#01Oct 21, 2026
math.ST
Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
Shayan Hundrieser, Tudor Manole
We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples. We show that the unconstrained NPMLE achieves the minimax optimal rate $\log(n)/n$ in squared Hellinger distance, when the true mixing measure is sub-Gaussian. In addition, we show that when the true mixing measure has compact support, the NMPLE constrained to a compact interval also achieves the minimax optimal rate, which is slightly faster and of order $\log(n)/(n \log \log n)$. Our proof consists of sharply characterizing the local Hellinger bracketing entropy of the class of finite Gaussian mixtures. One of our key technical innovations is to sharply bound the $L^2$ bracketing entropy of balls of bounded-degree polynomials, which may be of independent interest. As an application, we establish the regret-optimality of $g$-modeling procedures based on the NPMLE in the Gaussian Empirical Bayes problem with bounded priors.
#02Oct 21, 2026
cs.CL
LongZero: Enhancing Long-Context Reasoning in LLMs from Zero Data
Zhennan Wan, Jianfei Chen
Reinforcement learning (RL) is an effective way to strengthen the long-context reasoning of large language models (LLMs), but it needs training data that are long, diverse, challenging, and verifiable. Human annotation of such data is expensive, naturally occurring data are too scarce to sustain RL, and existing synthesis methods depend on external corpora or stronger teacher models, which become harder to obtain as the trained models get stronger. Recently, RL from zero data, in which a model learns from tasks it proposes itself, has achieved excellent performance, but existing methods target short-context tasks. Therefore, we propose $\textbf{LongZero}$, a method that lets an LLM improve its own long-context reasoning without any external data. Instead of writing questions and answers over existing documents, LongZero first has the model synthesize the question and answer with its supporting evidence in a compact structured form, and only then separately expands the evidence into a long multi-document context. LongZero combines these self-written multi-hop reasoning tasks with self-written multi-round retrieval tasks and trains the model with GRPO. We evaluate LongZero on two LLMs across five long-context reasoning benchmarks and compare it with RL on data synthesized from external corpora. Experimental results show that LongZero can generalize to real tasks, and outperforms both baselines, suggesting a viable and promising path to improving long-context reasoning of LLMs.
#03Oct 21, 2026
cs.CL
Quant-Arena: Benchmarking LLM Agents for Quantitative Trading Research
Houde Qian, Zheng Jiang, Wenyi Li and 9 more
Quantitative research is an iterative loop: a researcher proposes a market hypothesis, implements it as an executable signal, tests it on historical data, and decides what to keep. Existing benchmarks score formulas, code, or individual trading decisions, leaving open whether large language models (LLMs) can complete this loop and produce strategies that work beyond the research period. We introduce Quant-Arena, a benchmark and public leaderboard for end-to-end quantitative research on real A-share market data. A model constructs features and stock-scoring code, receives feedback only on 2022--2023, and freezes one strategy for assessment on the sealed year 2024. A cash-account evaluator applies trading constraints and costs, including market impact estimated from a simulated order book. Scores are dominated by realized excess return and complemented by signal quality and the diversity of features used by the strategy. We evaluate nine frontier models, among which GPT-6 Astra scores highest; yet no model beats the equal-weight market in 2024. Quant-Arena is open to submissions from any model or agent harness.
#04Oct 21, 2026
cs.CV
Rethinking Video Autoencoders for Interactive World Models
Adrien Ramanana Rahary, Yutong Bai, Nicolas Dufour and 2 more
Video world models predict future frames from past frames and actions. They serve as simulators in which agents train, plan or are evaluated, and that humans can control interactively. They generate in the latent space of a video autoencoder, whose compression sets their cost per frame and how long each action waits to take effect. Yet world models often reuse the autoencoders of text-to-video generators, built for offline generation with no agent waiting and, without their training data and code, not retrainable at another compression. We therefore ask how, where and how much a world model should compress. We build CADRE, an open family of causal diffusion representation autoencoders spanning multiple spatio-temporal compressions. Its members differ only in a small bottleneck on frozen features and share a diffusion decoder self-distilled to one or a few steps. We train the same world model on each autoencoder in two domains, manipulation and navigation, with two environments each. CADRE forms most of the latency-quality frontier, especially with a moving camera. Our study also leads to four findings. At strong compression, a diffusion decoder is sharper than perceptual regression. In robot manipulation, temporal compression is more effective in the autoencoder than in the world model. Manipulation and navigation call for opposite compressions: temporal compression costs little when the camera is still, and spatial compression when it moves. Surprisingly, with a still camera, coarser spatial tokens hurt motion far more than image quality. Code, models and a live demo are at https://kyutai.org/blog/2026-10-21-cadre
#05Oct 21, 2026
cs.CV
VoxProg: 3D Spatial Reasoning through Voxel Programming
Zhichao Zhai, Menglei Zhao, Guikun Chen and 4 more
Language models' abilities to interpret tasks and generate programs offer a promising basis for 3D spatial reasoning. Yet following spatial instructions in 3D scenes requires programs to construct geometric references that language leaves implicit. In this work, we introduce VoxProg, which formulates 3D object placement through voxel programming: a language model translates task interpretations into executable programs over local voxel views of scene surfaces. Because these views index surface geometry on regular grids with explicit coordinates and neighborhood relations, an evidence program can isolate task-relevant regions and boundaries directly from scene meshes, and a downstream pose program can measure the resulting geometry to compute a target $SE(3)$ pose. Visual and numerical feedback from execution lets the model inspect intermediate selections and candidate placements to iteratively revise its code. To evaluate open-ended placement across functional use, geometric fit, and contextual arrangements, we introduce the 71-task VoxProg-Bench benchmark along with an evaluation suite pairing perceptual Intent Alignment and 3D Physical Validity. Across VoxProg-Bench and external benchmarks, VoxProg consistently outperforms relation-based, keypoint-based, and mesh-based baselines.