Frontier reasoning models are produced by posttraining base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to "mix" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a "cut" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models.

We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling as a mirrored optimisation problem on the space of probability measures. Based on this viewpoint, we also introduce a unifying framework for several existing constrained sampling algorithms, including mirrored Langevin dynamics and mirrored Stein variational gradient descent. We demonstrate the performance of our algorithms on a range of numerical examples, including sampling from targets on the simplex, sampling with fairness constraints, and constrained sampling problems in postselection inference. Our results indicate that our algorithms achieve competitive performance with existing constrained sampling methods, without the need to tune any hyperparameters.

How can we make use of information parallelism in online decision making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online decision making problems, namely, stochastic multi-arm bandit and linear contextual bandit with finitely many arms. Over a time horizon T, our batch Thompson Sampling policy achieves the same (asymptotic) regret bound of a fully sequential one while carrying out only O(log T) batch queries. To achieve this exponential reduction, i.e., reducing the number of interactions from T to O(log T), our batch policy dynamically determines the duration of each batch in order to balance the exploration-exploitation trade-off. We also demonstrate experimentally that dynamic batch allocation dramatically outperforms natural baselines such as static batch allocations.

Black-box optimization has gained great attention for its success in recent applications. However, scaling up to high-dimensional problems with good query efficiency remains challenging. This paper proposes a novel Rank-1 Lattice Targeted Sampling (RLTS) technique to address this issue. Our RLTS benefits from random rank-1 lattice Quasi-Monte Carlo, which enables us to perform fast local exact Gaussian processes (GP) training and inference with O(nlogn)complexity w.r.t.

Silicon-photonics-based optical neural network (ONN) is a promising hardware platform that could represent a paradigm shift in efficient AI with its CMOScompatibility, flexibility, ultra-low execution latency, and high energy efficiency. In-situ training on the online programmable photonic chips is appealing but still encounters challenging issues in on-chip implementability, scalability, and efficiency. In this work, we propose a closed-loop ONN on-chip learning framework L2ight to enable scalable ONN mapping and efficient in-situ learning. L2ightadopts a three-stage learning flow that first calibrates the complicated photonic circuit states under challenging physical constraints, then performs photonic core mapping via combined analytical solving and zeroth-order optimization. A subspace learning procedure with multi-level sparsity is integrated into L2ightto enable in-situ gradient evaluation and fast adaptation, unleashing the power of optics for real on-chip intelligence. Extensive experiments demonstrate our proposed L2ightoutperforms prior ONN training protocols with 3-order-of-magnitude higher scalability and over 30 better efficiency, when benchmarked on various models and learning tasks. This synergistic framework is the first scalable on-chip learning solution that pushes this emerging field from intractable to scalable and further to efficient for next-generation self-learnable photonic neural chips. From a co-design perspective, L2ightalso provides essential insights for hardware-restricted unitary subspace optimization and efficient sparse training.

A.1 List of Neural Topic Modeling Works used in our Meta-Analysis In Table 6, we report the forty publications used in our meta-analysis (Section 3), which are sourced from a survey of neural topic models (Zhao et al., 2021b). A.2 Preprocessing Details Our steps are delineated in our implementation,22 but we list our choices here for easy reference. Corpus statistics are in Table 7. We use the default en-core-web-smspaCy model (Honnibal et al., 2020), version 3.0.5, Document processing - We do not process documents with fewer than 25 whitespace-separated tokens.

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetildeΩ(\sqrt{d})$ adaptive score queries. In particular, our proof shows that any sampler must search over $\widetildeΩ(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.