdaFlood: Adaptive Flood Regularization

Although neural networks are conventionally optimized towards zero training loss, it has been recently learned that targeting a non-zero training loss threshold, referred to as a flood level, often enables better test time generalization. Current approaches, however, apply the same constant flood level to all training samples, which inherently assumes all the samples have the same difficulty. We present AdaFlood, a novel flood regularization method that adapts the flood level of each training sample according to the difficulty of the sample. Intuitively, since training samples are not equal in difficulty, the target training loss should be conditioned on the instance. Experiments on datasets covering four diverse input modalities - text, images, asynchronous event sequences, and tabular - demonstrate the versatility of AdaFlood across data domains and noise levels.

Exploring Active Learning in Meta-Learning: Enhancing Context Set Labeling

Most meta-learning methods assume that the (very small) context set used to establish a new task at test time is passively provided. In some settings, however, it is feasible to actively select which points to label; the potential gain from a careful choice is substantial, but the setting requires major differences from typical active learning setups. We clarify the ways in which active meta-learning can be used to label a context set, depending on which parts of the meta-learning process use active learning. Within this framework, we propose a natural algorithm based on fitting Gaussian mixtures for selecting which points to label; though simple, the algorithm also has theoretical motivation. The proposed algorithm outperforms state-of-the-art active learning methods when used with various meta-learning algorithms across several benchmark datasets.

Improving Compositional Generalization Using Iterated Learning and Simplicial Embeddings

Compositional generalization, the ability of an agent to generalize to unseen combinations of latent factors, is easy for humans but hard for deep neural networks. A line of research in cognitive science has hypothesized a process, ``iterated learning,'' to help explain how human language developed this ability; the theory rests on simultaneous pressures towards compressibility (when an ignorant agent learns from an informed one) and expressivity (when it uses the representation for downstream tasks). Inspired by this process, we propose to improve the compositional generalization of deep networks by using iterated learning on models with simplicial embeddings, which can approximately discretize representations. This approach is further motivated by an analysis of compositionality based on Kolmogorov complexity. We show that this combination of changes improves compositional generalization over other approaches, demonstrating these improvements both on vision tasks with well-understood latent factors and on real molecular graph prediction tasks where the latent structure is unknown.