# The Scaling Properties of Implicit Deductive Reasoning in Transformers

Source: [The Scaling Properties of Implicit Deductive Reasoning in Transformers](<https://www.sota2.com/research/paper/69fc1c725497b3b670c88433>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-30T05:00:15.133Z

Authors: Enrico Vompa, Tanel Tammet

Published: 2026-05-05T22:35:46.000Z

## Abstract

We investigate the scaling properties of implicit deductive reasoning over Horn clauses in depth-bounded Transformers. By systematically decorrelating provability from spurious features and enforcing algorithmic alignment, we find that in sufficiently deep models with a bidirectional prefix mask, implicit reasoning approaches explicit CoT performance across graph topologies and problem widths, though CoT remains necessary for depth extrapolation.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Logical Reasoning on RP LP Domain, Npred ≤ 30, δ ≤ 6](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-lp-domain-npred-30-6.md>): Logical reasoning; RP LP Domain, Npred ≤ 30, δ ≤ 6; Accuracy: 100.

- [Logical Reasoning on RP LP Domain, Npred ≤ 30, 6 \< δ ≤ 12](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-lp-domain-npred-30-6-12.md>): Logical reasoning; RP LP Domain, Npred ≤ 30, 6 \< δ ≤ 12; Accuracy: 99.5.

- [Logical Reasoning on RP LP Domain, Npred ≤ 60, δ ≤ 6](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-lp-domain-npred-60-6.md>): Logical reasoning; RP LP Domain, Npred ≤ 60, δ ≤ 6; Accuracy: 99.4.

- [Logical Reasoning on RP LP Domain, Npred ≤ 60, 6 \< δ ≤ 12](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-lp-domain-npred-60-6-12.md>): Logical reasoning; RP LP Domain, Npred ≤ 60, 6 \< δ ≤ 12; Accuracy: 93.5.

- [Logical Reasoning on RP Npred ≤ 30, δ ≤ 6 (train)](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-npred-30-6-train.md>): Logical reasoning; RP Npred ≤ 30, δ ≤ 6 (train); Accuracy: 100.

- [Logical Reasoning on RP Npred ≤ 30, 6 \< δ ≤ 12 (train)](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-npred-30-6-12-train.md>): Logical reasoning; RP Npred ≤ 30, 6 \< δ ≤ 12 (train); Accuracy (RP Npred ≤ 30, 6 \< δ ≤ 12 train): 99.5.

- [Logical Reasoning on RP Distribution, Npred ≤ 60, δ ≤ 6 (train)](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-distribution-npred-60-6-train.md>): Logical reasoning; RP Distribution, Npred ≤ 60, δ ≤ 6 (train); Accuracy: 99.5.

- [Logical Reasoning on RP Distribution, Npred ≤ 60, 6 \< δ ≤ 12 (train)](<https://www.sota2.com/research/sota/logical-reasoning-on-rp-distribution-npred-60-6-12-train.md>): Logical reasoning; RP Distribution, Npred ≤ 60, 6 \< δ ≤ 12 (train); Accuracy: 88.9.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.04330>)

[PDF](<https://arxiv.org/pdf/2605.04330.pdf>)