Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

100-LongBench: Are de facto Long-Context Benchmarks Literally Evaluating Long-Context Ability?

Long-context capability is considered one of the most important abilities of LLMs, as a truly long context-capable LLM enables users to effortlessly process many originally exhausting tasks -- e.g., digesting a long-form document to find answers vs. directly asking an LLM about it. However, existing real-task-based long-context evaluation benchmarks have two major shortcomings. First, benchmarks like LongBench often do not provide proper metrics to separate long-context performance from the model's baseline ability, making cross-model comparison unclear. Second, such benchmarks are usually constructed with fixed input lengths, which limits their applicability across different models and fails to reveal when a model begins to break down. To address these issues, we introduce a length-controllable long-context benchmark and a novel metric that disentangles baseline knowledge from true long-context capabilities. Experiments demonstrate the superiority of our approach in effectively evaluating LLMs.

SELF: Self-Extend the Context Length With Logistic Growth Function

Large language models suffer issues when operated on long contexts that are larger than their training context length due to the standard position encoding for tokens in the attention layer. Tokens a long distance apart will rarely have an effect on each other and long prompts yield unexpected results. To solve this problem, we propose SELF (Self-Extend the Context Length With Logistic Growth Function): a solution of grouping consecutive tokens at varying group sizes using a logistic capacity equation combined with a constant group size at smaller relative distances. Our model had an increase in performance of up to 12% compared to the LongLM extension method in LEval (specifically on the Qwen model). On summarization related tasks in LongBench, our model performed up to 6.4% better than LongLM (specifically on the Llama-2-7b model). On reading comprehension tasks from LEval, our model performed up to 5.4% better than the LongLM. Our code is available at https://github.com/alexeipc/SELF-LLM.

Longer Context, Deeper Thinking: Uncovering the Role of Long-Context Ability in Reasoning

Recent language models exhibit strong reasoning capabilities, yet the influence of long-context capacity on reasoning remains underexplored. In this work, we hypothesize that current limitations in reasoning stem, in part, from insufficient long-context capacity, motivated by empirical observations such as (1) higher context window length often leads to stronger reasoning performance, and (2) failed reasoning cases resemble failed long-context cases. To test this hypothesis, we examine whether enhancing a model's long-context ability before Supervised Fine-Tuning (SFT) leads to improved reasoning performance. Specifically, we compared models with identical architectures and fine-tuning data but varying levels of long-context capacity. Our results reveal a consistent trend: models with stronger long-context capacity achieve significantly higher accuracy on reasoning benchmarks after SFT. Notably, these gains persist even on tasks with short input lengths, indicating that long-context training offers generalizable benefits for reasoning performance. These findings suggest that long-context modeling is not just essential for processing lengthy inputs, but also serves as a critical foundation for reasoning. We advocate for treating long-context capacity as a first-class objective in the design of future language models.

InfiGUI-R1: Advancing Multimodal GUI Agents from Reactive Actors to Deliberative Reasoners

Multimodal Large Language Models (MLLMs) have powered Graphical User Interface (GUI) Agents, showing promise in automating tasks on computing devices. Recent works have begun exploring reasoning in GUI tasks with encouraging results. However, many current approaches rely on manually designed reasoning templates, which may result in reasoning that is not sufficiently robust and adaptive for complex GUI environments. Meanwhile, some existing agents continue to operate as Reactive Actors, relying primarily on implicit reasoning that may lack sufficient depth for GUI tasks demanding planning and error recovery. We argue that advancing these agents requires a shift from reactive acting towards acting based on deliberate reasoning. To facilitate this transformation, we introduce InfiGUI-R1, an MLLM-based GUI agent developed through our Actor2Reasoner framework, a reasoning-centric, two-stage training approach designed to progressively evolve agents from Reactive Actors to Deliberative Reasoners. The first stage, Reasoning Injection, focuses on establishing a basic reasoner. We employ Spatial Reasoning Distillation to transfer cross-modal spatial reasoning capabilities from teacher models to MLLMs through trajectories with explicit reasoning steps, enabling models to integrate GUI visual-spatial information with logical reasoning before action generation. The second stage, Deliberation Enhancement, refines the basic reasoner into a deliberative one using Reinforcement Learning. This stage introduces two approaches: Sub-goal Guidance, which rewards models for generating accurate intermediate sub-goals, and Error Recovery Scenario Construction, which creates failure-and-recovery training scenarios from identified prone-to-error steps. Experimental results show InfiGUI-R1 achieves strong performance in GUI grounding and trajectory tasks. Resources at https://github.com/Reallm-Labs/InfiGUI-R1.

Speculative Thinking: Enhancing Small-Model Reasoning with Large Model Guidance at Inference Time

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free framework that enables large reasoning models to guide smaller ones during inference at the reasoning level, distinct from speculative decoding, which operates at the token level. Our approach is based on two observations: (1) reasoning-supportive tokens such as "wait" frequently appear after structural delimiters like "\n\n", serving as signals for reflection or continuation; and (2) larger models exhibit stronger control over reflective behavior, reducing unnecessary backtracking while improving reasoning quality. By strategically delegating reflective steps to a more capable model, our method significantly boosts the reasoning accuracy of reasoning models while shortening their output. With the assistance of the 32B reasoning model, the 1.5B model's accuracy on MATH500 increases from 83.2% to 89.4%, marking a substantial improvement of 6.2%. Simultaneously, the average output length is reduced from 5439 tokens to 4583 tokens, representing a 15.7% decrease. Moreover, when applied to a non-reasoning model (Qwen-2.5-7B-Instruct), our framework boosts its accuracy from 74.0% to 81.8% on the same benchmark, achieving a relative improvement of 7.8%.

CausalRAG: Integrating Causal Graphs into Retrieval-Augmented Generation

Large language models (LLMs) have revolutionized natural language processing (NLP), particularly through Retrieval-Augmented Generation (RAG), which enhances LLM capabilities by integrating external knowledge. However, traditional RAG systems face critical limitations, including disrupted contextual integrity due to text chunking, and over-reliance on semantic similarity for retrieval. To address these issues, we propose CausalRAG, a novel framework that incorporates causal graphs into the retrieval process. By constructing and tracing causal relationships, CausalRAG preserves contextual continuity and improves retrieval precision, leading to more accurate and interpretable responses. We evaluate CausalRAG against regular RAG and graph-based RAG approaches, demonstrating its superiority across several metrics. Our findings suggest that grounding retrieval in causal reasoning provides a promising approach to knowledge-intensive tasks.

You Only Debias Once: Towards Flexible Accuracy-Fairness Trade-offs at Inference Time

Deep neural networks are prone to various bias issues, jeopardizing their applications for high-stake decision-making. Existing fairness methods typically offer a fixed accuracy-fairness trade-off, since the weight of the well-trained model is a fixed point (fairness-optimum) in the weight space. Nevertheless, more flexible accuracy-fairness trade-offs at inference time are practically desired since: 1) stakes of the same downstream task can vary for different individuals, and 2) different regions have diverse laws or regularization for fairness. If using the previous fairness methods, we have to train multiple models, each offering a specific level of accuracy-fairness trade-off. This is often computationally expensive, time-consuming, and difficult to deploy, making it less practical for real-world applications. To address this problem, we propose You Only Debias Once (YODO) to achieve in-situ flexible accuracy-fairness trade-offs at inference time, using a single model that trained only once. Instead of pursuing one individual fixed point (fairness-optimum) in the weight space, we aim to find a "line" in the weight space that connects the accuracy-optimum and fairness-optimum points using a single model. Points (models) on this line implement varying levels of accuracy-fairness trade-offs. At inference time, by manually selecting the specific position of the learned "line", our proposed method can achieve arbitrary accuracy-fairness trade-offs for different end-users and scenarios. Experimental results on tabular and image datasets show that YODO achieves flexible trade-offs between model accuracy and fairness, at ultra-low overheads. For example, if we need $100$ levels of trade-off on the \acse dataset, YODO takes $3.53$ seconds while training $100$ fixed models consumes $425$ seconds. The code is available at https://github.com/ahxt/yodo.

More for Keys, Less for Values: Adaptive KV Cache Quantization

This paper introduces an information-aware quantization framework that adaptively compresses the key-value (KV) cache in large language models (LLMs). Although prior work has underscored the distinct roles of key and value cache during inference, our systematic analysis -- examining singular value distributions, spectral norms, and Frobenius norms -- reveals, for the first time, that key matrices consistently exhibit higher norm values and are more sensitive to quantization than value matrices. Furthermore, our theoretical analysis shows that matrices with higher spectral norms amplify quantization errors more significantly. Motivated by these insights, we propose a mixed-precision quantization strategy, KV-AdaQuant, which allocates more bit-width for keys and fewer for values since key matrices have higher norm values. With the same total KV bit budget, this approach effectively mitigates error propagation across transformer layers while achieving significant memory savings. Our extensive experiments on multiple LLMs (1B--70B) demonstrate that our mixed-precision quantization scheme maintains high model accuracy even under aggressive compression. For instance, using 4-bit for Key and 2-bit for Value achieves an accuracy of 75.2%, whereas reversing the assignment (2-bit for Key and 4-bit for Value) yields only 54.7% accuracy. The code is available at https://tinyurl.com/kv-adaquant

Thinking Preference Optimization

Supervised Fine-Tuning (SFT) has been a go-to and effective method for enhancing long chain-of-thought (CoT) reasoning in relatively small LLMs by fine-tuning them with long CoT responses from larger LLMs. To continually improve reasoning abilities, we can either collect new high-quality long CoT reasoning SFT data or repeatedly train on existing SFT datasets. However, acquiring new long CoT SFT data is costly and limited, while repeated training often results in a performance plateau or decline. To further boost the performance with the SFT data, we propose Thinking Preference Optimization (ThinkPO), a simple yet effective post-SFT method that enhances long CoT reasoning without requiring new long CoT responses. Instead, ThinkPO utilizes readily available or easily obtainable short CoT reasoning responses as rejected answers and long CoT responses as chosen answers for the same question. It then applies direct preference optimization to encourage the model to favor longer reasoning outputs. Experiments show that ThinkPO further improves the reasoning performance of SFT-ed models, e.g. it increases math reasoning accuracy of SFT-ed models by 8.6% and output length by 25.9%. Notably, ThinkPO is capable of continually boosting the performance of the publicly distilled SFT model, e.g., increasing the official DeepSeek-R1-Distill-Qwen-7B's performance on MATH500 from 87.4% to 91.2%.