Huaqing Zhang

Huaqing Zhang, Lesi Chen, Jing Xu et al.

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose a novel method by reformulating them into functionally constrained problems. Our method achieves near-optimal rates for both smooth and nonsmooth problems. To the best of our knowledge, this is the first near-optimal algorithm that works under standard assumptions of smoothness or Lipschitz continuity for the objective functions.

Amirhesam Abedsoltan, Huaqing Zhang, Kaiyue Wen et al.

Large language models (LLMs) exhibit remarkable task generalization, solving tasks they were never explicitly trained on with only a few demonstrations. This raises a fundamental question: When can learning from a small set of tasks generalize to a large task family? In this paper, we investigate task generalization through the lens of autoregressive compositional structure, where each task is a composition of $T$ operations, and each operation is among a finite family of $D$ subtasks. This yields a total class of size $D^T$. We first show that generalization to all $D^T$ tasks is theoretically achievable by training on only $\widetilde{O}(D)$ tasks. Empirically, we demonstrate that Transformers achieve such exponential task generalization on sparse parity functions via In-context Learning (ICL) and chain-of-thought (CoT) reasoning. We further show generalization in arithmetic and translation, beyond parity functions.

Jingchu Gai, Guanning Zeng, Huaqing Zhang et al.

It is widely recognized that reinforcement learning (RL) fine-tuning of large language models often leads to diversity collapse, where outputs lack variety. Prior work has proposed a range of heuristics to counteract this effect, but these methods are ad hoc: they frequently trade off correctness for diversity, their effectiveness varies across tasks, and in some cases they even contradict one another. In this work, we place these observations on a rigorous foundation. We first provide a formal proof of why RL fine-tuning exhibits diversity collapse via a selection and reinforcement bias. Next, we make a key observation that any reward modification to address diversity collapse only needs to be applied on the correct trajectories. Building directly on this analysis, we introduce a principled method -- differential smoothing -- that provably improves both correctness and diversity, outperforming vanilla RL as well as widely used entropy-based heuristics. Our theory precisely characterizes when existing heuristics help and why they fail, while showing that differential smoothing is universally superior. Extensive experiments with models from 1B to 7B parameters, across domains including CountDown and real-world mathematical reasoning, demonstrate consistent gains. Differential smoothing improves both Pass@1 and Pass@k, with up to 6.7% improvements on AIME24 dataset.

Dae Hoon Park, Chiu Man Ho, Yi Chang et al.

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their simplicity and effectiveness. However, we observe that imposing strong L1 or L2 regularization with stochastic gradient descent on deep neural networks easily fails, which limits the generalization ability of the underlying neural networks. To understand this phenomenon, we first investigate how and why learning fails when strong regularization is imposed on deep neural networks. We then propose a novel method, gradient-coherent strong regularization, which imposes regularization only when the gradients are kept coherent in the presence of strong regularization. Experiments are performed with multiple deep architectures on three benchmark data sets for image recognition. Experimental results show that our proposed approach indeed endures strong regularization and significantly improves both accuracy and compression (up to 9.9x), which could not be achieved otherwise.