arXiv subjects

Jixian Zhou

Publications and source records attributed to Jixian Zhou.

4 recordsLinked to original sources

arXiv2026

Dispelling the Curse of Singularities in Neural Network Optimizations

This work investigates the optimization instability of deep neural networks from a less-explored yet insightful perspective: the emergence and amplification of singularities in the parametric space. Our analysis reveals that parametric singularities inevitably grow with gradient updates and further intensify alignment with representations, leading to increased singularities in the representation space. We show that the gradient Frobenius norms are bounded by the top singular values of the weight matrices, and as training progresses, the mutually reinforcing growth of weight and representation singularities, termed the curse of singularities, relaxes these bounds, escalating the risk of sharp loss explosions. To counter this, we propose Parametric Singularity Smoothing (PSS), a lightweight, flexible, and effective method for smoothing the singular spectra of weight matrices. Extensive experiments across diverse datasets, architectures, and optimizers demonstrate that PSS mitigates instability, restores trainability even after failure, and improves both training efficiency and generalization.

cs.LG↗

arXiv2026

SD-MoE: Spectral Decomposition for Effective Expert Specialization

Mixture-of-Experts (MoE) architectures scale Large Language Models via expert specialization induced by conditional computation. In practice, however, expert specialization often fails: some experts become functionally similar, while others functioning as de facto shared experts, limiting the effective capacity and model performance. In this work, we analysis from a spectral perspective on parameter and gradient spaces, uncover that (1) experts share highly overlapping dominant spectral components in their parameters, (2) dominant gradient subspaces are strongly aligned across experts, driven by ubiquitous low-rank structure in human corpus, and (3) gating mechanisms preferentially route inputs along these dominant directions, further limiting specialization. To address this, we propose Spectral-Decoupled MoE (SD-MoE), which decomposes both parameter and gradient in the spectral space. SD-MoE improves performance across downstream tasks, enables effective expert specialization, incurring minimal additional computation, and can be seamlessly integrated into a wide range of existing MoE architectures, including Qwen and DeepSeek.

cs.LG↗

arXiv2026

Multi-Head Attention as a Source of Catastrophic Forgetting in MoE Transformers

Mixture-of-Experts (MoE) architectures are often considered a natural fit for continual learning because sparse routing should localize updates and reduce interference, yet MoE Transformers still forget substantially even with sparse, well-balanced expert utilization. We attribute this gap to a pre-routing bottleneck: multi-head attention concatenates head-specific signals into a single post-attention router input, forcing routing to act on co-occurring feature compositions rather than separable head channels. We show that this router input simultaneously encodes multiple separately decodable semantic and structural factors with uneven head support, and that different feature compositions induce weakly aligned parameter-gradient directions; as a result, routing maps many distinct compositions to the same route. We quantify this collision effect via a route-wise effective composition number $N_{eff}$ and find that higher $N_{eff}$ is associated with larger old-task loss increases after continual training. Motivated by these findings, we propose MH-MoE, which performs head-wise routing over sub-representations to increase routing granularity and reduce composition collisions. On TRACE with Qwen3-0.6B/8B, MH-MoE effectively mitigates forgetting, reducing BWT on Qwen3-0.6B from 11.2% (LoRAMoE) to 4.5%.

cs.LG↗

arXiv2025

Metis: Training LLMs with FP4 Quantization

This work identifies anisotropy in the singular value spectra of parameters, activations, and gradients as the fundamental barrier to low-bit training of large language models (LLMs). These spectra are dominated by a small fraction of large singular values, inducing wide numerical ranges that cause quantization bias and severe spectral distortion, ultimately degrading training performance. This work presents Metis, a spectral-domain quantization framework that partitions anisotropic spectra into narrower sub-distributions for independent quantization, thereby reducing errors and preserving spectral structure. To minimize overhead, Metis leverages two key properties of the dominant spectral subspace: preservation via sparsely random sampling and preservation via random projection, reducing decomposition cost to a negligible level. On LLaMA-3 8B trained with 100B tokens, Metis enables robust W4A4G4 training with FP4 quantization of weights, activations, and gradients, yielding only a 0.4% training loss gap and a 0.1% degradation in downstream accuracy relative to BF16. Beyond matching BF16 fidelity, Metis also surpasses our implementation of Nvidia's recently announced (yet to be publicly released) FP4 recipe, consistently achieving lower loss and higher downstream accuracy while incurring significantly lower computational overhead. The code implementation for Metis is available at: https://anonymous.4open.science/r/Metis-quantization-644B.

cs.LG↗