Uncovering Latent Chain of Thought Vectors in Language Models

As language models grow more influential and trusted in our society, our ability to reliably steer them toward favorable behaviors becomes increasingly paramount. For this, we investigate the technique of steering vectors: biasing the forward pass of language models using a "steering vector" derived from a specific task. We apply them to steer language models toward performing Chain of Thought (CoT) Reasoning without the need to prompt through natural language. We demonstrate this approach on Llama3 8b and Mistral 7b v0.2, and obtain competitive results compared to CoT-prompted performances on a series of reasoning benchmarks (GSM8k, MMLU, AGI Eval, ARC AI2) and qualitative examples. We find this approach yields consistent steering towards CoT responses and takes less compute than traditional methods of fine-tuning models towards CoT.

Markovian Agents for Truthful Language Modeling

Chain-of-Thought (CoT) reasoning could in principle enable a deeper understanding of a language model's (LM) internal reasoning. However, prior work suggests that some LMs answer questions similarly despite changes in their CoT, suggesting that those models are not truly using the CoT. We propose a training method to produce CoTs that are sufficient alone for predicting future text, independent of other context. This methodology gives a guarantee that if the LM can predict future tokens, then it must have used the CoT to understand its context. We formalize the idea that the truthfulness of a sender to a receiver LM is the degree to which the sender helps the receiver predict their future observations. Then we define a "Markovian" LM as one which predicts future text given only a CoT as context. We derive a "Markovian training" procedure by applying our definition of truthfulness to a Markovian LM and optimizing via policy gradient and Proximal Policy Optimization (PPO). We demonstrate the effectiveness of our training algorithm on long-context arithmetic problems, show that the model utilizes the CoT, and validate that the generated CoT is meaningful and usable by other models.

Explosive Proofs of Mathematical Truths

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because their probability of error grows exponentially as the argument expands. Here we show that under a cognitively-plausible belief formation mechanism that combines deductive and abductive reasoning, mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with four hand-constructed cases from Euclid, Apollonius, Spinoza, and Andrew Wiles. Our results bear both on recent work in the history and philosophy of mathematics, and on a question, basic to cognitive science, of how we form beliefs, and justify them to others.