Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

Efficient online decision-making in contextual bandits is challenging, as methods without informative priors often suffer from computational or statistical inefficiencies. In this work, we leverage pre-trained diffusion models as expressive priors to capture complex action dependencies and develop a practical algorithm that efficiently approximates posteriors under such priors, enabling both fast updates and sampling. Empirical results demonstrate the effectiveness and versatility of our approach across diverse contextual bandit settings.

Large language models (LLMs) have recently transformed from text-based assistants to autonomous agents capable of planning, reasoning, and iteratively improving their actions. While numerical reward signals and verifiers can effectively rank candidate actions, they often provide limited contextual guidance.

Prompt caching is critical for reducing latency and cost in LLM inference--OpenAI and Anthropic report up to 50-90% cost savings through prompt reuse. Despite its widespread success, little is known about what constitutes an optimal prompt caching policy, particularly when optimizing tail latency--a metric of central importance to practitioners. The widely used Least Recently Used (LRU) policy can perform arbitrarily poor on this metric, as it is oblivious to the heterogeneity of conversation lengths. To address this gap, we propose Tail-Optimized LRU, a simple two-line modification that reallocates KV cache capacity to prioritize high-latency conversations by evicting cache entries that are unlikely to affect future turns. Though the implementation is simple, we prove its optimality under a natural stochastic model of conversation dynamics, providing the first theoretical justification for LRU in this setting--a result that may be of independent interest to the caching community. Experimentally, on real conversation data WildChat [Zhao et al., 2024], Tail-Optimized LRU achieves up to 27.5% reduction in P90 tail Time to First Token latency and 23.9% in P95 tail latency compared to LRU, along with up to 38.9% decrease in SLO violations of 200ms. We believe this provides a practical and theoretically grounded option for practitioners seeking to optimize tail latency in real-world LLM deployments.

Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.

Monitoring AIs at runtime can help us detect and stop harmful actions. In this paper, we study how to efficiently combine multiple runtime monitors into a single monitoring protocol. The protocol's objective is to maximize the probability of applying a safety intervention on misaligned outputs (i.e., maximize recall). Since running monitors and applying safety interventions are costly, the protocol also needs to adhere to an average-case budget constraint. Taking the monitors' performance and cost as given, we develop an algorithm to find the best protocol. The algorithm exhaustively searches over when and which monitors to call, and allocates safety interventions based on the Neyman-Pearson lemma. By focusing on likelihood ratios and strategically trading off spending on monitors against spending on interventions, we more than double our recall rate compared to a naive baseline in a code review setting. We also show that combining two monitors can Pareto dominate using either monitor alone. Our framework provides a principled methodology for combining existing monitors to detect undesirable behavior in cost-sensitive settings.

Molecular synthetic space projecting is a critical technique in de novo molecular design, which aims to rectify molecules without synthesizability guarantee by converting them into synthetic postfix notations. However, the vast synthesizable chemical space and the discrete data modalities involved pose significant challenges to postfix notation conversion benchmarking. In this paper, we exploit conditional probability transitions in discrete state space and introduce MoleBridge, a deep generative model built on the Markov bridge approach for designing postfix notations of molecular synthesis pathways. MoleBridge consists of two iterative optimizations: i) Autoregressive extending of notation tokens from molecular graphs, and ii) generation of discrete reaction postfix notations through Markov bridge, where noisy token blocks are progressively denoised over multi-step iterations. For the challenging second iteration, which demands sensitivity to incorrect generative probability paths within intricate chemical spaces, we employ a thinking and denoising separation approach to denoise. Empirically, we find that MoleBridge is capable of accurately predicting synthesis pathways while exhibiting excellent performance in a variety of application scenarios.

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.

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.

Large Language Models (LLMs) with inference-time scaling techniques show promise for code generation, yet face notable efficiency and scalability challenges. Construction-based tree-search methods suffer from rapid growth in tree size, high token consumption, and lack of anytime property. In contrast, improvementbased methods offer better performance but often struggle with uninformative reward signals and inefficient search strategies. In this work, we propose ReLoc, a unified local search framework which effectively performs step-by-step code revision. Specifically, ReLoc explores a series of local revisions through four key algorithmic components: initial code drafting, neighborhood code generation, candidate evaluation, and incumbent code updating, each of which can be instantiated with specific decision rules to realize different local search algorithms such as Hill Climbing (HC) or Genetic Algorithm (GA). Furthermore, we develop a specialized revision reward model that evaluates code quality based on revision distance to produce fine-grained preferences that guide the local search toward more promising candidates. Finally, our extensive experimental results demonstrate that our approach achieves superior performance across diverse code generation tasks, significantly outperforming both construction-based tree search as well as the state-of-the-art improvement-based code generation methods.