Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be misaligned with pass@N in that pass@N accuracy decreases with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Selecting artificial intelligence (AI) models, such as large language models (LLMs), from multiple candidates requires accurate performance estimation. This is ideally achieved through empirical evaluations involving abundant real-world data. However, such evaluations are costly and impractical at scale. To address this challenge, autoevaluation methods leverage synthetic data produced by automated evaluators, such as LLMs-as-judges, reducing variance but potentially introducing bias. Recent approaches have employed semi-supervised prediction-powered inference (PPI) to correct for the bias of autoevaluators. However, the use of autoevaluators may lead in practice to a degradation in sample efficiency compared to conventional methods using only real-world data. In this paper, we propose R-AutoEval+, a novel framework that provides finite-sample reliability guarantees on the model evaluation, while also ensuring an enhanced (or at least no worse) sample efficiency compared to conventional methods. The key innovation of R-AutoEval+ is an adaptive construction of the model evaluation variable, which dynamically tunes its reliance on synthetic data, reverting to conventional methods when the autoevaluator is insufficiently accurate. Experiments on the use of LLMs-as-judges for the optimization of quantization settings for the weights of an LLM, for prompt design in LLMs, and for test-time reasoning budget allocation in LLMs confirm the reliability and efficiency of R-AutoEval+.

Medical time-series analysis differs fundamentally from general ones by requiring specialized domain knowledge to interpret complex signals and clinical context. Large language models (LLMs) hold great promise for augmenting medical timeseries analysis by complementing raw series with rich contextual knowledge drawn from biomedical literature and clinical guidelines. However, realizing this potential depends on precise and meaningful prompts that guide the LLM to key information. Yet, determining what constitutes effective prompt content remains non-trivial--especially in medical settings where signal interpretation often hinges on subtle, expert-defined decision-making indicators. To this end, we propose InDiGO, a knowledge-aware evolutionary learning framework that integrates clinical signals and decision-making indicators through iterative optimization. Across four medical benchmarks, InDiGO consistently outperforms prior methods.

Watermarking LLM-generated text is critical for content attribution and misinformation prevention, yet existing methods compromise text quality and require white-box model access with logit manipulation or training, which exclude APIbased models and multilingual scenarios. We propose SAEMARK, an inferencetime framework for multi-bit watermarking that embeds personalized information through feature-based rejection sampling, fundamentally different from logit-based or rewriting-based approaches: we do not modify model outputs directly and require only black-box access, while naturally supporting multi-bit message embedding and generalizing across diverse languages and domains. We instantiate the framework using Sparse Autoencoders as deterministic feature extractors and provide theoretical worst-case analysis relating watermark accuracy to computational budget. Experiments across 4 datasets demonstrate strong watermarking performance on English, Chinese, and code while preserving text quality. SAEMARK establishes a new paradigm for scalable, quality-preserving watermarks that work seamlessly with closed-source LLMs across languages and domains.

Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers sampling from a constrained distribution that is described by an unconstrained density, as well as additional equality and/or inequality constraints, which often make the constraint set nonconvex. Existing methods struggle in the presence of such nonconvex constraints, as they rely on projections, which are computationally expensive or intractable, are specialized to either inequality or equality constraints, and often lack rigorous quantitative convergence guarantees. In this paper, we introduce Overdamped Langevin with LAnding (OLLA), a new framework that can design overdamped Langevin dynamics accommodating both nonlinear equality and inequality constraints. The proposed dynamics also deterministically corrects trajectories along the normal direction of the constraint surface, thus obviating the need for explicit projections. We show that, under suitable regularity conditions on the target density and the feasible set Σ Rd, OLLA converges exponentially fast in 2-Wasserstein distance to the constrained target density ρΣ(x) exp( f(x))dσΣ. Lastly, through experiments, we demonstrate the efficiency of OLLA compared to known constrained Langevin algorithms and their slack variable variants, highlighting its favorable computational cost and fast empirical mixing.1

Modern foundation models often undergo iterative "bootstrapping" in their posttraining phase: a model generates synthetic data, an external verifier filters out low-quality samples, and the high-quality subset is used for further fine-tuning. Over multiple iterations, the model performance improves, raising a crucial question: How should the total budget for generation and training be allocated across iterations to maximize final performance? In this work, we develop a theoretical framework for analyzing budget allocation strategies. Specifically, we show that constant policies fail to converge with high probability, while increasing policies-- particularly exponential growth policies--exhibit significant theoretical advantages. Experiments on image denoising with diffusion probabilistic models and math reasoning with large language models show that both exponential and polynomial growth policies consistently outperform constant policies, with exponential policies often providing more stable performance.

We study the problem of offline imitation learning in Markov decision processes (MDPs), where the goal is to learn a well-performing policy given a dataset of state-action pairs generated by an expert policy. Complementing a recent line of work on this topic that assumes the expert belongs to a tractable class of known policies, we approach this problem from a new angle and leverage a different type of structural assumption about the environment. Specifically, for the class of linear Qπ-realizable MDPs, we introduce a new algorithm called saddle-point offline imitation learning (SPOIL), which is guaranteed to match the performance of any expert up to an additive error ε with access to O(ε 2) samples. Moreover, we extend this result to possibly nonlinear Qπ-realizable MDPs at the cost of a worse sample complexity of order O(ε 4). Finally, our analysis suggests a new loss function for training critic networks from expert data in deep imitation learning. Empirical evaluations on standard benchmarks demonstrate that the neural net implementation of SPOIL is superior to behavior cloning and competitive with state-of-the-art algorithms.

Quantum Implicit Neural Representations (QINRs) have emerged as a promising paradigm that leverages parametrised quantum circuits to encode and process classical information. However, significant challenges remain in areas such as ansatz architecture design, the effective utility of quantum-mechanical properties, training efficiency, and the integration with classical modules. This paper advances the field by introducing a novel QINR architecture for 2D image and 3D geometric field learning, which we collectively refer to as Quantum Visual Field (QVF). QVF encodes classical data into quantum statevectors using neural amplitude encoding grounded in a learnable energy manifold, ensuring meaningful Hilbert space embeddings. Our ansatz follows a fully entangled design of learnable parametrised quantum circuits, with quantum (unitary) operations performed in the real Hilbert space, resulting in numerically stable training with fast convergence. QVF does not rely on classical post-processing--in contrast to the previous QINR learning approach--and directly employs measurements to extract learned signals encoded in the ansatz. Experiments on a quantum hardware simulator demonstrate that QVF outperforms existing quantum approach and competes widely used classical foundational baselines in terms of visual representation accuracy across various metrics and model characteristics. We also show applications of QVF in 2D and 3D field completion and 3D shape interpolation, highlighting its practical potential.

Recent advances in text-to-video (T2V) and image-to-video (I2V) models, have enabled the creation of visually compelling and dynamic videos from simple textual descriptions or initial frames. However, these models often fail to provide an explicit representation of motion separate from content, limiting their applicability for content creators. To address this gap, we propose DisMo, a novel paradigm for learning abstract motion representations directly from raw video data via an image-space reconstruction objective. Our representation is generic and independent of static information such as appearance, object identity, or pose. This enables open-world motion transfer, allowing motion to be transferred across semantically unrelated entities without requiring object correspondences, even between vastly different categories. Unlike prior methods, which trade off motion fidelity and prompt adherence, are overfitting to source structure or drifting from the described action, our approach disentangles motion semantics from appearance, enabling accurate transfer and faithful conditioning. Furthermore, our motion representation can be combined with any existing video generator via lightweight adapters, allowing us to effortlessly benefit from future advancements in video models. We demonstrate the effectiveness of our method through a diverse set of motion transfer tasks. Finally, we show that the learned representations are well-suited for downstream motion understanding tasks, consistently outperforming state-of-the-art video representation models such as V-JEPA in zero-shot action classification on benchmarks including Something-Something v2 and Jester.

Diffusion transformers demonstrate significant potential for various generation tasks but are challenged by high computational cost. Recently, feature caching methods have been introduced to improve inference efficiency by storing features at certain timesteps and reusing them at subsequent timesteps. However, their effectiveness is limited as they rely only on choosing between cached features and performing model inference. Motivated by high cosine similarity between features across consecutive timesteps, we propose a cache-based framework that reuses features and selectively adapts them through linear modulation. In our framework, the selection is performed via a modulation gate, and both the gate and modulation parameters are learned. Extensive experiments show that our method achieves similar generation performance to the original sampler while requiring significantly less computation. For example, FLOPs and inference latency are reduced by 2.93 and 2.15 for DiT-XL/2 and by 2.83 and 1.50 for PixArt-α, respectively. We find that modulation is effective when applied to as little as 2% of layers, resulting in negligible computation overhead.