We demonstrate that geometrically distinctive keys during LLM inference tend to have high attention scores. Based on the phenomenon we propose KEYDIFF, a training-free KV cache eviction method based solely on key similarity. Unlike other KV cache eviction methods, KEYDIFF can process arbitrarily long prompts within strict resource constraints and efficiently generate responses. We provide a theoretical basis for KEYDIFF by relating key diversity with attention scores. These results imply KEYDIFF can efficiently identify the most important tokens to retain. Notably KEYDIFF does not rely on attention scores, allowing the use of optimized attention mechanisms like FlashAttention. Under a strict memory allowance, we demonstrate the effectiveness of KEYDIFF for the Llama and Qwen model families by observing a performance gap of less than 0.04% with 8K cache budget ( 23% KV cache reduction) from the non-evicting baseline on LongBench for Llama 3.1-8B and Llama 3.2-3B. We also observe near baseline performance for Deepseek-R1-Distill-Llama-8B on the Math500 reasoning benchmark and decrease end-to-end inference latency by up to 30% compared to the other token-eviction methods.

The remarkable performance of Large Language Models (LLMs) can be enhanced with test-time computation, which relies on external tools and even other deep learning models. However, existing approaches for integrating non-text modality representations into LLMs typically require additional costly supervised training, restricting on-the-fly adaptation to new domains and modalities. In this work, we explore the feasibility of integrating representations from non-text foundational models (FMs) into text-based LLMs in a training-free manner. We propose InContext Representation Learning (ICRL) as a proof-of-concept to allow LLMs to adaptively utilize non-text modality representations with few-shot learning. Unlike traditional in-context learning, which incorporates text-label pairs, ICRL replaces text inputs with FM representations, enabling the LLM to perform multimodal inference without fine-tuning. We evaluate ICRL on a suite of tasks in the molecular domain, investigating three core research questions: (i) how to map FM representations into LLMs in a training-free manner, (ii) what factors influence ICRL performance, and (iii) what mechanisms underlie the effectiveness of ICRL. To the best of our knowledge, ICRL is the first training-free framework for integrating non-text modality representations into text-based LLMs, presenting a promising direction for adaptable, multi-modal generalization.3

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the reasoning trace, and (ii) compute is most effective when reasoning is systematic and incremental, forming structured chains of thought (CoTs) akin to human problemsolving. To study these factors in isolation, we introduce a controlled setting based on shortest-path tasks in layered graphs. We train decoder-only transformers on question-trace-answer triples using a custom tokenizer, comparing models trained on optimal bottom-up dynamic programming traces with those trained on longer, valid traces involving backtracking. Surprisingly, with the same training-token budget, models trained on inefficient traces generalize better to unseen graphs. This benefit is not due to length alone--injecting arbitrary redundancy into reasoning traces fails to help and can even hurt performance. Instead, we find that generalization correlates with the model's confidence in next-token prediction, suggesting that long, coherent, and locally incremental traces make the training signal easier to optimize.

Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize the length of the flow integration trajectories. We investigate the benefits of using path gradients to fine-tune CNFs initially trained by Flow Matching, in the setting where a target energy is known. Our experiments show that this hybrid approach yields up to a threefold increase in sampling efficiency for molecular systems, all while using the same model, a similar computational budget and without the need for additional sampling. Furthermore, by measuring the length of the flow trajectories during fine-tuning, we show that path gradients largely preserve the learned structure of the flow.

We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on n data points. Our main contribution leverages the high dimensionality of the ambient space, which implies low correlation of the input samples, to demonstrate that a network with width of order log(n)neurons suffices for global convergence with high probability. Our analysis uses a Polyak-Łojasiewicz viewpoint along the gradient-flow trajectory, which provides an exponential rate of convergence of 1n. When the data are exactly orthogonal, we give further refined characterizations of the convergence speed, proving its asymptotic behavior lies between the orders 1n and 1 n, and exhibiting a phase-transition phenomenon in the convergence rate, during which it evolves from the lower bound to the upper, and in a relative time of order 1log(n).

This paper presents a pioneering exploration of reinforcement learning (RL) via group relative policy optimization for unified multimodal large language models (ULMs), aimed at simultaneously reinforcing generation and understanding capabilities. Through systematic pilot studies, we uncover the significant potential of ULMs to enable the synergistic co-evolution of dual capabilities within a shared policy optimization framework. Building on this insight, we introduce CoRL, a Co-Reinforcement Learning framework comprising a unified RL stage for joint optimization and a refined RL stage for task-specific enhancement. With the proposed CoRL, our resulting model, ULM-R1, achieves average improvements of 7% on three text-to-image generation datasets and 23% on nine multimodal understanding benchmarks. These results demonstrate the effectiveness of CoRL and highlight the substantial benefits of reinforcement learning in facilitating cross-task synergy and optimization for ULMs. Code is available at https://github.com/mm-vl/ULM-R1.

Visual reasoning abilities play a crucial role in understanding complex multimodal data, advancing both domain-specific applications and artificial general intelligence (AGI). Existing methods improve Vision-Language Models (VLMs) reasoning via Chain-of-Thought (CoT) supervised fine-tuning, using meticulously annotated training data to enhance visual reasoning capabilities. However, this training paradigm may lead to overfitting and cognitive rigidity, restricting the model's generalization ability to transfer visual reasoning skills under domain shift and limiting its real-world applicability. To address these limitations, we propose Reason-RFT, the first two-stage reinforcement fine-tuning framework for visual reasoning: (1) Supervised Fine-Tuning (SFT) with curated CoT data activates the reasoning potential of VLMs, followed by (2) Group Relative Policy Optimization (GRPO)-based reinforcement learning that generates multiple reasoning-response pairs, significantly enhancing the capability to address ubiquitous domain shift in visual reasoning tasks. To evaluate the visual reasoning capabilities of Reason-RFT, we reconstructed a comprehensive dataset encompassing visual counting, structural perception, and spatial transformation, serving as a benchmark for systematic assessment across three core dimensions. Experimental results demonstrate three key advantages: (1) Performance Enhancement: achieving state-of-the-art results across multiple tasks, outperforming mainstream open-source and proprietary models; (2) Generalization Superiority: consistently maintaining robust performance in addressing domain shift in typical visual reasoning tasks, outperforming alternative paradigms; (3) Data Efficiency: excelling in few-shot learning scenarios while surpassing full-dataset SFT baselines. Reason-RFT introduces a rebust training paradigm in visual reasoning, and please refer to project website: Reason-RFT.

Equivariant models have recently been shown to improve the data efficiency of diffusion policy by a significant margin. However, prior work that explored this direction focused primarily on point cloud inputs generated by multiple cameras fixed in the workspace. This type of point cloud input is not compatible with the now-common setting where the primary input modality is an eye-in-hand RGB camera like a GoPro. This paper closes this gap by incorporating into the diffusion policy model a process that projects features from the 2DRGB camera image onto a sphere. This enables us to reason about symmetries in SO(3)without explicitly reconstructing a point cloud. We perform extensive experiments in both simulation and the real world that demonstrate that our method consistently outperforms strong baselines in terms of both performance and sample efficiency. Our work, Image-toSphere Policy (ISP), is the first SO(3)-equivariant policy learning framework for robotic manipulation that works using only monocular RGB inputs.

Many controlled complex systems have an inherent network structure, such as power grids, traffic light systems, or computer networks. Automatically controlling these systems is highly challenging due to their combinatorial complexity.

Many controlled complex systems have an inherent network structure, such as power grids, traffic light systems, or computer networks. Automatically controlling these systems is highly challenging due to their combinatorial complexity.