MathNet: a Global Multimodal Benchmark for Mathematical Reasoning and Retrieval

Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models and mathematical retrieval in embedding-based systems. MathNet spans 47 countries, 17 languages, and two decades of competitions, comprising 30,676 expert-authored problems with solutions across diverse domains. In addition to the core dataset, we construct a retrieval benchmark consisting of mathematically equivalent and structurally similar problem pairs curated by human experts. MathNet supports three tasks: (i) Problem Solving, (ii) Math-Aware Retrieval, and (iii) Retrieval-Augmented Problem Solving. Experimental results show that even state-of-the-art reasoning models (78.4% for Gemini-3.1-Pro and 69.3% for GPT-5) remain challenged, while embedding models struggle to retrieve equivalent problems. We further show that retrieval-augmented generation performance is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. MathNet provides the largest high-quality Olympiad dataset together with the first benchmark for evaluating mathematical problem retrieval, and we publicly release both the dataset and benchmark at https://mathnet.mit.edu.

End-to-End Training for Unified Tokenization and Latent Denoising

Latent diffusion models (LDMs) enable high-fidelity synthesis by operating in learned latent spaces. However, training state-of-the-art LDMs requires complex staging: a tokenizer must be trained first, before the diffusion model can be trained in the frozen latent space. We propose UNITE - an autoencoder architecture for unified tokenization and latent diffusion. UNITE consists of a Generative Encoder that serves as both image tokenizer and latent generator via weight sharing. Our key insight is that tokenization and generation can be viewed as the same latent inference problem under different conditioning regimes: tokenization infers latents from fully observed images, whereas generation infers them from noise together with text or class conditioning. Motivated by this, we introduce a single-stage training procedure that jointly optimizes both tasks via two forward passes through the same Generative Encoder. The shared parameters enable gradients to jointly shape the latent space, encouraging a "common latent language". Across image and molecule modalities, UNITE achieves near state of the art performance without adversarial losses or pretrained encoders (e.g., DINO), reaching FID 2.12 and 1.73 for Base and Large models on ImageNet 256 x 256. We further analyze the Generative Encoder through the lenses of representation alignment and compression. These results show that single stage joint training of tokenization & generation from scratch is feasible.

The Dual Mechanisms of Spatial Reasoning in Vision-Language Models

Many multimodal tasks, such as image captioning and visual question answering, require vision-language models (VLMs) to associate objects with their properties and spatial relations. Yet it remains unclear where and how such associations are computed within VLMs. In this work, we show that VLMs rely on two concurrent mechanisms to represent such associations. In the language model backbone, intermediate layers represent content-independent spatial relations on top of visual tokens corresponding to objects. However, this mechanism plays only a secondary role in shaping model predictions. Instead, the dominant source of spatial information originates in the vision encoder, whose representations encode the layout of objects and are directly exploited by the language model backbone. Notably, this spatial signal is distributed globally across visual tokens, extending beyond object regions into surrounding background areas. We show that enhancing these vision-derived spatial representations globally across all image tokens improves spatial reasoning performance on naturalistic images. Together, our results clarify how spatial association is computed within VLMs and highlight the central role of vision encoders in enabling spatial reasoning.

Pitfalls in Evaluating Interpretability Agents

Automated interpretability systems aim to reduce the need for human labor and scale analysis to increasingly large models and diverse tasks. Recent efforts toward this goal leverage large language models (LLMs) at increasing levels of autonomy, ranging from fixed one-shot workflows to fully autonomous interpretability agents. This shift creates a corresponding need to scale evaluation approaches to keep pace with both the volume and complexity of generated explanations. We investigate this challenge in the context of automated circuit analysis -- explaining the roles of model components when performing specific tasks. To this end, we build an agentic system in which a research agent iteratively designs experiments and refines hypotheses. When evaluated against human expert explanations across six circuit analysis tasks in the literature, the system appears competitive. However, closer examination reveals several pitfalls of replication-based evaluation: human expert explanations can be subjective or incomplete, outcome-based comparisons obscure the research process, and LLM-based systems may reproduce published findings via memorization or informed guessing. To address some of these pitfalls, we propose an unsupervised intrinsic evaluation based on the functional interchangeability of model components. Our work demonstrates fundamental challenges in evaluating complex automated interpretability systems and reveals key limitations of replication-based evaluation.

Seeing Through the PRISM: Compound & Controllable Restoration of Scientific Images

Scientific and environmental imagery often suffer from complex mixtures of noise related to the sensor and the environment. Existing restoration methods typically remove one degradation at a time, leading to cascading artifacts, overcorrection, or loss of meaningful signal. In scientific applications, restoration must be able to simultaneously handle compound degradations while allowing experts to selectively remove subsets of distortions without erasing important features. To address these challenges, we present PRISM (Precision Restoration with Interpretable Separation of Mixtures). PRISM is a prompted conditional diffusion framework which combines compound-aware supervision over mixed degradations with a weighted contrastive disentanglement objective that aligns primitives and their mixtures in the latent space. This compositional geometry enables high-fidelity joint removal of overlapping distortions while also allowing flexible, targeted fixes through natural language prompts. Across microscopy, wildlife monitoring, remote sensing, and urban weather datasets, PRISM outperforms state-of-the-art baselines on complex compound degradations, including zero-shot mixtures not seen during training. Importantly, we show that selective restoration significantly improves downstream scientific accuracy in several domains over standard "black-box" restoration. These results establish PRISM as a generalizable and controllable framework for high-fidelity restoration in domains where scientific utility is a priority.

VideoSketcher: Video Models Prior Enable Versatile Sequential Sketch Generation

Sketching is inherently a sequential process, in which strokes are drawn in a meaningful order to explore and refine ideas. However, most generative models treat sketches as static images, overlooking the temporal structure that underlies creative drawing. We present a data-efficient approach for sequential sketch generation that adapts pretrained text-to-video diffusion models to generate sketching processes. Our key insight is that large language models and video diffusion models offer complementary strengths for this task: LLMs provide semantic planning and stroke ordering, while video diffusion models serve as strong renderers that produce high-quality, temporally coherent visuals. We leverage this by representing sketches as short videos in which strokes are progressively drawn on a blank canvas, guided by text-specified ordering instructions. We introduce a two-stage fine-tuning strategy that decouples the learning of stroke ordering from the learning of sketch appearance. Stroke ordering is learned using synthetic shape compositions with controlled temporal structure, while visual appearance is distilled from as few as seven manually authored sketching processes that capture both global drawing order and the continuous formation of individual strokes. Despite the extremely limited amount of human-drawn sketch data, our method generates high-quality sequential sketches that closely follow text-specified orderings while exhibiting rich visual detail. We further demonstrate the flexibility of our approach through extensions such as brush style conditioning and autoregressive sketch generation, enabling additional controllability and interactive, collaborative drawing.

Fairness Aware Reward Optimization

Demographic skews in human preference data propagate systematic unfairness through reward models into aligned LLMs. We introduce Fairness Aware Reward Optimization (Faro), an in-processing framework that trains reward models under demographic parity, equalized odds, or counterfactual fairness constraints. We provide the first theoretical analysis of reward-level fairness in LLM alignment, establishing: (i) provable fairness certificates for Faro-trained rewards with controllable slack; a (ii) formal characterization of the accuracy-fairness trade-off induced by KL-regularized fine-tuning, proving fairness transfers from reward to policy; and the (iii) existence of a non-empty Pareto frontier. Unlike pre- and post-processing methods, Faro ensures reward models are simultaneously ordinal (ranking correctly), cardinal (calibrated), and fair. Across multiple LLMs and benchmarks, Faro significantly reduces bias and harmful generations while maintaining or improving model quality.

Ambient Dataloops: Generative Models for Dataset Refinement

We propose Ambient Dataloops, an iterative framework for refining datasets that makes it easier for diffusion models to learn the underlying data distribution. Modern datasets contain samples of highly varying quality, and training directly on such heterogeneous data often yields suboptimal models. We propose a dataset-model co-evolution process; at each iteration of our method, the dataset becomes progressively higher quality, and the model improves accordingly. To avoid destructive self-consuming loops, at each generation, we treat the synthetically improved samples as noisy, but at a slightly lower noisy level than the previous iteration, and we use Ambient Diffusion techniques for learning under corruption. Empirically, Ambient Dataloops achieve state-of-the-art performance in unconditional and text-conditional image generation and de novo protein design. We further provide a theoretical justification for the proposed framework that captures the benefits of the data looping procedure.

Motion Attribution for Video Generation

Despite the rapid progress of video generation models, the role of data in influencing motion is poorly understood. We present Motive (MOTIon attribution for Video gEneration), a motion-centric, gradient-based data attribution framework that scales to modern, large, high-quality video datasets and models. We use this to study which fine-tuning clips improve or degrade temporal dynamics. Motive isolates temporal dynamics from static appearance via motion-weighted loss masks, yielding efficient and scalable motion-specific influence computation. On text-to-video models, Motive identifies clips that strongly affect motion and guides data curation that improves temporal consistency and physical plausibility. With Motive-selected high-influence data, our method improves both motion smoothness and dynamic degree on VBench, achieving a 74.1% human preference win rate compared with the pretrained base model. To our knowledge, this is the first framework to attribute motion rather than visual appearance in video generative models and to use it to curate fine-tuning data.

VirtualEnv: A Platform for Embodied AI Research

As large language models (LLMs) continue to improve in reasoning and decision-making, there is a growing need for realistic and interactive environments where their abilities can be rigorously evaluated. We present VirtualEnv, a next-generation simulation platform built on Unreal Engine 5 that enables fine-grained benchmarking of LLMs in embodied and interactive scenarios. VirtualEnv supports rich agent-environment interactions, including object manipulation, navigation, and adaptive multi-agent collaboration, as well as game-inspired mechanics like escape rooms and procedurally generated environments. We provide a user-friendly API built on top of Unreal Engine, allowing researchers to deploy and control LLM-driven agents using natural language instructions. We integrate large-scale LLMs and vision-language models (VLMs), such as GPT-based models, to generate novel environments and structured tasks from multimodal inputs. Our experiments benchmark the performance of several popular LLMs across tasks of increasing complexity, analyzing differences in adaptability, planning, and multi-agent coordination. We also describe our methodology for procedural task generation, task validation, and real-time environment control. VirtualEnv is released as an open-source platform, we aim to advance research at the intersection of AI and gaming, enable standardized evaluation of LLMs in embodied AI settings, and pave the way for future developments in immersive simulations and interactive entertainment.