Beyond Homogeneous Attention: Memory-Efficient LLMs via Fourier-Approximated KV Cache

Large Language Models struggle with memory demands from the growing Key-Value (KV) cache as context lengths increase. Existing compression methods homogenize head dimensions or rely on attention-guided token pruning, often sacrificing accuracy or introducing computational overhead. We propose FourierAttention, a training-free framework that exploits the heterogeneous roles of transformer head dimensions: lower dimensions prioritize local context, while upper ones capture long-range dependencies. By projecting the long-context-insensitive dimensions onto orthogonal Fourier bases, FourierAttention approximates their temporal evolution with fixed-length spectral coefficients. Evaluations on LLaMA models show that FourierAttention achieves the best long-context accuracy on LongBench and Needle-In-A-Haystack (NIAH). Besides, a custom Triton kernel, FlashFourierAttention, is designed to optimize memory via streamlined read-write operations, enabling efficient deployment without performance compromise.

Spectra-to-Structure and Structure-to-Spectra Inference Across the Periodic Table

X-ray Absorption Spectroscopy (XAS) is a powerful technique for probing local atomic environments, yet its interpretation remains limited by the need for expert-driven analysis, computationally expensive simulations, and element-specific heuristics. Recent advances in machine learning have shown promise for accelerating XAS interpretation, but many existing models are narrowly focused on specific elements, edge types, or spectral regimes. In this work, we present XAStruct, a learning framework capable of both predicting XAS spectra from crystal structures and inferring local structural descriptors from XAS input. XAStruct is trained on a large-scale dataset spanning over 70 elements across the periodic table, enabling generalization to a wide variety of chemistries and bonding environments. The model includes the first machine learning approach for predicting neighbor atom types directly from XAS spectra, as well as a unified regression model for mean nearest-neighbor distance that requires no element-specific tuning. While we explored integrating the two pipelines into a single end-to-end model, empirical results showed performance degradation. As a result, the two tasks were trained independently to ensure optimal accuracy and task-specific performance. By combining deep neural networks for complex structure-property mappings with efficient baseline models for simpler tasks, XAStruct offers a scalable and extensible solution for data-driven XAS analysis and local structure inference. The source code will be released upon paper acceptance.

Safe: Enhancing Mathematical Reasoning in Large Language Models via Retrospective Step-aware Formal Verification

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework $Safe$. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework $Safe$ across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose $FormalStep$ as a benchmark for step correctness theorem proving with $30,809$ formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Stepwise Reasoning Checkpoint Analysis: A Test Time Scaling Method to Enhance LLMs' Reasoning

Mathematical reasoning through Chain-of-Thought (CoT) has emerged as a powerful capability of Large Language Models (LLMs), which can be further enhanced through Test-Time Scaling (TTS) methods like Beam Search and DVTS. However, these methods, despite improving accuracy by allocating more computational resources during inference, often suffer from path homogenization and inefficient use of intermediate results. To address these limitations, we propose Stepwise Reasoning Checkpoint Analysis (SRCA), a framework that introduces checkpoints between reasoning steps. It incorporates two key strategies: (1) Answer-Clustered Search, which groups reasoning paths by their intermediate checkpoint answers to maintain diversity while ensuring quality, and (2) Checkpoint Candidate Augmentation, which leverages all intermediate answers for final decision-making. Our approach effectively reduces path homogenization and creates a fault-tolerant mechanism by utilizing high-quality intermediate results. Experimental results show that SRCA improves reasoning accuracy compared to existing TTS methods across various mathematical datasets.

ToolACE-R: Tool Learning with Adaptive Self-Refinement

Tool learning, which allows Large Language Models (LLMs) to leverage external tools for solving complex user tasks, has emerged as a promising avenue for extending model capabilities. However, current approaches primarily focus on data synthesis for fine-tuning LLMs to invoke tools effectively, largely ignoring how to fully stimulate the potential of the model. In this paper, we propose ToolACE-R, a novel method that introduces adaptive self-refinement for tool invocations. Our approach features a model-aware iterative training procedure that progressively incorporates more training samples based on the model's evolving capabilities. Additionally, it allows LLMs to iteratively refine their tool calls, optimizing performance without requiring external feedback. To further enhance computational efficiency, we integrate an adaptive mechanism when scaling the inference time, enabling the model to autonomously determine when to stop the refinement process. We conduct extensive experiments across several benchmark datasets, showing that ToolACE-R achieves competitive performance compared to advanced API-based models, even without any refinement. Furthermore, its performance can be further improved efficiently through adaptive self-refinement. Our results demonstrate the effectiveness of the proposed method, which is compatible with base models of various sizes, offering a promising direction for more efficient tool learning.

DAST: Difficulty-Aware Self-Training on Large Language Models

Present Large Language Models (LLM) self-training methods always under-sample on challenging queries, leading to inadequate learning on difficult problems which limits LLMs' ability. Therefore, this work proposes a difficulty-aware self-training (DAST) framework that focuses on improving both the quantity and quality of self-generated responses on challenging queries during self-training. DAST is specified in three components: 1) sampling-based difficulty level estimation, 2) difficulty-aware data augmentation, and 3) the self-training algorithm using SFT and DPO respectively. Experiments on mathematical tasks demonstrate the effectiveness and generalization of DAST, highlighting the critical role of difficulty-aware strategies in advancing LLM self-training.

KnowLogic: A Benchmark for Commonsense Reasoning via Knowledge-Driven Data Synthesis

Current evaluations of commonsense reasoning in LLMs are hindered by the scarcity of natural language corpora with structured annotations for reasoning tasks. To address this, we introduce KnowLogic, a benchmark generated through a knowledge-driven synthetic data strategy. KnowLogic integrates diverse commonsense knowledge, plausible scenarios, and various types of logical reasoning. One of the key advantages of KnowLogic is its adjustable difficulty levels, allowing for flexible control over question complexity. It also includes fine-grained labels for in-depth evaluation of LLMs' reasoning abilities across multiple dimensions. Our benchmark consists of 3,000 bilingual (Chinese and English) questions across various domains, and presents significant challenges for current LLMs, with the highest-performing model achieving only 69.57\%. Our analysis highlights common errors, such as misunderstandings of low-frequency commonsense, logical inconsistencies, and overthinking. This approach, along with our benchmark, provides a valuable tool for assessing and enhancing LLMs' commonsense reasoning capabilities and can be applied to a wide range of knowledge domains.

Tgea: An error-annotated dataset and benchmark tasks for text generation from pretrained language models

In order to deeply understand the capability of pretrained language models in text generation and conduct a diagnostic evaluation, we propose TGEA, an error-annotated dataset with multiple benchmark tasks for text generation from pretrained language models (PLMs). We use carefully selected prompt words to guide GPT-2 to generate candidate sentences, from which we select 47K for error annotation. Crowdsourced workers manually check each of these sentences and detect 12k erroneous sentences. We create an error taxonomy to cover 24 types of errors occurring in these erroneous sentences according to the nature of errors with respect to linguistics and knowledge (eg, common sense). For each erroneous span in PLM-generated sentences, we also detect another span that is closely associated with it. Each error is hence manually labeled with comprehensive annotations, including the span of the error, the associated span, minimal correction to the error, the type of the error, and rationale behind the error. Apart from the fully annotated dataset, we also present a detailed description of the data collection procedure, statistics and analysis of the dataset. This is the first dataset with comprehensive annotations for PLM-generated texts, which facilitates the diagnostic evaluation of PLM-based text generation. Furthermore, we use TGEA as a benchmark dataset and propose a series of automatic diagnosis tasks, including error detection, error type classification, associated span detection, error rationale generation, to further promote future study on the automatic error detection and correction on texts generated by pretrained language models.

The Box is in the Pen: Evaluating Commonsense Reasoning in Neural Machine Translation

Does neural machine translation yield translations that are congenial with common sense? In this paper, we present a test suite to evaluate the commonsense reasoning capability of neural machine translation. The test suite consists of three test sets, covering lexical and contextless/contextual syntactic ambiguity that requires commonsense knowledge to resolve. We manually create 1,200 triples, each of which contain a source sentence and two contrastive translations, involving 7 different common sense types. Language models pretrained on large-scale corpora, such as BERT, GPT-2, achieve a commonsense reasoning accuracy of lower than 72% on target translations of this test suite. We conduct extensive experiments on the test suite to evaluate commonsense reasoning in neural machine translation and investigate factors that have impact on this capability. Our experiments and analyses demonstrate that neural machine translation performs poorly on commonsense reasoning of the three ambiguity types in terms of both reasoning accuracy (60.1%) and reasoning consistency (31%). The built commonsense test suite is available at https://github.com/tjunlp-lab/CommonMT.

Learning to Align Multi-Faceted Evaluation: A Unified and Robust Framework

Large Language Models (LLMs) are being used more and more extensively for automated evaluation in various scenarios. Previous studies have attempted to fine-tune open-source LLMs to replicate the evaluation explanations and judgments of powerful proprietary models, such as GPT-4. However, these methods are largely limited to text-based analyses under predefined general criteria, resulting in reduced adaptability for unseen instructions and demonstrating instability in evaluating adherence to quantitative and structural constraints. To address these limitations, we propose a novel evaluation framework, ARJudge, that adaptively formulates evaluation criteria and synthesizes both text-based and code-driven analyses to evaluate LLM responses. ARJudge consists of two components: a fine-tuned Analyzer that generates multi-faceted evaluation analyses and a tuning-free Refiner that combines and refines all analyses to make the final judgment. We construct a Composite Analysis Corpus that integrates tasks for evaluation criteria generation alongside text-based and code-driven analysis generation to train the Analyzer. Our results demonstrate that ARJudge outperforms existing fine-tuned evaluators in effectiveness and robustness. Furthermore, it demonstrates the importance of multi-faceted evaluation and code-driven analyses in enhancing evaluation capabilities.