Peifeng Gao

Peifeng Gao, Qianqian Xu, Peisong Wen et al.

In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally separates features of every two classes on a sphere and does not require a larger feature dimension than the number of classes. Out of curiosity about the symmetry of Grassmannian Frame, we conduct experiments to explore if models with different Grassmannian Frames have different performance. As a result, we discover the Symmetric Generalization phenomenon. We provide a theorem to explain Symmetric Generalization of permutation. However, the question of why different directions of features can lead to such different generalization is still open for future investigation.

Peifeng Gao, Qianqian Xu, Yibo Yang et al.

Neural Collapse (NC) is a well-known phenomenon of deep neural networks in the terminal phase of training (TPT). It is characterized by the collapse of features and classifier into a symmetrical structure, known as simplex equiangular tight frame (ETF). While there have been extensive studies on optimization characteristics showing the global optimality of neural collapse, little research has been done on the generalization behaviors during the occurrence of NC. Particularly, the important phenomenon of generalization improvement during TPT has been remaining in an empirical observation and lacking rigorous theoretical explanation. In this paper, we establish the connection between the minimization of CE and a multi-class SVM during TPT, and then derive a multi-class margin generalization bound, which provides a theoretical explanation for why continuing training can still lead to accuracy improvement on test set, even after the train accuracy has reached 100%. Additionally, our further theoretical results indicate that different alignment between labels and features in a simplex ETF can result in varying degrees of generalization improvement, despite all models reaching NC and demonstrating similar optimization performance on train set. We refer to this newly discovered property as "non-conservative generalization". In experiments, we also provide empirical observations to verify the indications suggested by our theoretical results.

Junnan Liu, Xinyan Liu, Peifeng Gao et al.

In long-context decoding for LLMs and LMMs, attention becomes increasingly memory-bound because each decoding step must load a large amount of KV-cache data from GPU memory. Existing acceleration strategies often trade efficiency for accuracy by relying on heuristic pruning that may discard useful information. At a deeper level, they also tend to indiscriminately preserve all high-scoring tokens, treat early tokens as indispensable anchors, or rely on heuristic head routing, reflecting an insufficient mechanistic understanding of the attention sink phenomenon. In this paper, we show that the attention sink phenomenon corresponds to a stable, reachable, and error-controllable fixed point constructed during training. Based on this insight, we propose SinkRouter, a training-free selective routing framework that detects the sink signal and skips computations that would otherwise produce near-zero output. To translate this mechanism into real-world acceleration, we develop a hardware-aware Triton kernel with block-level branching and Split-K parallelism. We conduct extensive evaluations on a diverse suite of long-context benchmarks, including LongBench, InfiniteBench, CVBench, MileBench, and MMVP, using both text-only and multimodal backbones such as Llama-3.1-8B, Llama-3.1-70B, Yi-9B-200K, LLaVA-1.5-7B, and LLaVA-1.5-13B. Across these settings, SinkRouter consistently improves decoding efficiency while maintaining competitive accuracy, and reaches 2.03x speedup with a 512K context.

Peifeng Gao, Wenyi Fang, Yang Zheng et al.

Delayed loss spikes have been reported in neural-network training, but existing theory mainly explains earlier non-monotone behavior caused by overly large fixed learning rates. We study one stylized hypothesis: normalization can postpone instability by gradually increasing the effective learning rate during otherwise stable descent. To test this hypothesis at theorem level, we analyze batch-normalized linear models. Our flagship result concerns whitened square-loss linear regression, where we derive explicit no-rising-edge and delayed-onset conditions, bound the waiting time to directional onset, and show that the rising edge self-stabilizes within finitely many iterations. Combined with a square-loss decomposition, this yields a concrete delayed-spike mechanism in the whitened regime. For logistic regression, under highly restrictive active-margin assumptions, we prove only a supporting finite-horizon directional precursor in a knife-edge regime, with an optional appendix-only loss lower bound under an extra non-degeneracy condition. The paper should therefore be read as a stylized mechanism study rather than a general explanation of neural-network loss spikes. Within that scope, the results isolate one concrete delayed-instability pathway induced by batch normalization.

Chenyang Zhang, Peifeng Gao, Difan Zou et al.

Modern neural networks are usually highly over-parameterized. Behind the wide usage of over-parameterized networks is the belief that, if the data are simple, then the trained network will be automatically equivalent to a simple predictor. Following this intuition, many existing works have studied different notions of "ranks" of neural networks and their relation to the rank of data. In this work, we study the rank of convolutional neural networks (CNNs) trained by gradient descent, with a specific focus on the robustness of the rank to image background noises. Specifically, we point out that, when adding background noises to images, the rank of the CNN trained with gradient descent is affected far less compared with the rank of the data. We support our claim with a theoretical case study, where we consider a particular data model to characterize low-rank clean images with added background noises. We prove that CNNs trained by gradient descent can learn the intrinsic dimension of clean images, despite the presence of relatively large background noises. We also conduct experiments on synthetic and real datasets to further validate our claim.