arXiv subjects

Qingyu Han

Publications and source records attributed to Qingyu Han.

4 recordsLinked to original sources

arXiv2026

Why Post-Norm Transformers Collapse: Attention Amplification and Gradient Repair Failure

Deep decoder-only Transformers often replace the original Post-Norm architecture with Pre-Norm variants because Post-Norm training is highly sensitive to warmup and learning rate under conventional initialization schemes. Although prior work has identified rank collapse and gradient vanishing as related symptoms, it remains poorly understood how causal attention creates high-similarity representations and why training dynamics fail to repair them. We give a two-stage analysis of Post-Norm rank collapse using token similarity as a scalar state variable. First, at initialization, causal attention acts approximately as a prefix-averaging operator that increases token similarity across depth, while the SwiGLU branch contributes only a smaller damping effect. Second, once training enters a high-similarity regime, growth of pre-normalization residual norms makes the RMSNorm backward factor contractive; under mild conditions, gradients to earlier layers decay geometrically. As a complementary result, we characterize the properties of a collapsed network: its best predictor is frequency distribution with relatively high loss floor, and gradients in collapsed layers vanish at frequency distribution. Experiments on 48-layer decoder-only Transformers trained on C4 dataset match the predicted initialization-time similarity growth and collapse-time gradient contraction, and show that collapsed runs stay near the predicted frequency loss. Together, these results distinguish the forward similarity amplification and backward repair incapacity in Post-Norm collapse, while also characterizing the behavior of collapsed networks.

cs.LG↗

arXiv2025

Feature Augmentation of GNNs for ILPs: Local Uniqueness Suffices

Integer Linear Programs (ILPs) are central to real-world optimizations but notoriously difficult to solve. Learning to Optimize (L2O) has emerged as a promising paradigm, with Graph Neural Networks (GNNs) serving as the standard backbone. However, standard anonymous GNNs are limited in expressiveness for ILPs, and the common enhancement of augmenting nodes with globally unique identifiers (UIDs) typically introduces spurious correlations that severely harm generalization. To address this tradeoff, we propose a parsimonious Local-UID scheme based on d-hop uniqueness coloring, which ensures identifiers are unique only within each node's d-hop neighborhood. Building on this scheme, we introduce ColorGNN, which incorporates color information via color-conditioned embeddings, and ColorUID, a lightweight feature-level variant. We prove that for d-layer networks, Local-UIDs achieve the expressive power of Global-UIDs while offering stronger generalization. Extensive experiments show that our approach yields substantial and robust gains across ILP benchmarks.

cs.LG↗

arXiv2024

SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods -- achieving $50.3\%$, $66.5\%$, and $45.4\%$ average improvements, respectively.

math.OC↗

arXiv2023

A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are capable of capturing common patterns across these MILP instances. In this work, we combine ML with optimization and propose a novel predict-and-search framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize graph neural networks to predict the marginal probability of each variable, and then search for the best feasible solution within a properly defined ball around the predicted solution. We conduct extensive experiments on public datasets, and computational results demonstrate that our proposed framework achieves 51.1% and 9.9% performance improvements to MILP solvers SCIP and Gurobi on primal gaps, respectively.

math.OC↗