# Inverse Knowledge Search over Verifiable Reasoning: Synthesizing a Scientific Encyclopedia from a Long Chains-of-Thought Knowledge Base

arXiv: https://arxiv.org/abs/2510.26854 · HTML: https://mlsanity.com/paper/2510.26854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Retrieval Augmentation Reduces Hallucination in Conversation](https://mlsanity.com/paper/2104.07567/) (2021)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Increasing Faithfulness in Knowledge-Grounded Dialogue with Controllable Features](https://mlsanity.com/paper/2107.06963/) (2021)
- [Dated Data: Tracing Knowledge Cutoffs in Large Language Models](https://mlsanity.com/paper/2403.12958/) (2024)
- [Automatic Generation of Socratic Subquestions for Teaching Math Word Problems](https://mlsanity.com/paper/2211.12835/) (2022)
- [Large Language Models and the Reverse Turing Test](https://mlsanity.com/paper/2207.14382/) (2022)
- [Logical Reasoning over Natural Language as Knowledge Representation: A Survey](https://mlsanity.com/paper/2303.12023/) (2023)
- [Scalable detection of statistically significant communities and hierarchies, using message-passing for modularity](https://mlsanity.com/paper/1403.5787/) (2014)
- [Improving Socratic Question Generation using Data Augmentation and Preference Optimization](https://mlsanity.com/paper/2403.00199/) (2024)
- [Emergent Slow Thinking in LLMs as Inverse Tree Freezing](https://mlsanity.com/paper/2509.23629/) (2025)
- [Language-Agnostic Modeling of Wikipedia Articles for Content Quality Assessment across Languages](https://mlsanity.com/paper/2404.09764/) (2024)
- [Learning-at-Criticality in Large Language Models for Quantum Field Theory and Beyond](https://mlsanity.com/paper/2506.03703/) (2025)
- [Weighted Community Detection and Data Clustering Using Message Passing](https://mlsanity.com/paper/1801.09829/) (2018)

## Built on by (most cited first, 2 of 2)

- [Bohrium + SciMaster: Building the Infrastructure and Ecosystem for Agentic Science at Scale](https://mlsanity.com/paper/2512.20469/) (2025)
- [PRAGMA: Evaluating Personalized Guidance with Memory Alignment in Lifelong Conversations](https://mlsanity.com/paper/2609.09664/) (2026)

## Abstract (arXiv)

Most scientific materials compress reasoning, presenting conclusions while omitting the derivational chains that justify them. This compression hinders verification by lacking explicit, step-wise justifications and inhibits cross-domain links by collapsing the very pathways that establish the logical and causal connections between concepts. We introduce a scalable framework that decompresses scientific reasoning, constructing a verifiable Long Chain-of-Thought (LCoT) knowledge base and projecting it into an emergent encyclopedia, SciencePedia. Our pipeline operationalizes an endpoint-driven, reductionist strategy: a Socratic agent, guided by a curriculum of around 200 courses, generates approximately 3 million first-principles questions. To ensure high fidelity, multiple independent solver models generate LCoTs, which are then rigorously filtered by prompt sanitization and cross-model answer consensus, retaining only those with verifiable endpoints. This verified corpus powers the Brainstorm Search Engine, which performs inverse knowledge search -- retrieving diverse, first-principles derivations that culminate in a target concept. This engine, in turn, feeds the Plato synthesizer, which narrates these verified chains into coherent articles. The initial SciencePedia comprises approximately 200,000 fine-grained entries spanning mathematics, physics, chemistry, biology, engineering, and computation. In evaluations across six disciplines, Plato-synthesized articles (conditioned on retrieved LCoTs) exhibit substantially higher knowledge-point density and significantly lower factual error rates than an equally-prompted baseline without retrieval (as judged by an external LLM). Built on this verifiable LCoT knowledge base, this reasoning-centric approach enables trustworthy, cross-domain scientific synthesis at scale and establishes the foundation for an ever-expanding encyclopedia.