# Stored in Optimizer State, Valued by Later Training: A Causal Account of Subliminal Trait Transfer

arXiv: https://arxiv.org/abs/2608.20442 · HTML: https://mlsanity.com/paper/2608.20442/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 30 of 38)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Sleeper Agents: Training Deceptive LLMs that Persist Through Safety Training](https://mlsanity.com/paper/2401.05566/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMs](https://mlsanity.com/paper/2502.17424/) (2025)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Asymmetry in Low-Rank Adapters of Foundation Models](https://mlsanity.com/paper/2402.16842/) (2024)
- [Unlearning or Obfuscating? Jogging the Memory of Unlearned LLMs via Benign Relearning](https://mlsanity.com/paper/2406.13356/) (2024)
- [Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learning](https://mlsanity.com/paper/1909.10300/) (2019)
- [Unlearning Isn't Deletion: Investigating Reversibility of Machine Unlearning in LLMs](https://mlsanity.com/paper/2505.16831/) (2025)
- [Towards Understanding Subliminal Learning: When and How Hidden Biases Transfer](https://mlsanity.com/paper/2509.23886/) (2025)
- [On the Transferability of Pre-trained Language Models: A Study from Artificial Datasets](https://mlsanity.com/paper/2109.03537/) (2021)
- [Personality Vector: Modulating Personality of Large Language Models by Model Merging](https://mlsanity.com/paper/2509.19727/) (2025)
- [Subliminal Steering: Stronger Encoding of Hidden Signals](https://mlsanity.com/paper/2604.25783/) (2026)
- [Subliminal Learning Is Steering Vector Distillation](https://mlsanity.com/paper/2606.00995/) (2026)
- [The Geometry of Sequential Learning: Lie-Bracket Prediction of Transfer Order](https://mlsanity.com/paper/2606.24993/) (2026)
- [Emergent and Subliminal Misalignment Through the Lens of Data-Mediated Transfer](https://mlsanity.com/paper/2605.12798/) (2026)
- [Persistent Backdoor Attacks under Continual Fine-Tuning of LLMs](https://mlsanity.com/paper/2512.14741/) (2025)
- [Learning Through Noise: Why Subliminal Learning Works and When It Fails](https://mlsanity.com/paper/2605.23645/) (2026)
- [Channel Location Constrains the Auditability of Subliminal Learning](https://mlsanity.com/paper/2606.22019/) (2026)
- [Optimizer Memory Makes Shuffle Order a First-Order Source of Fine-Tuning Noise](https://mlsanity.com/paper/2606.29554/) (2026)
- [How Memory in Optimization Algorithms Implicitly Modifies the Loss](https://mlsanity.com/paper/2502.02132/) (2025)
- [Subliminal Learning is a LoRA Artifact](https://mlsanity.com/paper/2606.00831/) (2026)

## Built on by (most cited first, 3 of 3)

- [When Does Backpropagating Through Policy Memory Matter? Physical Credit, Optimizer Updates, and Observability](https://mlsanity.com/paper/2609.33169/) (2026)
- [Cross-Trait Transfer in Subliminal Learning](https://mlsanity.com/paper/2610.04260/) (2026)
- [How Shared Representations Become Specialized: Formation, Maintenance, and Latent Susceptibility](https://mlsanity.com/paper/2610.15830/) (2026)

## Abstract (arXiv)

Subliminal trait transfer allows a student model to acquire behavioral dispositions from teacher-generated data in which the trait is not semantically expressed. Recent work explains how such signals enter gradients, but not how they survive source removal or acquire different signs under later training. We treat parameters and optimizer moments as a single trainer state and derive an exact transport-valuation identity separating observer-independent propagation of the source perturbation from the value assigned by a future continuation and behavioral readout. State surgery identifies the first moment as a causal carrier. Transplanting it alone leaves parameters, hidden states, and outputs unchanged at the cut, yet source-free updates generate growing parameter and hidden-state differences; transplanting parameters with the first moment recovers the terminal behavioral response. Sending the same source-induced difference through matched futures produces negative, near-zero, and positive Qwen effects (-0.658, +0.008, and +0.658 seed means). This ordering recurs in all 12 Llama-3.2-1B seeds after eight updates, while state-difference norms remain nearly equal across routes. Both contrasts grow in every paired seed when the continuation extends to sixteen updates. A full-horizon costate predicts all 42 Qwen route-mean signs and all 21 resolved Llama ordinary-route signs. Observer-independent transport also replicates across Qwen, SmolLM2, and Llama, while the complete-state recurrence predicts physical, hidden, and fixed-head responses in non-LoRA MNIST systems, including CNNs trained with AdamW and momentum SGD. Together, these results identify a two-stage mechanism for subliminal trait transfer: optimizer state transports the source perturbation, and later training determines its behavioral value.