Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems?

Graph), a comprehensive benchmark of graph-based problem solving designed in natural language.

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more. While LLMs have advanced the state-of-the-art on these tasks with structure implications, whether LLMs could explicitly process textual descriptions of graphs and structures, map them to grounded conceptual spaces, and perform structured operations remains underexplored. To this end, we propose NLGraph (Natural Language Graph), a comprehensive benchmark of graph-based problem solving designed in natural language. NLGraph contains 29,370 problems, covering eight graph reasoning tasks with varying complexity from simple tasks such as connectivity and shortest path up to complex problems such as maximum flow and simulating graph neural networks. We evaluate LLMs (GPT-3/4) with various prompting approaches on the NLGraph benchmark and find that 1) language models do demonstrate preliminary graph reasoning abilities, 2) the benefit of advanced prompting and in-context learning diminishes on more complex graph problems, while 3) LLMs are also (un)surprisingly brittle in the face of spurious correlations in graph and problem settings. We then propose Build-a-Graph Prompting and Algorithmic Prompting, two instruction-based approaches to enhance LLMs in solving natural language graph problems. Build-a-Graph and Algorithmic prompting improve the performance of LLMs on NLGraph by 3.07% to 16.85% across multiple tasks and settings, while how to solve the most complicated graph reasoning tasks in our setup with language models remains an open research question.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems?

Large Language Models (LLMs) for Graph Reasoning have been extensively studied over the past two years, involving enabling LLMs to understand graph structures and reason on graphs to solve various graph problems, with graph algorithm problems being the most prevalent. Recent studies underscore the potential of LLMs in handling graph reasoning tasks, but their performance is underwhelming. In this work, we point out issues with existing methods and benchmarks, and rethink the direction that LLMs for graph reasoning should strive toward. We find that base models, e.g., GPT-4o-mini, are largely underestimated due to improper reasoning focus. Base models with reasoning focus redirected from replicating graph algorithms to designing them can easily solve most graph reasoning tasks in existing benchmarks. To truly evaluate the graph reasoning capabilities of LLMs, we construct a more challenging GraphAlgorithm benchmark, comprising 239 different graph problems and 3,041 test instances collected from 4 competition platforms. Finally, we introduce a simple and strong baseline Simple-Reasoning-Then-Coding (Simple-RTC)-which guides LLMs to design graph algorithms first and then code to address graph reasoning tasks. Simple-RTC achieves near-perfect accuracy on existing benchmarks and significantly outperforms GPT-4o-mini and all prior methods on the GraphAlgorithm benchmark. This strong baseline encourages further advancements in LLMs for Graph Reasoning in the future.

Large language models (LLMs) show promising performance on small-scale graph reasoning tasks but fail when handling real-world graphs with complex queries. This phenomenon arises from LLMs' working memory constraints, which result in their inability to retain long-range graph topology over extended contexts while sustaining coherent multi-step reasoning. However, real-world graphs are often structurally complex, such as Web, Transportation, Social, and Citation networks. To address these limitations, we propose GraphCogent, a collaborative agent framework inspired by human Working Memory Model that decomposes graph reasoning into specialized cognitive processes: sense, buffer, and execute. The framework consists of three modules: Sensory Module standardizes diverse graph text representations via subgraph sampling, Buffer Module integrates and indexes graph data across multiple formats, and Execution Module combines tool calling and tool creation for efficient reasoning. We also introduce Graph4real, a comprehensive benchmark that contains four domains of real-world graphs (Web, Transportation, Social, and Citation) to evaluate LLMs' graph reasoning capabilities. Our Graph4real covers 21 different graph reasoning tasks, categorized into three types (Structural Querying, Algorithmic Reasoning, and Predictive Modeling tasks), with graph scales up to 10 times larger than existing benchmarks. Experiments show that Llama3.1-8B based GraphCogent achieves a 50% improvement over massive-scale LLMs like DeepSeek-R1 (671B). Compared to state-of-the-art agent-based baseline, our framework outperforms by 20% in accuracy while reducing token usage by 80% for in-toolset tasks and 30% for out-toolset tasks. Code will be available after review.

Transformer-based LLMs demonstrate strong performance on graph reasoning tasks, yet their internal mechanisms remain underexplored. To uncover these reasoning process mechanisms in a fundamental and unified view, we set the basic decoder-only transformers and explain them using the circuit-tracer framework. Through this lens, we visualize reasoning traces and identify two core mechanisms in graph reasoning: token merging and structural memorization, which underlie both path reasoning and substructure extraction tasks. We further quantify these behaviors and analyze how they are influenced by graph density and model size. Our study provides a unified interpretability framework for understanding structural reasoning in decoder-only Transformers.

We propose a new, training-free method, Graph Reasoning via Retrieval Augmented Framework (GRRAF), that harnesses retrieval-augmented generation (RAG) alongside the code-generation capabilities of large language models (LLMs) to address a wide range of graph reasoning tasks. In GRRAF, the target graph is stored in a graph database, and the LLM is prompted to generate executable code queries that retrieve the necessary information. This approach circumvents the limitations of existing methods that require extensive finetuning or depend on predefined algorithms, and it incorporates an error feedback loop with a time-out mechanism to ensure both correctness and efficiency. Experimental evaluations on the GraphInstruct dataset reveal that GRRAF achieves 100% accuracy on most graph reasoning tasks, including cycle detection, bipartite graph checks, shortest path computation, and maximum flow, while maintaining consistent token costs regardless of graph sizes. Imperfect but still very high performance is observed on subgraph matching. Notably, GRRAF scales effectively to large graphs with up to 10,000 nodes.

Large Language Models (LLMs) have shown strong capabilities in solving problems across domains, including graph-related tasks traditionally addressed by symbolic or algorithmic methods. In this work, we present a framework for structured context injection, where task-specific information is systematically embedded in the input to guide LLMs in solving a wide range of graph problems. Our method does not require fine-tuning of LLMs, making it cost-efficient and lightweight. We observe that certain graph reasoning tasks remain challenging for LLMs unless they are mapped to conceptually grounded representations. However, achieving such mappings through fine-tuning or repeated multi-step querying can be expensive and inefficient. Our approach offers a practical alternative by injecting structured context directly into the input, enabling the LLM to implicitly align the task with grounded conceptual spaces. We evaluate the approach on multiple graph tasks using both lightweight and large models, highlighting the trade-offs between accuracy and computational cost. The results demonstrate consistent performance improvements, showing that structured input context can rival or surpass more complex approaches. Our findings underscore the value of structured context injection as an effective and scalable strategy for graph understanding with LLMs.