Cross-Modal Memory Compression for Efficient Multi-Agent Debate

Multi-agent debate can improve reasoning quality and reduce hallucinations, but it incurs rapidly growing context as debate rounds and agent count increase. Retaining full textual histories leads to token usage that can exceed context limits and often requires repeated summarization, adding overhead and compounding information loss. We introduce DebateOCR, a cross-modal compression framework that replaces long textual debate traces with compact image representations, which are then consumed through a dedicated vision encoder to condition subsequent rounds. This design compresses histories that commonly span tens to hundreds of thousands of tokens, cutting input tokens by more than 92% and yielding substantially lower compute cost and faster inference across multiple benchmarks. We further provide a theoretical perspective showing that diversity across agents supports recovery of omitted information: although any single compressed history may discard details, aggregating multiple agents' compressed views allows the collective representation to approach the information bottleneck with exponentially high probability.

A Universal Banach--Bregman Framework for Stochastic Iterations: Unifying Stochastic Mirror Descent, Learning and LLM Training

Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert spaces, relying on inner-product frameworks and orthogonality. This paradigm fails to capture non-Euclidean settings, such as mirror descent on simplices, Bregman proximal methods for sparse learning, natural gradient descent in information geometry, or Kullback--Leibler-regularized language model training. Unlike Euclidean-based Hilbert-space methods, this approach embraces general Banach spaces. This work introduces a pioneering Banach--Bregman framework for stochastic iterations, establishing Bregman geometry as a foundation for next-generation optimization. It (i) provides a unified template via Bregman projections and Bregman--Fejer monotonicity, encompassing stochastic approximation, mirror descent, natural gradient, adaptive methods, and mirror-prox; (ii) establishes super-relaxations ($\lambda > 2$) in non-Hilbert settings, enabling flexible geometries and elucidating their acceleration effect; and (iii) delivers convergence theorems spanning almost-sure boundedness to geometric rates, validated on synthetic and real-world tasks. Empirical studies across machine learning (UCI benchmarks), deep learning (e.g., Transformer training), reinforcement learning (actor--critic), and large language models (WikiText-2 with distilGPT-2) show up to 20% faster convergence, reduced variance, and enhanced accuracy over classical baselines. These results position Banach--Bregman geometry as a cornerstone unifying optimization theory and practice across core AI paradigms.