Abstract
Recent advances in Large Language Models (LLMs) have driven the adoption of copilots in complex technical scenarios, underscoring the growing need for specialized information retrieval solutions. In this paper, we introduce FLAIR, a lightweight, feedback learning framework that adapts copilot systems' retrieval strategies by integrating domain-specific expert feedback. FLAIR operates in two stages: an offline phase obtains indicators from (1) user feedback and (2) questions synthesized from documentation, storing these indicators in a decentralized manner. An online phase then employs a two-track ranking mechanism to combine raw similarity scores with the collected indicators. This iterative setup refines retrieval performance for any query. Extensive real-world evaluations of FLAIR demonstrate significant performance gains on both previously seen and unseen queries, surpassing state-of-the-art approaches. The system has been successfully integrated into Copilot DECO, serving thousands of users at Microsoft, demonstrating its scalability and effectiveness in operational environments.

Abstract
Recent advancements in Large Language Models (LLMs) have significantly improved reasoning capabilities, with in-context learning (ICL) emerging as a key technique for adaptation without retraining. While previous works have focused on leveraging correct examples, recent research highlights the importance of learning from errors to enhance performance. However, existing methods lack a structured framework for analyzing and mitigating errors, particularly in Multimodal Large Language Models (MLLMs), where integrating visual and textual inputs adds complexity. To address this issue, we propose REFINE: Retrieval-Enhanced Feedback via In-context Neural Error-book, a teacher-student framework that systematically structures errors and provides targeted feedback. REFINE introduces three systematic queries to construct structured feedback -- Feed-Target, Feed-Check, and Feed-Path -- to enhance multimodal reasoning by prioritizing relevant visual information, diagnosing critical failure points, and formulating corrective actions. Unlike prior approaches that rely on redundant retrievals, REFINE optimizes structured feedback retrieval, improving inference efficiency, token usage, and scalability. Our results demonstrate substantial speedup, reduced computational costs, and successful generalization, highlighting REFINE's potential for enhancing multimodal reasoning.

Abstract
Lyapunov functions are fundamental to establishing the stability of Markovian models, yet their construction typically demands substantial creativity and analytical effort. In this paper, we show that deep learning can automate this process by training neural networks to satisfy integral equations derived from first-transition analysis. Beyond stability analysis, our approach can be adapted to solve Poisson's equation and estimate stationary distributions. While neural networks are inherently function approximators on compact domains, it turns out that our approach remains effective when applied to Markov chains on non-compact state spaces. We demonstrate the effectiveness of this methodology through several examples from queueing theory and beyond.

Abstract
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss.

Abstract
The optimal signaling schemes in information design (Bayesian persuasion) problems often involve non-explainable randomization or disconnected partitions of state space, which are too intricate to be audited or communicated. We propose explainable information design in the context of information design with a continuous state space, restricting the information designer to use $K$-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We first prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of 2. We then study the complexity of computing optimal explainable signaling schemes. We show that the exact optimization problem is NP-hard in general. But for Lipschitz utility functions, an $\varepsilon$-approximately optimal explainable signaling scheme can be computed in polynomial time. And for piecewise constant utility functions, we provide an efficient algorithm to find an explainable signaling scheme that provides a $1/2$ approximation to the optimal unrestricted signaling scheme, which matches the worst-case PoE bound. A technical tool we develop is a conversion from any optimal signaling scheme (which satisfies a bi-pooling property) to a partitional signaling scheme that achieves $1/2$ fraction of the expected utility of the former. We use this tool in the proofs of both our PoE result and algorithmic result.

Abstract
Recent advances in NeRF and 3DGS have significantly enhanced the efficiency and quality of 3D content synthesis. However, efficient personalization of generated 3D content remains a critical challenge. Current 3D personalization approaches predominantly rely on knowledge distillation-based methods, which require computationally expensive retraining procedures. To address this challenge, we propose \textbf{Invert3D}, a novel framework for convenient 3D content personalization. Nowadays, vision-language models such as CLIP enable direct image personalization through aligned vision-text embedding spaces. However, the inherent structural differences between 3D content and 2D images preclude direct application of these techniques to 3D personalization. Our approach bridges this gap by establishing alignment between 3D representations and text embedding spaces. Specifically, we develop a camera-conditioned 3D-to-text inverse mechanism that projects 3D contents into a 3D embedding aligned with text embeddings. This alignment enables efficient manipulation and personalization of 3D content through natural language prompts, eliminating the need for computationally retraining procedures. Extensive experiments demonstrate that Invert3D achieves effective personalization of 3D content. Our work is available at: https://github.com/qsong2001/Invert3D.

Abstract
Test-time scaling (TTS) for large language models (LLMs) has thus far fallen into two largely separate paradigms: (1) reinforcement learning (RL) methods that optimize sparse outcome-based rewards, yet suffer from instability and low sample efficiency; and (2) search-based techniques guided by independently trained, static process reward models (PRMs), which require expensive human- or LLM-generated labels and often degrade under distribution shifts. In this paper, we introduce AIRL-S, the first natural unification of RL-based and search-based TTS. Central to AIRL-S is the insight that the reward function learned during RL training inherently represents the ideal PRM for guiding downstream search. Specifically, we leverage adversarial inverse reinforcement learning (AIRL) combined with group relative policy optimization (GRPO) to learn a dense, dynamic PRM directly from correct reasoning traces, entirely eliminating the need for labeled intermediate process data. At inference, the resulting PRM simultaneously serves as the critic for RL rollouts and as a heuristic to effectively guide search procedures, facilitating robust reasoning chain extension, mitigating reward hacking, and enhancing cross-task generalization. Experimental results across eight benchmarks, including mathematics, scientific reasoning, and code generation, demonstrate that our unified approach improves performance by 9 % on average over the base model, matching GPT-4o. Furthermore, when integrated into multiple search algorithms, our PRM consistently outperforms all baseline PRMs trained with labeled data. These results underscore that, indeed, your reward function for RL is your best PRM for search, providing a robust and cost-effective solution to complex reasoning tasks in LLMs.

Abstract
Query optimization is a crucial problem in database systems that has been studied for decades. Learned query optimizers (LQOs) can improve performance over time by incorporating feedback; however, they suffer from cold-start issues and often require retraining when workloads shift or schemas change. Recent LLM-based query optimizers leverage pre-trained and fine-tuned LLMs to mitigate these challenges. Nevertheless, they neglect LLMs' in-context learning and execution records as feedback for continuous evolution. In this paper, we present SEFRQO, a Self-Evolving Fine-tuned RAG-based Query Optimizer. SEFRQO mitigates the cold-start problem of LQOs by continuously learning from execution feedback via a Retrieval-Augmented Generation (RAG) framework. We employ both supervised fine-tuning and reinforcement fine-tuning to prepare the LLM to produce syntactically correct and performance-efficient query hints. Moreover, SEFRQO leverages the LLM's in-context learning capabilities by dynamically constructing prompts with references to similar queries and the historical execution record of the same query. This self-evolving paradigm iteratively optimizes the prompt to minimize query execution latency. Evaluations show that SEFRQO outperforms state-of-the-art LQOs, achieving up to 65.05% and 93.57% reductions in query latency on the CEB and Stack workloads, respectively, compared to PostgreSQL.

Abstract
Traditional ranking systems rely on proxy loss functions that assume simplistic user behavior, such as users preferring a rank list where items are sorted by hand-crafted relevance. However, real-world user interactions are influenced by complex behavioral biases, including position bias, brand affinity, decoy effects, and similarity aversion, which these objectives fail to capture. As a result, models trained on such losses often misalign with actual user utility, such as the probability of any click or purchase across the ranked list. In this work, we propose a data-driven framework for modeling user behavior through counterfactual reward learning. Our method, RewardRank, first trains a deep utility model to estimate user engagement for entire item permutations using logged data. Then, a ranking policy is optimized to maximize predicted utility via differentiable soft permutation operators, enabling end-to-end training over the space of factual and counterfactual rankings. To address the challenge of evaluation without ground-truth for unseen permutations, we introduce two automated protocols: (i) $\textit{KD-Eval}$, using a position-aware oracle for counterfactual reward estimation, and (ii) $\textit{LLM-Eval}$, which simulates user preferences via large language models. Experiments on large-scale benchmarks, including Baidu-ULTR and the Amazon KDD Cup datasets, demonstrate that our approach consistently outperforms strong baselines, highlighting the effectiveness of modeling user behavior dynamics for utility-optimized ranking. Our code is available at: https://github.com/GauravBh1010tt/RewardRank

Abstract
We present an algorithm to recover a minimal local apolar scheme to a homogeneous polynomial $F$. The socle degree of the scheme determines whether it is evinced by a Generalized Additive Decomposition (GAD) of $F$ or of an extension. We give constructive procedures for both cases and compute the Hilbert function efficiently via Hankel operators.