Kunlin Lyu | Searcharxiv

arXiv2026

MOON: Multi-Objective OrthoNormalized Updates for Multitask Learning

Multi-objective optimization (MOO) has demonstrated significant success in multi-task learning by mitigating task conflicts through gradient manipulation. However, most existing methods flatten model parameters into vectors and perform gradient manipulation under Euclidean geometry, thereby overlooking the matrix structure prevalent in modern architectures such as Transformers. In this paper, we show that gradient manipulation in Euclidean space does not generally yield the steepest descent direction under matrix geometry, potentially limiting optimization efficiency. Drawing from the theory of steepest descent for matrix-valued parameters, we propose MOON (Multi-Objective OrthoNormalized Updates), which performs gradient manipulation under spectral--nuclear norm geometry and uses the orthonormalized manipulated gradient for parameter updates. Theoretically, for smooth non-convex objectives, we establish convergence of the averaged Pareto-stationarity measure at rates of $\mathcal{O}(T^{-1/2})$ in the deterministic setting and $\mathcal{O}(T^{-1/4})$ under stochastic gradients. Empirical results across various benchmarks show that MOON consistently improves both optimization efficiency and final multi-task performance. Our code is available at https://github.com/KunlinLyu/MOON.

cs.LG↗

arXiv2025

The Achilles' Heel of LLMs: How Altering a Handful of Neurons Can Cripple Language Abilities

Large Language Models (LLMs) have become foundational tools in natural language processing, powering a wide range of applications and research. Many studies have shown that LLMs share significant similarities with the human brain. Recent neuroscience research has found that a small subset of biological neurons in the human brain are crucial for core cognitive functions, which raises a fundamental question: do LLMs also contain a small subset of critical neurons? In this paper, we investigate this question by proposing a Perturbation-based Causal Identification of Critical Neurons method to systematically locate such critical neurons in LLMs. Our findings reveal three key insights: (1) LLMs contain ultra-sparse critical neuron sets. Disrupting these critical neurons can cause a 72B-parameter model with over 1.1 billion neurons to completely collapse, with perplexity increasing by up to 20 orders of magnitude; (2) These critical neurons are not uniformly distributed, but tend to concentrate in the outer layers, particularly within the MLP down\_proj components; (3) Performance degradation exhibits sharp phase transitions, rather than a gradual decline, when these critical neurons are disrupted. Through comprehensive experiments across diverse model architectures and scales, we provide deeper analysis of these phenomena and their implications for LLM robustness and interpretability. These findings can offer guidance for developing more robust model architectures and improving deployment security in safety-critical applications. Our code is available at https://github.com/qqqqqqqzx/The-Achilles-Heel-of-LLMs.

cs.AI↗