ICML 2023 论文列表

Federated Learning (FL) is a collaborative machine learning paradigm for data privacy preservation. Recently, a knowledge distillation (KD) based information sharing approach in FL, which conducts ensemble distillation on an unlabeled public dataset, has been proposed. However, despite its experimental success and usefulness, the theoretical analysis of the KD based approach has not been satisfactorily conducted. In this work, we build a theoretical foundation of the ensemble distillation framework in federated learning from the perspective of kernel ridge regression (KRR). In this end, we propose a KD based FL algorithm for KRR models which is related with some existing KD based FL algorithms, and analyze our algorithm theoretically. We show that our algorithm makes local prediction models as much powerful as the centralized KRR model (which is a KRR model trained by all of local datasets) in terms of the convergence rate of the generalization error if the unlabeled public dataset is sufficiently large. We also provide experimental results to verify our theoretical results on ensemble distillation in federated learning.

Self-distillation (SD) is the process of first training a "teacher" model and then using its predictions to train a "student" model that has the *same* architecture. Specifically, the student's loss is $\big(\xi*\ell(\text{teacher's predictions}, \text{ student's predictions}) + (1-\xi)*\ell(\text{given labels}, \text{ student's predictions})\big)$, where $\ell$ is the loss function and $\xi$ is some parameter $\in [0,1]$. SD has been empirically observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with *noisy labels*. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of $\xi$ that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that $\xi > 1$ works better than $\xi \leq 1$ even with the cross-entropy loss for several classification datasets when 50% or 30% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher (w.r.t. accuracy). To our knowledge, this is the first result of its kind for the cross-entropy loss.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks---but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn ``semantic structure'', understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of mathematical analysis and experiments on Wikipedia data and synthetic data modeled by Latent Dirichlet Allocation (LDA), that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics and follows an incremental learning procedure: GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the *under-parameterized* regime. Finally, we conduct numerical experiments to confirm our theoretical findings.