arXiv subjects

Yilong Song

Publications and source records attributed to Yilong Song.

4 recordsLinked to original sources

arXiv2025

Decentralized Optimization over Time-Varying Row-Stochastic Digraphs

Decentralized optimization over directed graphs is essential for applications such as robotic swarms, sensor networks, and distributed learning. In many practical scenarios, the underlying network takes the form of a Time-Varying Broadcast Network (TVBN), where only row-stochastic mixing matrices can be constructed due to the unavailability of out-degree information. Achieving exact convergence for decentralized optimization over TVBNs has remained a long-standing open problem, as the limiting distribution of time-varying row-stochastic mixing matrices depends on unpredictable future graph realizations, rendering standard bias-correction techniques infeasible. This paper develops the first decentralized optimization algorithm that achieves exact convergence using only time-varying row-stochastic matrices. We first propose PULM (Pull-with-Memory), a gossip protocol that achieves average consensus with exponential convergence by alternating between row-stochastic mixing and local adjustment steps. Building on PULM, we develop PULM-DGD, which converges to a stationary solution at a rate of $\mathcal{O}(\ln(T)/T)$ for smooth nonconvex objectives, where $T$ denotes the communication round. Our results significantly broaden the applicability of decentralized optimization to highly dynamic communication environments.

math.OC↗

arXiv2025

Hierarchical Frequency Tagging Probe (HFTP): A Unified Approach to Investigate Syntactic Structure Representations in Large Language Models and the Human Brain

Large Language Models (LLMs) demonstrate human-level or even superior language abilities, effectively modeling syntactic structures, yet the specific computational modules responsible remain unclear. A key question is whether LLM behavioral capabilities stem from mechanisms akin to those in the human brain. To address these questions, we introduce the Hierarchical Frequency Tagging Probe (HFTP), a tool that utilizes frequency-domain analysis to identify neuron-wise components of LLMs (e.g., individual Multilayer Perceptron (MLP) neurons) and cortical regions (via intracranial recordings) encoding syntactic structures. Our results show that models such as GPT-2, Gemma, Gemma 2, Llama 2, Llama 3.1, and GLM-4 process syntax in analogous layers, while the human brain relies on distinct cortical regions for different syntactic levels. Representational similarity analysis reveals a stronger alignment between LLM representations and the left hemisphere of the brain (dominant in language processing). Notably, upgraded models exhibit divergent trends: Gemma 2 shows greater brain similarity than Gemma, while Llama 3.1 shows less alignment with the brain compared to Llama 2. These findings offer new insights into the interpretability of LLM behavioral improvements, raising questions about whether these advancements are driven by human-like or non-human-like mechanisms, and establish HFTP as a valuable tool bridging computational linguistics and cognitive neuroscience. This project is available at https://github.com/LilTiger/HFTP.

cs.CL↗

arXiv2025

Distributed Retraction-Free and Communication-Efficient Optimization on the Stiefel Manifold

Optimization problems on the Stiefel manifold, ranging from principal component analysis to enhancing neural network robustness, are ubiquitous in machine learning. The Landing algorithm avoids computationally expensive retraction operations on manifolds, making it highly competitive for large-scale problems. This paper extends this method to distributed settings, introducing *EF-Landing*, the first retraction-free and communication-efficient algorithm for distributed stochastic optimization on the Stiefel manifold. By incorporating communication compression and error feedback, EF-Landing ensures convergence and constraint feasibility while significantly reducing communication overhead. We provide sharp convergence guarantees, demonstrating that EF-Landing achieves the same asymptotic linear speedup convergence rate as existing methods without communication compression. Furthermore, our analysis is highly versatile, applying to both deterministic and stochastic settings and encompassing algorithms based on gradient descent or momentum-based gradient descent. We also generalize EF-Landing to operate on block-wise Stiefel manifolds, enabling greater flexibility for structured constraints. Extensive numerical experiments validate our theoretical results.

math.OC↗

arXiv2025

Imitation Learning with Precisely Labeled Human Demonstrations

Within the imitation learning paradigm, training generalist robots requires large-scale datasets obtainable only through diverse curation. Due to the relative ease to collect, human demonstrations constitute a valuable addition when incorporated appropriately. However, existing methods utilizing human demonstrations face challenges in inferring precise actions, ameliorating embodiment gaps, and fusing with frontier generalist robot training pipelines. In this work, building on prior studies that demonstrate the viability of using hand-held grippers for efficient data collection, we leverage the user's control over the gripper's appearance--specifically by assigning it a unique, easily segmentable color--to enable simple and reliable application of the RANSAC and ICP registration method for precise end-effector pose estimation. We show in simulation that precisely labeled human demonstrations on their own allow policies to reach on average 88.1% of the performance of using robot demonstrations, and boost policy performance when combined with robot demonstrations, despite the inherent embodiment gap.

cs.RO↗