In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements.

Machine learning technologies have been used in a wide range of practical systems.In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements.However, it is difficult to obtain a model that satisfies requirements by just learning from examples.A simple solution is to add a module that checks whether the input-output pairs meet the requirements and then modifies the model's outputs. Such a module, which we call a {\em concurrent verifier} (CV), can give a certification, although how the generalizability of the machine learning model changes using a CV is unclear. This paper gives a generalization analysis of learning with a CV. We analyze how the learnability of a machine learning model changes with a CV and show a condition where we can obtain a guaranteed hypothesis using a verifier only in the inference time.We also show that typical error bounds based on Rademacher complexity will be no larger than that of the original model when using a CV in multi-class classification and structured prediction settings.

Existing LLM-based automatic test generation methods mainly produce input and expected output pairs to categorize the intended behavior of correct programs. Although straightforward, these methods have limited diversity in generated tests and cannot provide enough debugging information. We propose HarnessLLM, a two-stage training pipeline that enables LLMs to write harness code for testing. Particularly, LLMs generate code that synthesizes inputs and validates the observed outputs, allowing complex test cases and flexible output validation such as invariant checking. To achieve this, we train LLMs with SFT followed by RLVR with a customized reward design. Experiments show that HarnessLLM outperforms input-output-based testing in bug finding and testing strategy diversity. HarnessLLM further benefits the code generation performance through test-time scaling with our generated test cases as inference-phase validation. Our code is available at https://github.com/UCSB-NLP-Chang/HarnessLLM.git.

Recent advances in artificial intelligence have demonstrated the learnability of symbolic computation through end-to-end deep learning. Given a sufficient number of examples of symbolic expressions before and after the target computation, Transformer models - highly effective learners of sequence-to-sequence functions - can be trained to emulate the computation. This development opens up several intriguing challenges and new research directions, which require active contributions from the symbolic computation community. In this work, we introduce Computer Algebra with Transformer (CALT), a user-friendly Python library designed to help non-experts in deep learning train models for symbolic computation tasks.

In-context learning (ICL) enables Large Language Models (LLMs) to adapt to new tasks using few examples, with task vectors - specific hidden state activations - hypothesized to encode task information. Existing studies are limited by small-scale benchmarks, restricting comprehensive analysis. We introduce QuiteAFew, a novel dataset of 3,096 diverse few-shot tasks, each with 30 input-output pairs derived from the Alpaca dataset. Experiments with Llama-3-8B on QuiteAFew reveal: (1) task vector performance peaks at an intermediate layer (e.g., 15th), (2) effectiveness varies significantly by task type, and (3) complex tasks rely on multiple, subtask-specific vectors rather than a single vector, suggesting distributed task knowledge representation.

It is sometimes assumed that Large Language Models (LLMs) know language, or for example that they know that Paris is the capital of France. But what -- if anything -- do LLMs actually know? In this paper, I argue that LLMs can acquire tacit knowledge as defined by Martin Davies (1990). Whereas Davies himself denies that neural networks can acquire tacit knowledge, I demonstrate that certain architectural features of LLMs satisfy the constraints of semantic description, syntactic structure, and causal systematicity. Thus, tacit knowledge may serve as a conceptual framework for describing, explaining, and intervening on LLMs and their behavior.

Multilingual hallucination detection stands as an underexplored challenge, which the Mu-SHROOM shared task seeks to address. In this work, we propose an efficient, training-free LLM prompting strategy that enhances detection by translating multilingual text spans into English. Our approach achieves competitive rankings across multiple languages, securing two first positions in low-resource languages. The consistency of our results highlights the effectiveness of our translation strategy for hallucination detection, demonstrating its applicability regardless of the source language.

Large Language Model (LLM)-based agents have demonstrated remarkable success in solving complex tasks across a wide range of general-purpose applications. However, their performance often degrades in context-specific scenarios, such as specialized industries or research domains, where the absence of domain-relevant knowledge leads to imprecise or suboptimal outcomes. To address this challenge, our work introduces a systematic approach to enhance the contextual adaptability of LLM-based agents by optimizing their underlying prompts-critical components that govern agent behavior, roles, and interactions. Manually crafting optimized prompts for context-specific tasks is labor-intensive, error-prone, and lacks scalability. In this work, we introduce an Extractor-Generator framework designed to automate the optimization of contextual LLM-based agents. Our method operates through two key stages: (i) feature extraction from a dataset of gold-standard input-output examples, and (ii) prompt generation via a high-level optimization strategy that iteratively identifies underperforming cases and applies self-improvement techniques. This framework substantially improves prompt adaptability by enabling more precise generalization across diverse inputs, particularly in context-specific tasks where maintaining semantic consistency and minimizing error propagation are critical for reliable performance. Although developed with single-stage workflows in mind, the approach naturally extends to multi-stage workflows, offering broad applicability across various agent-based systems. Empirical evaluations demonstrate that our framework significantly enhances the performance of prompt-optimized agents, providing a structured and efficient approach to contextual LLM-based agents.