Entropy-Regularized Process Reward Model

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

$\textbf{Only-IF}$:Revealing the Decisive Effect of Instruction Diversity on Generalization

Understanding and accurately following instructions is critical for large language models (LLMs) to be effective across diverse tasks. In this work, we rigorously examine the key factors that enable models to generalize to unseen instructions, providing insights to guide the collection of data for instruction-tuning. Through controlled experiments, inspired by the Turing-complete Markov algorithm, we demonstrate that such generalization $\textbf{only emerges}$ when training data is diversified enough across semantic domains. Our findings also reveal that merely diversifying within limited domains fails to ensure robust generalization. In contrast, cross-domain data diversification, even under constrained data budgets, significantly enhances a model's adaptability. We further extend our analysis to real-world scenarios, including fine-tuning of $\textit{$\textbf{specialist}$}$ and $\textit{$\textbf{generalist}$}$ models. In both cases, we demonstrate that 1) better performance can be achieved by increasing the diversity of an established dataset while keeping the data size constant, and 2) when scaling up the data, diversifying the semantics of instructions is more effective than simply increasing the quantity of similar data. Our research provides important insights for dataset collation, particularly when optimizing model performance by expanding training data for both specialist and generalist scenarios. We show that careful consideration of data diversification is key: training specialist models with data extending beyond their core domain leads to significant performance improvements, while generalist models benefit from diverse data mixtures that enhance their overall instruction-following capabilities across a wide range of applications. Our results highlight the critical role of strategic diversification and offer clear guidelines for improving data quality.

Visual Prompting in LLMs for Enhancing Emotion Recognition

Vision Large Language Models (VLLMs) are transforming the intersection of computer vision and natural language processing. Nonetheless, the potential of using visual prompts for emotion recognition in these models remains largely unexplored and untapped. Traditional methods in VLLMs struggle with spatial localization and often discard valuable global context. To address this problem, we propose a Set-of-Vision prompting (SoV) approach that enhances zero-shot emotion recognition by using spatial information, such as bounding boxes and facial landmarks, to mark targets precisely. SoV improves accuracy in face count and emotion categorization while preserving the enriched image context. Through a battery of experimentation and analysis of recent commercial or open-source VLLMs, we evaluate the SoV model's ability to comprehend facial expressions in natural environments. Our findings demonstrate the effectiveness of integrating spatial visual prompts into VLLMs for improving emotion recognition performance.

QEDCartographer: Automating Formal Verification Using Reward-Free Reinforcement Learning

Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a search through the proof space using a theorem prover. Unfortunately, the theorem prover provides only the crudest estimate of progress, resulting in effectively undirected search. To address this problem, we create QEDCartographer, an automated proof-synthesis tool that combines supervised and reinforcement learning to more effectively explore the proof space. QEDCartographer incorporates the proofs' branching structure, enabling reward-free search and overcoming the sparse reward problem inherent to formal verification. We evaluate QEDCartographer using the CoqGym benchmark of 68.5K theorems from 124 open-source Coq projects. QEDCartographer fully automatically proves 21.4% of the test-set theorems. Previous search-based proof-synthesis tools Tok, Tac, ASTactic, Passport, and Proverbot9001, which rely only on supervised learning, prove 9.6%, 9.8%, 10.9%, 12.5%, and 19.8%, respectively. Diva, which combines 62 tools, proves 19.2%. Comparing to the most effective prior tool, Proverbot9001, QEDCartographer produces 26% shorter proofs 27% faster, on average over the theorems both tools prove. Together, QEDCartographer and non-learning-based CoqHammer prove 31.8% of the theorems, while CoqHammer alone proves 26.6%. Our work demonstrates that reinforcement learning is a fruitful research direction for improving proof-synthesis tools' search mechanisms.

PLUM: Preference Learning Plus Test Cases Yields Better Code Language Models

Instruction-finetuned code language models (LMs) have shown promise in various programming tasks. They are trained, using a language modeling objective, on natural language instructions and gold code snippet pairs. Recent evidence suggests that these models, never exposed to incorrect solutions during training, often struggle to distinguish between correct and incorrect solutions. This observation raises our inquiry: Can preference learning, which trains models to prefer correct solutions over incorrect ones, help push the boundaries of code LMs even further? We propose PLUM, a novel \textbf{p}reference \textbf{l}earning framework a\textbf{u}gmented with test cases tailored for code L\textbf{M}s.PLUM aims to investigate the key success factors and potential benefits of preference learning in code LMs, which remain elusive despite its success in aligning LMs with human values. PLUM consists of three stages: (1) Generating test cases for natural language instructions, (2) sampling candidate solutions from the policy and evaluating them against the test cases to create a preference dataset, which is then used to (3) train the policy with a preference learning algorithm. Experiments demonstrate that PLUM substantially improves the performance of existing code LMs on established code generation benchmarks such as HumanEval (+) and MBPP (+), even for the state-of-the-art open-source language model CodeQwen-1.5-7B-Chat. PLUM complements the supervised fine-tuning (SFT) stage, demonstrating synergistic effects.

From Symbolic Tasks to Code Generation: Diversification Yields Better Task Performers

Instruction tuning -- tuning large language models on instruction-output pairs -- is a promising technique for making models better adapted to the real world. Yet, the key factors driving the model's capability to understand and follow instructions not seen during training remain under-explored. Our investigation begins with a series of synthetic experiments within the theoretical framework of a Turing-complete algorithm called Markov algorithm, which allows fine-grained control over the instruction-tuning data. Generalization and robustness with respect to the training distribution emerge once a diverse enough set of tasks is provided, even though very few examples are provided for each task. We extend these initial results to a real-world application scenario of code generation and find that a more diverse instruction set, extending beyond code-related tasks, improves the performance of code generation. Our observations suggest that a more diverse semantic space for instruction-tuning sets greatly improves the model's ability to follow instructions and perform tasks.

Instruction Diversity Drives Generalization To Unseen Tasks

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such \emph{unseen tasks} are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

Transformer-Based Models Are Not Yet Perfect At Learning to Emulate Structural Recursion

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general \textit{syntax} of structural recursion, coupled with two different frameworks for understanding their \textit{semantics} -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

PACE-LM: Prompting and Augmentation for Calibrated Confidence Estimation with GPT-4 in Cloud Incident Root Cause Analysis

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.