Xiaowen Dong
Publications
A Mechanistic Analysis of Looped Reasoning Language Models
Reasoning has become a central capability in large language models. Recent research has shown that reasoning performance can be improved by looping an LLM's layers in the latent dimension, resulting in looped reasoning language models. Despite promising results, few works have investigated how their internal dynamics differ from those of standard feedforward models. In this paper, we conduct a mechanistic analysis of the latent states in looped language models, focusing in particular on how the stages of inference observed in feedforward models compare to those observed in looped ones. To this end, we analyze cyclic recurrence and show that for many of the studied models each layer in the cycle converges to a distinct fixed point; consequently, the recurrent block follows a consistent cyclic trajectory in the latent space. We provide evidence that as these fixed points are reached, attention-head behavior stabilizes, leading to constant behavior across recurrences. Empirically, we discover that recurrent blocks learn stages of inference that closely mirror those of feedforward models, repeating these stages in depth with each iteration. We study how recurrent block size, input injection, and normalization influence the emergence and stability of these cyclic fixed points. We believe these findings help translate mechanistic insights into practical guidance for architectural design.
k-Maximum Inner Product Attention for Graph Transformers and the Expressive Power of GraphGPS The Expressive Power of GraphGPS
Graph transformers have shown promise in overcoming limitations of traditional graph neural networks, such as oversquashing and difficulties in modelling long-range dependencies. However, their application to large-scale graphs is hindered by the quadratic memory and computational complexity of the all-to-all attention mechanism. Although alternatives such as linearized attention and restricted attention patterns have been proposed, these often degrade performance or limit expressive power. To better balance efficiency and effectiveness, we introduce k-Maximum Inner Product (k-MIP) attention for graph transformers. k-MIP attention selects the most relevant key nodes per query via a top-k operation, yielding a sparse yet flexible attention pattern. Combined with an attention score computation based on symbolic matrices, this results in linear memory complexity and practical speedups of up to an order of magnitude compared to all-to-all attention, enabling the processing of graphs with over 500k nodes on a single A100 GPU. We provide a theoretical analysis of expressive power, showing that k-MIP attention does not compromise the expressiveness of graph transformers: specifically, we prove that k-MIP transformers can approximate any full-attention transformer to arbitrary precision. In addition, we analyze the expressive power of the GraphGPS framework, in which we integrate our attention mechanism, and establish an upper bound on its graph distinguishing capability in terms of the S-SEG-WL test. Finally, we validate our approach on the Long Range Graph Benchmark, the City-Networks benchmark, and two custom large-scale inductive point cloud datasets, consistently ranking among the top-performing scalable graph transformers.