The Implicit Bias of Steepest Descent with Mini-batch Stochastic Gradient

A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries. In this work, we study the implicit bias of mini-batch stochastic steepest descent in multi-class classification, characterizing how batch size, momentum, and variance reduction shape the limiting max-margin behavior and convergence rates under general entry-wise and Schatten-$p$ norms. We show that without momentum, convergence only occurs with large batches, yielding a batch-dependent margin gap but the full-batch convergence rate. In contrast, momentum enables small-batch convergence through a batch-momentum trade-off, though it slows convergence. This approach provides fully explicit, dimension-free rates that improve upon prior results. Moreover, we prove that variance reduction can recover the exact full-batch implicit bias for any batch size, albeit at a slower convergence rate. Finally, we further investigate the batch-size-one steepest descent without momentum, and reveal its convergence to a fundamentally different bias via a concrete data example, which reveals a key limitation of purely stochastic updates. Overall, our unified analysis clarifies when stochastic optimization aligns with full-batch behavior, and paves the way for perform deeper explorations of the training behavior of stochastic gradient steepest descent algorithms.

Long-range Modeling and Processing of Multimodal Event Sequences

Temporal point processes (TPPs) have emerged as powerful tools for modeling asynchronous event sequences. While recent advances have extended TPPs to handle textual information, existing approaches are limited in their ability to generate rich, multimodal content and reason about event dynamics. A key challenge is that incorporating multimodal data dramatically increases sequence length, hindering the ability of attention-based models to generate coherent, long-form textual descriptions that require long-range understanding. In this paper, we propose a novel framework that extends LLM-based TPPs to the visual modality, positioning text generation as a core capability alongside time and type prediction. Our approach addresses the long-context problem through an adaptive sequence compression mechanism based on temporal similarity, which reduces sequence length while preserving essential patterns. We employ a two-stage paradigm of pre-training on compressed sequences followed by supervised fine-tuning for downstream tasks. Extensive experiments, including on the challenging DanmakuTPP-QA benchmark, demonstrate that our method outperforms state-of-the-art baselines in both predictive accuracy and the quality of its generated textual analyses.

DanmakuTPPBench: A Multi-modal Benchmark for Temporal Point Process Modeling and Understanding

We introduce DanmakuTPPBench, a comprehensive benchmark designed to advance multi-modal Temporal Point Process (TPP) modeling in the era of Large Language Models (LLMs). While TPPs have been widely studied for modeling temporal event sequences, existing datasets are predominantly unimodal, hindering progress in models that require joint reasoning over temporal, textual, and visual information. To address this gap, DanmakuTPPBench comprises two complementary components: (1) DanmakuTPP-Events, a novel dataset derived from the Bilibili video platform, where user-generated bullet comments (Danmaku) naturally form multi-modal events annotated with precise timestamps, rich textual content, and corresponding video frames; (2) DanmakuTPP-QA, a challenging question-answering dataset constructed via a novel multi-agent pipeline powered by state-of-the-art LLMs and multi-modal LLMs (MLLMs), targeting complex temporal-textual-visual reasoning. We conduct extensive evaluations using both classical TPP models and recent MLLMs, revealing significant performance gaps and limitations in current methods' ability to model multi-modal event dynamics. Our benchmark establishes strong baselines and calls for further integration of TPP modeling into the multi-modal language modeling landscape. The code and dataset have been released at https://github.com/FRENKIE-CHIANG/DanmakuTPPBench