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Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset \textsc{MathTrap} by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent ``unseen&#39;&#39; cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not \textbf{spontaneously} combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. We find that LLMs&#39; performance can be improved through the above external intervention. Overall, systematic compositionality remains an open challenge for large language models.

EMNLP 2024

Exploring the Compositional Deficiency of Large Language Models in Mathematical Reasoning Through Trap Problems

scaling law

linear attention

large language model

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ACL 2026

The 64th Annual Meeting of the Association for Computational Linguistics (ACL 2026) will take place in San Diego, California, from July 2 - 7, 2026.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset \textsc{MathTrap} by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent ``unseen'' cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not \textbf{spontaneously} combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. We find that LLMs' performance can be improved through the above external intervention. Overall, systematic compositionality remains an open challenge for large language models.

poster

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Despite demonstrating emergent reasoning abilities, Large Language Models (LLMS) often lose track of complex, multi-step reasoning. Existing studies show that providing guidance via decomposing the original question into multiple subproblems elicits more robustness in LLM reasoning -- a decomposer generates the subproblems, and a solver solves each of these subproblems. However, these techniques fail to accommodate coordination between the decomposer and the solver modules (either in a single model or different specialized ones) -- the decomposer does not keep track of the ability of the solver to follow the decomposed reasoning. In this paper, we propose LM2 to address these challenges. LM2 modularizes the decomposition, solution, and verification into three different language models. The decomposer module identifies the key concepts necessary to solve the problem and generates step-by-step subquestions according to the reasoning requirement. The solver model generates the solution to the subproblems that are then checked by the verifier module; depending upon the feedback from the verifier, the reasoning context is constructed using the subproblems and the solutions. These models are trained to coordinate using policy learning. Exhaustive experimentation suggests the superiority of LM2 over existing methods on in- and out-domain reasoning problems, outperforming the best baselines by 8.1% on MATH, 7.71% on JEEBench, and 9.7% on MedQA problems (code available at https://github.com/ LCS2-
IIITD/Language_Model_Multiplex).

LM2: A Simple Society of Language Models Solves Complex Reasoning

Understanding the inner workings of large language models (LLMs) is crucial for advancing their theoretical foundations and real-world applications. While the attention mechanism and multi-layer perceptrons (MLPs) have been studied independently, their interactions remain largely unexplored. This study investigates how attention heads and next-token neurons interact in LLMs to predict new words. We propose a methodology to identify next-token neurons, find prompts that highly activate them, and determine the upstream attention heads responsible. We then generate and evaluate explanations for the activity of these attention heads in an automated manner. Our findings reveal that some attention heads recognize specific contexts relevant to predicting a token and activate a downstream token-predicting neuron accordingly. This mechanism provides a deeper understanding of how attention heads work with MLP neurons to perform next-token prediction. Our approach offers a foundation for further research into the intricate workings of LLMs and their impact on text generation and understanding.

Interpreting Context Look-ups in Transformers: Investigating Attention-MLP Interactions

Understanding commonsense causality is a unique mark of intelligence for humans. It helps people understand the principles of the real world better and benefits the decision-making process related to causation. For instance, commonsense causality is crucial in judging whether a defendant's action causes the plaintiff's loss in determining legal liability. Despite its significance, a systematic exploration of this topic is notably lacking. Our comprehensive survey bridges this gap by focusing on taxonomies, benchmarks, acquisition methods, qualitative reasoning, and quantitative measurements in commonsense causality, synthesizing insights from over 200 representative articles. Our work aims to provide a systematic overview, update scholars on recent advancements, provide a practical guide for beginners, and highlight promising future research directions in this vital field. A summary of the related literature is available at https://github.com/cui-shaobo/causality-papers .

The Odyssey of Commonsense Causality: From Foundational Benchmarks to Cutting-Edge Reasoning

The advancement of large language models (LLMs) has extended their use to dynamic and interactive real-world applications, where models engage continuously with their environment and potentially enhance their performance over time. Most existing LLM benchmarks evaluate LLMs on i.i.d. tasks, overlooking their ability to learn iteratively from past experiences. Our paper bridges this evaluation gap by proposing a novel framework, LLM-Evolve, which extends established benchmarks to sequential problem-solving settings. LLM-Evolve evaluates LLMs over multiple rounds, providing feedback after each round to build a demonstration memory that the models can query in future tasks. We applied LLM-Evolve to the MMLU, GSM8K, and AgentBench benchmarks, testing 8 state-of-the-art open-source and closed-source models. Results show that LLMs can achieve performance improvements of up to 17% by learning from past interactions, with the quality of retrieval algorithms and feedback significantly influencing this capability. These insights advocate for more understanding and benchmarks for LLMs' performance in evolving interactive scenarios.

LLM-Evolve: Evaluation for LLM’s Evolving Capability on Benchmarks

As machine learning models continue to swiftly advance, calibrating their performance has become a major concern prior to practical and widespread implementation. Most existing calibration methods often negatively impact model accuracy due to the lack of diversity of validation data, resulting in reduced generalizability. To address this, we propose a calibration method that incorporates synthetic data without compromising accuracy. We derive the expected calibration error (ECE) bound using the Probably Approximately Correct (PAC) learning framework. Large language models (LLMs), known for their ability to mimic real data and generate text with mixed class labels, are utilized as a synthetic data generation strategy to lower the ECE bound and improve model accuracy on real test data. Additionally, we propose data generation mechanisms for efficient calibration. Testing our method on four different natural language processing tasks, we observed an average up to 34% increase in accuracy and 33% decrease in ECE.

Fill In The Gaps: Model Calibration and Generalization with Synthetic Data

Entity tracking is essential for complex reasoning. To perform in-context entity tracking, language models (LMs) must bind an entity to its attribute (e.g., bind a container to its content) to recall attribute for a given entity. For example, given a context mentioning "The coffee is in Box Z, the stone is in Box M, the map is in Box H", to infer "Box Z contains the coffee" later, LMs must bind "Box Z" to "coffee". To explain the binding behaviour of LMs, existing research introduces a Binding ID mechanism and states that LMs use a abstract concept called Binding ID (BI) to internally mark entity-attribute pairs. However, they have not directly captured the BI information from entity activations. In this work, we provide a novel view of the Binding ID mechanism by localizing the BI information. Specifically, we discover that there exists a low-rank subspace in the hidden state (or activation) of LMs, that primarily encodes BIs. To identify this subspace, we take principle component analysis as our first attempt and it is empirically proven to be effective. Moreover, we also discover that when editing representations along directions in the subspace, LMs tend to bind a given entity to other attributes accordingly. For example, by patching activations along the BI encoding direction we can make the LM to infer "Box Z contains the stone" and "Box Z contains the map".

Low-rank Subspace for Binding in Large Language Models

Large Language Models (LLMs) have shown remarkable reasoning performance but struggle with multi-step deductive reasoning involving a series of rule application steps, especially when rules are presented non-sequentially. Our preliminary analysis shows that while LLMs excel in single-step rule application, their performance drops significantly in multi-step scenarios due to the challenge in rule grounding. It requires anchoring the applicable rule and supporting facts at each step, amidst multiple input rules, facts, and inferred facts. To address this, we propose augmenting LLMs with external working memory and introduce a neurosymbolic framework for rule application. The memory stores facts and rules in both natural language and symbolic forms, enabling precise tracking. Utilizing this memory, our framework iteratively performs symbolic rule grounding and LLM-based rule implementation. The former matches predicates and variables of symbolic rules and facts to ground applicable rules at each step. Experiments indicate our framework's effectiveness in rule application and its robustness across various steps and settings.

Symbolic Working Memory Enhances Language Models for Complex Rule Application

Accurately attributing answer text to its source document is crucial for developing a reliable question-answering system. However, attribution for long documents remains largely unexplored. Post-hoc attribution systems are designed to map answer text back to the source document, yet the granularity of this mapping has not been addressed. Furthermore, a critical question arises: What exactly should be attributed? This involves identifying the specific information units within an answer that require grounding. In this paper, we propose and investigate a novel approach to the factual decomposition of generated answers for attribution, employing template-based in-context learning. To accomplish this, we utilize the question and integrate negative sampling during few-shot in-context learning for decomposition. This approach enhances the semantic understanding of both abstractive and extractive answers. We examine the impact of answer decomposition by providing a thorough examination of various attribution approaches, ranging from retrieval-based techniques to LLM-based attributors.

Enhancing Post-Hoc Attributions in Long Document Comprehension via Coarse Grained Answer Decomposition

Available training data for named entity recognition (NER) often contains a significant percentage of incorrect labels for entity types and entity boundaries. Such label noise poses challenges for supervised learning and may significantly deteriorate model quality. To address this, prior work proposed various noise-robust learning approaches capable of learning from data with partially incorrect labels. These approaches are typically evaluated using simulated noise where the labels in a clean dataset are automatically corrupted. However, as we show in this paper, this leads to unrealistic noise that is far easier to handle than real noise caused by human error or semi-automatic annotation. To enable the study of the impact of various types of real noise, we introduce NoiseBench, an NER benchmark consisting of clean training data corrupted with 6 types of real noise, including expert errors, crowdsourcing errors, automatic annotation errors and LLM errors. We present an analysis that shows that real noise is significantly more challenging than simulated noise, and show that current state-of-the-art models for noise-robust learning fall far short of their achievable upper bound. We release NoiseBench for both English and German to the research community.

NoiseBench: Benchmarking the Impact of Real Label Noise on Named Entity Recognition

Full-parameter fine-tuning (FPFT) has become the go-to choice for adapting language models (LMs) to downstream tasks due to its excellent performance. As LMs grow in size, fine-tuning the full parameters of LMs requires a prohibitively large amount of GPU memory. Existing approaches utilize zeroth-order optimizer to conserve GPU memory, which potentially compromises the performance of LMs as non-zero order optimizers tend to converge more readily on most downstream tasks. We propose a novel, memory-efficient, optimizer-independent, end-to-end hierarchical fine-tuning strategy, HiFT, which only updates a subset of parameters at each training step. HiFT significantly reduces the amount of gradients and optimizer state parameters residing in GPU memory at the same time, thereby reducing GPU memory usage. Our results demonstrate that: (1) HiFT achieves comparable performance with parameter-efficient fine-tuning and standard FPFT. (2) Results on six models show that HiFT reduces the number of trainable parameters by about 89.18% on average compared to FPFT. (3) HiFT supports FPFT of 7B models for 24G GPU memory devices under mixed precision without using any memory saving techniques. (4) HiFT supports various optimizers including AdamW, AdaGrad, SGD, etc. The source code link is https://github.com/misonsky/HiFT.

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LM2: A Simple Society of Language Models Solves Complex Reasoning

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