A teacher has a trait.
A preference, response style, or other behavioral disposition.
01 / The problem
The dataset looks clean.
The signal isn’t.
Subliminal learning transfers behavioral traits through outputs that appear semantically unrelated to those traits—even after explicit mentions are filtered out.
→
It generates ordinary data.
Number sequences or correct math reasoning, screened for direct references to the trait.
→
The student can acquire it.
Fine-tuning may transfer an unrequested behavior alongside the intended task signal.
02 / Liminal training
Constrain early.
Anneal to zero.
Liminal training adds a KL-divergence penalty toward the frozen base model to the cross-entropy objective. The weight is held at λ₀ for the first epoch, then decays linearly to zero.
Training objective
Limit early distributional drift.
In the main experiments, training runs for three epochs with λ₀ = 1.0. The KL term is computed token-wise over completion tokens.
L(θ; t) = LCE + λKL(t) · DKL(θ₀ ‖ θ)
Liminal schedule · 3 epochs
hold λ₀anneal to 0
03 / Main results
Less measured trait transfer,
similar average task gains.
In the aggregate chain-of-thought results across five models, liminal fine-tuning reduced mean animal-trait acquisition relative to preference fine-tuning while producing a similar average GSM8K gain. Outcomes vary by model and trait.
Example trajectories
Liminal training stays closer to the control.
We measure trait-related probabilities at fixed checkpoints throughout fine-tuning. In this Qwen2.5-1.5B-Instruct example, preference fine-tuning produces larger increases for several animal traits, while liminal fine-tuning remains closer to no-preference fine-tuning.
CoT · five-model average
Mean ΔP(animal)
3.32 → 0.85
preference FT (%) → liminal FT (%)
Average change from baseline, using mean trait probability across training checkpoints.
CoT · five-model average
Mean ΔGSM8K
23.0 → 22.2
preference FT (pp) → liminal FT (pp)
Aggregate task gains are close, although the difference varies across individual models.
04 / KL timing
When KL is applied matters.
The main result raises a natural question: is the benefit due only to regularization strength, or also to when the constraint is applied? Holding peak weight fixed shows that timing changes the task–trait trade-off.
Early-weighted schedules lie on or near the empirical Pareto frontier; late-weighted schedules fall below the fixed-KL curve in the configurations studied.
Hold λ₀ for epoch one, then decay linearly to zero.
Apply λ₀ for epoch one, then switch it off.
Sweeping λ traces a smooth task–trait trade-off curve.
Increase the penalty from zero to λ₀ over training.
Apply λ₀ only during the final epoch.
05 / Additional findings
Beyond animal-preference mitigation.
The paper also compares alternative mitigations, tests a response-style trait, and examines instability under no-preference fine-tuning.
Alternative mitigations are less consistent.
Paraphrasing still produces trait acquisition in many configurations. Freezing more layers partially reduces acquisition while increasingly reducing task learning.
The response-style experiment shows the same timing pattern.
For one Qwen2.5-1.5B experiment trained on French math traces, mean P(French) was 74.6% with standard fine-tuning and 5.5% with liminal training; GSM8K accuracy was 59.1% and 51.8%, respectively.
Fine-tuning on control data can still shift trait probabilities.
Initial trait probability strongly correlates with trajectory variation under the control condition in both CoT and number-sequence experiments.
06 / Boundaries
Limitations
Our experiments establish a consistent empirical pattern, but leave important questions open.
Traits
Most experiments concern animal preferences, plus one French response-style study. Subliminal transfer of misalignment was not studied because it could not be reliably reproduced in the models tested.
Tasks
The evidence covers number sequences and GSM8K chain-of-thought data. Broader datasets and task settings remain future work.
Mechanism
The experiments do not provide a mechanistic explanation of subliminal learning or why liminal training suppresses trait acquisition.
07 / Paper
Read, reproduce,
build on it.
@inproceedings{yanagisawa2026liminal,
title = {On Mitigation of Subliminal Learning in Large Language Models},
author = {Yanagisawa, Atsushi and Gho, Brendan and
Rajendran Ramesh Babu, Manoj Narender and
Zhu, Kevin and Mari, Antonio},
booktitle = {Findings of the Association for Computational Linguistics: EMNLP 2026},
publisher = {Association for Computational Linguistics},
year = {2026}
}