Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought
Authors: Hanlin Zhu, Shibo Hao, Zhiting Hu, Jiantao Jiao, Stuart J Russell, Yuandong Tian
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this paper, we prove that a two-layer transformer with D steps of continuous Co T can solve the directed graph reachability problem, where D is the diameter of the graph, while the best known result of constant-depth transformers with discrete Co T requires O(n2) decoding steps where n is the number of vertices (D < n). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete Co T must choose a single path sampled from the superposition state, which leads to a sequential search that requires many more steps and may be trapped in local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. |
| Researcher Affiliation | Collaboration | Hanlin Zhu UC Berkeley EMAIL Shibo Hao UCSD EMAIL Zhiting Hu UCSD EMAIL Jiantao Jiao UC Berkeley EMAIL Stuart Russell UC Berkeley EMAIL Yuandong Tian Meta AI EMAIL |
| Pseudocode | Yes | Algorithm 1 Transformer (TF) Algorithm 2 Causal Self-Attention (Attn) and (position-wise) Multilayer Perceptron (MLP) |
| Open Source Code | Yes | Our code is available at https://github.com/Ber666/reasoning-by-superposition. |
| Open Datasets | Yes | Dataset. We construct a subset of Pros QA [Hao et al., 2024], with questions whose solutions require 3 4 reasoning hops. |
| Dataset Splits | Yes | The split statistics are summarised in Table 4. Train 14785 22.8 36.5 3.5 Val 257 22.7 36.3 3.5 Test 419 22.7 36.0 3.5 |
| Hardware Specification | Yes | Each run of COCONUT takes about 24 hours on two Nvidia A100 80GB GPUs. |
| Software Dependencies | No | The paper mentions 'Adam W' as an optimizer and 'GPT-2 style decoder' as an architecture but does not specify software dependencies with version numbers (e.g., Python, PyTorch). |
| Experiment Setup | Yes | Model. We adopt a GPT-2 style decoder with two transformer layers, dmodel=768, nheads=8. We train from scratch using Adam W (β1=0.9, β2=0.95, weight-decay 10 2) and a constant learning rate of 1 10 4. |