LEDOM: Reverse Language Model

TL;DR

This paper introduces LEDOM, a large-scale reverse autoregressive language model trained to predict past tokens from future context, revealing unique reasoning abilities and enabling improved output reranking through reverse posterior estimates.

Contribution

The paper presents LEDOM, the first large-scale reverse language model, demonstrating its distinct reasoning capabilities and proposing a novel reranking method called Reverse Reward.

Findings

LEDOM develops abductive inference and question synthesis abilities.

Reverse Reward improves answer accuracy by up to 15%.

Bidirectional scoring reduces hallucinated reasoning in language models.

Abstract

Autoregressive language models are trained exclusively left-to-right. We explore the complementary factorization, training right-to-left at scale, and ask what reasoning patterns emerge when a model conditions on future context to predict the past. We train LEDOM, an open-source purely reverse autoregressive language model (2B/7B parameters, 435B tokens), and find it develops capabilities distinct from forward models, including abductive inference, question synthesis, and natural resolution of the reversal curse. We then explore one application of the reverse model: combining forward likelihood $P(y \mid x)$ with reverse posterior $P(x \mid y)$ through noisy channel duality. We propose Reverse Reward, which reranks forward outputs using reverse posterior estimates, and prove that bidirectional scoring penalizes hallucinated reasoning chains whose backward reconstruction degrades. Reverse Reward yields gains of up to 6.6\% on AIME 2024 and 15\% on AMC 2023 across multiple strong baselines. We release all models, code, and data here.