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2026-10-04The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models
Shuo Xing, Zilin Dai, Chengyuan Qian, Fangzhou Lin, Wenjing Chen, Ping He, et al.
arXiv:2610.02191v1Large language models can solve many math problems, but they often do so without truly understanding the structure behind the answer. This paper asks a deeper question: what is the missing primitive that makes mathematical reasoning reliable? The authors introduce a new benchmark that breaks math ability into four parts: discovering the right idea, generating a solution, digesting information, and executing the plan. Their diagnosis shows that many models look strong on final accuracy while actually struggling most with discovery, the step of finding the right mathematical insight in the first place. That matters because if a model cannot identify the key idea, it may fail even when it seems capable on surface-level tests. Building on this insight, they propose a self-distillation method that teaches models using primitive-guided reasoning. The result is a practical way to repair a common weakness in math reasoning and improve performance across model sizes and harder benchmarks.
Also spotted that day
One Basis to Animate Them All: Gaussian Blendshape Distillation for Real-Time AvatarsKaliBench: A Fine-Grained Benchmark for Cybersecurity Tool Use on Kali Linux with Runtime-Free Verifiable RewardsReconstruct, Practice, Go Real: Guided Self-Improvement for Embodied AgentsEmbedding Prediction Helps Image GenerationScholarCatalyst: A Benchmark for Retrieving Papers That Inspire New ResearchSILSA: Sliding-Window Slice Latents for Topology-Preserving High-Resolution 3D GenerationVISTA: A Visual Harness for Reasoning in an Interactive WorldTACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-TuningFERPO: Forward Entropy-Regularized Policy OptimizationCost-augmented Schrödinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned controlHierarchical Continuous Diffusion Language ModelsTrust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-TuningGenerative modeling of intrinsically disordered protein regions by reinforcing sparse autoencoder featuresDMAD: Distribution Matching as Adversarial Distillation for Fast Visual Generation
Previous daily papers
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