J-CoT: Chain-of-Thought in J-Space

2026-07-27 · Source: cs.CL updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

J-CoT is a recurrent reasoning framework that enhances large language model (LLM) reasoning by using a "J-thought" state within a vocabulary-indexed coordinate system called J-space. Unlike traditional Chain-of-Thought (CoT) which relies on natural language, or dense latent methods that pass entire hidden vectors, J-CoT expresses intermediate states as vocabulary-indexed coefficients at cycle boundaries. This allows for linguistically grounded yet non-sentential information transfer. Evaluated on Qwen3-8B-Base, J-CoT-Zero matches or exceeds the strongest latent-reasoning baselines across mathematical, scientific, coding, and structured path-reasoning tasks. J-CoT-Train, which optimizes carrier embeddings and a read gate, achieves the highest scores, improving the overall average from 47.5% to 50.2%. The framework also demonstrates favorable scaling with model capacity (7B to 405B parameters) and recurrent depth.

Key takeaway

For AI Scientists and Machine Learning Engineers developing advanced reasoning capabilities in LLMs, J-CoT offers a superior recurrent interface. You should consider implementing J-CoT-Train to achieve higher accuracy across mathematical, scientific, and coding tasks, as it consistently outperforms both linguistic and dense latent reasoning methods. Its favorable scaling with model capacity and adaptive reasoning depth suggests it will be increasingly effective for future, larger models.

Key insights

J-CoT improves LLM reasoning by using vocabulary-indexed "J-thoughts" as a non-sentential, linguistically grounded recurrent interface.

Principles

• Intermediate states need not be fully verbalized.
• Vocabulary-indexed coefficients enable cross-layer transport.
• Adaptive recurrence improves efficiency.

Method

J-CoT reads J-thought coefficients at layer ℓ_r, integrates them into carrier activations, propagates through Transformer blocks to layer ℓ_w, and extracts new coefficients for the next cycle.

In practice

• Apply J-CoT for complex mathematical reasoning.
• Use J-CoT for scientific question answering.
• Implement J-CoT for enhanced code generation.

Topics

• Chain-of-Thought
• J-space
• Recurrent Reasoning
• Large Language Models
• Mathematical Reasoning
• Code Generation
• Latent Reasoning

Best for: Research Scientist, AI Engineer, AI Scientist, Machine Learning Engineer, NLP Engineer

Related on AIssential

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CL updates on arXiv.org.