Fusion Academy & Learning Center (often referred to as Fusion Academy or Fusion) is a private, alternative school for grades 6-12. All classes are taught on a one-to-one basis with one student and one teacher per classroom. Students generally complete schoolwork on-site, instead of at home..
Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy Optimization (GRPO), often converge to low-entropy policies, leading to severe mode collapse and limited output diversity. We analyze this issue from the perspective of sampling probability dynamics, identifying that the standard objective disproportionately reinforces the highest-likelihood paths, thereby suppressing valid alternative reasoning chains. To address this, we propose a novel Advantage Re-weighting Mechanism (ARM) designed to equilibrate the confidence levels across all correct responses. By incorporating Prompt Perplexity and Answer Confidence into the advantage estimation, our method dynamically reshapes the reward signal to attenuate the gradient updates of over-confident reasoning paths, while redistributing probability mass toward under-explored correct solutions. Empirical results demonstrate that our approach significantly enhances generative diversity and response entropy while maintaining competitive accuracy, effectively achieving a superior trade-off between exploration and exploitation in reasoning tasks. Empirical results on Qwen2.5 and DeepSeek models across mathematical and coding benchmarks show that ProGRPO significantly mitigates entropy collapse. Specifically, on Qwen2.5-7B, our method outperforms GRPO by 5.7
The performance of pre-trained masked diffusion models is often constrained by their sampling procedure, which makes decisions irreversible and struggles in low-step generation regimes. We introduce a novel sampling algorithm that works with pre-trained models and, after a lightweight fine-tuning of a single layer, significantly improves sample quality and efficiency. Our method reformulates the generation process using a star-shaped paradigm, which inherently allows for error correction. To make this process effective, we augment it with a learnable re-masking scheduler that intelligently identifies and revises likely errors. This approach yields a substantial quality boost, particularly when using a small number of sampling steps. We extensively ablate key components of our approach and show its usability in different scenarios. In comprehensive experiments on text, and code generation, our sampling algorithm outperforms or matches existing methods.
The ability to understand long videos is vital for embodied intelligent agents, because their effectiveness depends on how well they can accumulate, organize, and leverage long-horizon perceptual memories. Recently, multimodal LLMs have been gaining popularity for solving the long video understanding task due to their general ability to understand natural language and to leverage world knowledge. However, as the number of frames provided to an MLLM increases, the quality of its responses tends to degrade, and inference time grows. Therefore, when using MLLMs for long video understanding, a crucial step is selecting key frames from the video to answer user queries. In this work, we develop FocusGraph, a framework for keyframe selection for question answering over long egocentric videos. It leverages a lightweight trainable Scene-Caption LLM Selector that selects query-relevant clips based on their graph-based captions, and a training-free method for selecting keyframes from these clips. Unlike existing methods, the proposed Scene-Caption LLM Selector does not rely on the original sequence of low-resolution frames; instead, it operates on a compact textual representation of the scene. We then design a training-free Patch-wise Sparse-Flow Retention (PSFR) method to select keyframes from the resulting sequence of clips, which are fed into an MLLM to produce the final answer. Together, these components enable FocusGraph to achieve state-of-the-art results on challenging egocentric long-video question answering benchmarks, including FindingDory and HourVideo, while significantly reducing inference time relative to baseline approaches.
Vision encoders power modern vision-only and vision-language systems, yet the geometry of their internal features remains opaque. In this work, we introduce a simple, general approach for vision latent analysis: reconstruct images from frozen encoder features and treat reconstructability as a proxy for retained information and feature organization. Concretely, we train a lightweight reconstructor to invert feature tensors and use it to compare various vision encoders — CLIP-based ViT, SigLIP, SAM, and InternViT. We rank models by the informativeness of their features and observe consistent gains with image-centric objectives and higher spatial resolution. Beyond measurement, controlled manipulations in feature space produce predictable pixel-level edits: orthogonal rotations (rather than spatial transformations) implement channel permutations and drive systematic color changes; linear contractions implement channel suppression; and a learned linear map enables plausible colorization of grayscale inputs. VLM-based experiments confirm that feature-space color swaps translate into semantic color changes in reconstructions. Our approach is encoder-agnostic in principle (demonstrated on ViT-based models), requires only access to features, and offers a practical diagnostic of what encoders remember, how that information is organized, and how it can be manipulated.
We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.
