{"ID":2946563,"CreatedAt":"2026-06-02T09:31:37.03791814Z","UpdatedAt":"2026-06-02T12:33:44.556013874Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.08605","arxiv_id":"2605.08605","title":"Lattice Deduction Transformers","abstract":"We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An $800$K-parameter LDT achieves $100\\%$ accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A $1.8$M-parameter variant reaches $99.9\\%$ accuracy on Maze-Hard. Frontier LLMs score $0\\%$ on all three benchmarks.","short_abstract":"We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domai...","url_abs":"https://arxiv.org/abs/2605.08605","url_pdf":"https://arxiv.org/pdf/2605.08605v1","authors":"[\"Liam Davis\",\"Leopold Haller\",\"Alberto Alfarano\",\"Mark Santolucito\"]","published":"2026-05-09T01:55:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.LO\"]","methods":"[\"Transformer\",\"Large Language Model\"]","has_code":false}