Unraveling the Reversal Curse and Harnessing Continuous Thought Chains in LLM Reasoning

Reliability and Efficiency Framework

The thesis frames large‑language‑model (LLM) reasoning along two axes. Reliability concerns how models acquire atomic facts during training and combine them at test time. Efficiency concerns the inference cost of generating long reasoning chains.

Reversal Curse

When a model observes a directed fact A → B during training, it often fails to answer the inverse query B → A . Experiments on synthetic data train a one‑layer linear‑attention model on only the forward direction. Training loss on the seen direction quickly drops to near zero, while loss on the unseen reverse direction remains high, matching random‑guess performance. Weight visualizations show strong diagonal entries for the trained direction and near‑zero weights for the reverse, supporting the claim that autoregressive training biases the model toward memorising sequence direction rather than learning symmetric relations.

Out‑of‑Context Reasoning (OCR)

OCR is defined as the ability to combine newly learned facts with pre‑existing world knowledge to infer conclusions that never appear together in the training context. Example: after learning “Alice lives in Paris” and using the background rule “People in Paris speak French”, the model can infer “Alice speaks French”. The same mechanism explains hallucinations: if the injected fact is only statistically correlated with existing knowledge, the model may compose them into a fabricated statement.

The analysis compares a single‑layer linear‑attention model with factorized and non‑factorized parameterisations. Factorized models are biased toward low‑rank, structured weights that support OCR, whereas non‑factorized models tend to memorise training facts without enabling compositional reasoning.

Continuous Chain‑of‑Thought (continuous CoT)

Traditional CoT generates discrete token sequences, incurring high inference cost and committing early to a single reasoning path. Continuous CoT keeps reasoning steps in a latent vector space, allowing multiple candidate solutions to be superimposed. For graph reachability, the author proves that a two‑layer Transformer with O(n) continuous thoughts can solve an n‑node, diameter‑D reachability problem more efficiently than discrete CoT.

Empirical evaluation on the ProsQA graph‑reasoning subset shows that the “Coconut” continuous CoT method outperforms standard CoT, no‑CoT, and deeper CoT variants, confirming that superposition reduces the number of required reasoning steps while improving accuracy.

Emergence of Superposition

Training dynamics split into two phases:

Thought‑generation phase : the model learns to encode, at each step, the set of frontier nodes reachable from the start node within a bounded number of hops.

Prediction phase : the model reads the final continuous thought to decide reachability.

During prediction, two signals emerge:

Residual carryover propagates explored nodes from the last thought into the answer token.

Candidate lift boosts the logit of candidate nodes, enabling the model to select reachable nodes.

Training curves show rapid growth of these signals after the thought‑generation stage, and the model increasingly focuses on frontier edges. Once learned, the mechanism generalises to longer reasoning steps, demonstrating length‑generalisation.

Key Visual Evidence

Implications

The work shows that improving LLM reasoning requires understanding how models memorise facts, how they compose knowledge (OCR), why knowledge injection can cause hallucinations, and how latent‑space reasoning (continuous CoT) can achieve lower‑cost, reliable inference. The PDF of the full thesis is available at https://www2.eecs.berkeley.edu/Pubs/TechRpts/2026/EECS-2026-119.pdf.