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Neural Reasoning for Sure Through Constructing Explainable Models

AAAI 2025 · Large language models › Language, safety and interpretability · approach: Faithfulness of LLM explanations · 3 citations (OpenAlex)

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Introduces Hyperbolic Sphere Neural Network (HSphNN), a training-free neural model that constructs Poincaré sphere configurations to decide Aristotelian syllogistic validity for sure within one epoch, and uses it to check and feed back on ChatGPT outputs.

Problem

Neural networks, including LLMs, are not sure about their reasoning results and make unpredictable errors on syllogistic reasoning; the paper seeks networks that reason for sure with a constant bound on iterations.

Approach

Extends vector embeddings to hyperbolic sphere embeddings in which part-whole relations are encoded by sphere boundaries; reasoning is performed as explicit model construction through neighbourhood transitions with constraint optimisation, proved to terminate within M=1 epoch, requiring no training data.

Key results

• HSphNN determined all 2304 cases (24 valid, 232 invalid across dimensions 2 to 3000) with the reasoning-for-sure property within M=1 epoch.
• With feedback from HSphNN (two rounds), gpt-3.5-turbo improved from 46.875% to 58.98% and gpt-4o from 82.42% to 84.76%.
• Without feedback, gpt-3.5-turbo reached 46.875% correct decision and explanation; gpt-4o reached 82.42% with random symbols.

Measured effects reported in the paper

Surprising findings

• Increasing feedback rounds to ten only raised gpt-4o performance to 85.16%, suggesting prompt feedback is limited as a System 2 to System 1 loop.

Limitations

• Only covers syllogistic reasoning; extensions to other logic and Bayesian reasoning are described but not evaluated.
• Prompt feedback has limited effect on LLM performance beyond a few rounds.

Experimental setup

Datasets: 256 Aristotelian syllogistic reasoning types

Benchmarks: Aristotelian syllogistic reasoning (256 types)

Metrics: accuracy irrationality ratio time cost

Baselines: gpt-3.5-turbo gpt-4o

Builds on: Sphere Neural Networks (SphNN) Poincaré embeddings TELeR prompt structure

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