How does Transformer Learn Implicit Reasoning?

Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly -- producing correct answers without explicitly verbalizing intermediate steps -- but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a three-stage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

How Is LLM Reasoning Distracted by Irrelevant Context? An Analysis Using a Controlled Benchmark

We introduce Grade School Math with Distracting Context (GSM-DC), a synthetic benchmark to evaluate Large Language Models' (LLMs) reasoning robustness against systematically controlled irrelevant context (IC). GSM-DC constructs symbolic reasoning graphs with precise distractor injections, enabling rigorous, reproducible evaluation. Our experiments demonstrate that LLMs are significantly sensitive to IC, affecting both reasoning path selection and arithmetic accuracy. Additionally, training models with strong distractors improves performance in both in-distribution and out-of-distribution scenarios. We further propose a stepwise tree search guided by a process reward model, which notably enhances robustness in out-of-distribution conditions.

ConciseRL: Conciseness-Guided Reinforcement Learning for Efficient Reasoning Models

Large language models excel at complex tasks by breaking down problems into structured reasoning steps. However, reasoning traces often extend beyond reaching a correct answer, causing wasted computation, reduced readability, and hallucinations. To address this, we introduce a novel hyperparameter-free conciseness score used as a reward signal within a reinforcement learning framework to guide models toward generating correct and concise reasoning traces. This score is evaluated by a large language model acting as a judge, enabling dynamic, context-aware feedback beyond simple token length. Our method achieves state-of-the-art efficiency-accuracy trade-offs on the MATH dataset, reducing token usage by up to 31x on simple problems while improving accuracy by 7%, and on the hardest problems, it outperforms full reasoning by +7.5% accuracy with up to 3.6x fewer tokens. On TheoremQA, our method improves accuracy by +2.2% using 12.5x fewer tokens. We also conduct ablation studies on the judge model, reward composition, and problem difficulty, showing that our method dynamically adapts reasoning length based on problem difficulty and benefits significantly from stronger judges. The code, model weights, and datasets are open-sourced at https://github.com/RazvanDu/ConciseRL.

FinTMMBench: Benchmarking Temporal-Aware Multi-Modal RAG in Finance

Finance decision-making often relies on in-depth data analysis across various data sources, including financial tables, news articles, stock prices, etc. In this work, we introduce FinTMMBench, the first comprehensive benchmark for evaluating temporal-aware multi-modal Retrieval-Augmented Generation (RAG) systems in finance. Built from heterologous data of NASDAQ 100 companies, FinTMMBench offers three significant advantages. 1) Multi-modal Corpus: It encompasses a hybrid of financial tables, news articles, daily stock prices, and visual technical charts as the corpus. 2) Temporal-aware Questions: Each question requires the retrieval and interpretation of its relevant data over a specific time period, including daily, weekly, monthly, quarterly, and annual periods. 3) Diverse Financial Analysis Tasks: The questions involve 10 different tasks, including information extraction, trend analysis, sentiment analysis and event detection, etc. We further propose a novel TMMHybridRAG method, which first leverages LLMs to convert data from other modalities (e.g., tabular, visual and time-series data) into textual format and then incorporates temporal information in each node when constructing graphs and dense indexes. Its effectiveness has been validated in extensive experiments, but notable gaps remain, highlighting the challenges presented by our FinTMMBench.

InductionBench: LLMs Fail in the Simplest Complexity Class

Large language models (LLMs) have shown remarkable improvements in reasoning and many existing benchmarks have been addressed by models such as o1 and o3 either fully or partially. However, a majority of these benchmarks emphasize deductive reasoning, including mathematical and coding tasks in which rules such as mathematical axioms or programming syntax are clearly defined, based on which LLMs can plan and apply these rules to arrive at a solution. In contrast, inductive reasoning, where one infers the underlying rules from observed data, remains less explored. Such inductive processes lie at the heart of scientific discovery, as they enable researchers to extract general principles from empirical observations. To assess whether LLMs possess this capacity, we introduce InductionBench, a new benchmark designed to evaluate the inductive reasoning ability of LLMs. Our experimental findings reveal that even the most advanced models available struggle to master the simplest complexity classes within the subregular hierarchy of functions, highlighting a notable deficiency in current LLMs' inductive reasoning capabilities. Coda and data are available https://github.com/Wenyueh/inductive_reasoning_benchmark.

Aristotle: Mastering Logical Reasoning with A Logic-Complete Decompose-Search-Resolve Framework

In the context of large language models (LLMs), current advanced reasoning methods have made impressive strides in various reasoning tasks. However, when it comes to logical reasoning tasks, major challenges remain in both efficacy and efficiency. This is rooted in the fact that these systems fail to fully leverage the inherent structure of logical tasks throughout the reasoning processes such as decomposition, search, and resolution. To address this, we propose a logic-complete reasoning framework, Aristotle, with three key components: Logical Decomposer, Logical Search Router, and Logical Resolver. In our framework, symbolic expressions and logical rules are comprehensively integrated into the entire reasoning process, significantly alleviating the bottlenecks of logical reasoning, i.e., reducing sub-task complexity, minimizing search errors, and resolving logical contradictions. The experimental results on several datasets demonstrate that Aristotle consistently outperforms state-of-the-art reasoning frameworks in both accuracy and efficiency, particularly excelling in complex logical reasoning scenarios. We will open-source all our code at https://github.com/Aiden0526/Aristotle.

AntiLeak-Bench: Preventing Data Contamination by Automatically Constructing Benchmarks with Updated Real-World Knowledge

Data contamination hinders fair LLM evaluation by introducing test data into newer models' training sets. Existing studies solve this challenge by updating benchmarks with newly collected data. However, they fail to guarantee contamination-free evaluation as the newly collected data may contain pre-existing knowledge, and their benchmark updates rely on intensive human labor. To address these issues, we in this paper propose AntiLeak-Bench, an automated anti-leakage benchmarking framework. Instead of simply using newly collected data, we construct samples with explicitly new knowledge absent from LLMs' training sets, which thus ensures strictly contamination-free evaluation. We further design a fully automated workflow to build and update our benchmark without human labor. This significantly reduces the cost of benchmark maintenance to accommodate emerging LLMs. Through extensive experiments, we highlight that data contamination likely exists before LLMs' cutoff time and demonstrate AntiLeak-Bench effectively overcomes this challenge.

Combating Multimodal LLM Hallucination via Bottom-up Holistic Reasoning

Recent advancements in multimodal large language models (MLLMs) have shown unprecedented capabilities in advancing various vision-language tasks. However, MLLMs face significant challenges with hallucinations, and misleading outputs that do not align with the input data. While existing efforts are paid to combat MLLM hallucinations, several pivotal challenges are still unsolved. First, while current approaches aggressively focus on addressing errors at the perception level, another important type at the cognition level requiring factual commonsense can be overlooked. In addition, existing methods might fall short in finding a more effective way to represent visual input, which is yet a key bottleneck that triggers visual hallucinations. Moreover, MLLMs can frequently be misled by faulty textual inputs and cause hallucinations, while unfortunately, this type of issue has long been overlooked by existing studies. Inspired by human intuition in handling hallucinations, this paper introduces a novel bottom-up reasoning framework. Our framework systematically addresses potential issues in both visual and textual inputs by verifying and integrating perception-level information with cognition-level commonsense knowledge, ensuring more reliable outputs. Extensive experiments demonstrate significant improvements in multiple hallucination benchmarks after integrating MLLMs with the proposed framework. In-depth analyses reveal the great potential of our methods in addressing perception- and cognition-level hallucinations.

RuleArena: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios

This paper introduces RuleArena, a novel and challenging benchmark designed to evaluate the ability of large language models (LLMs) to follow complex, real-world rules in reasoning. Covering three practical domains -- airline baggage fees, NBA transactions, and tax regulations -- RuleArena assesses LLMs' proficiency in handling intricate natural language instructions that demand long-context understanding, logical reasoning, and accurate mathematical computation. Two key attributes distinguish RuleArena from traditional rule-based reasoning benchmarks: (1) it extends beyond standard first-order logic representations, and (2) it is grounded in authentic, practical scenarios, providing insights into the suitability and reliability of LLMs for real-world applications. Our findings reveal several notable limitations in LLMs: (1) they struggle to identify and apply the appropriate rules, frequently becoming confused by similar but distinct regulations, (2) they cannot consistently perform accurate mathematical computations, even when they correctly identify the relevant rules, and (3) in general, they perform poorly in the benchmark. These results highlight significant challenges in advancing LLMs' rule-guided reasoning capabilities in real-life applications.

Improving Causal Reasoning in Large Language Models: A Survey

Causal reasoning (CR) is a crucial aspect of intelligence, essential for problem-solving, decision-making, and understanding the world. While large language models (LLMs) can generate rationales for their outputs, their ability to reliably perform causal reasoning remains uncertain, often falling short in tasks requiring a deep understanding of causality. In this survey, we provide a comprehensive review of research aimed at enhancing LLMs for causal reasoning. We categorize existing methods based on the role of LLMs: either as reasoning engines or as helpers providing knowledge or data to traditional CR methods, followed by a detailed discussion of the methodologies in each category. We then evaluate the performance of LLMs on various causal reasoning tasks, providing key findings and in-depth analysis. Finally, we provide insights from current studies and highlight promising directions for future research. We aim for this work to serve as a comprehensive resource, fostering further advancements in causal reasoning with LLMs. Resources are available at https://github.com/chendl02/Awesome-LLM-causal-reasoning.