Comments & Extensions of Subliminal Learning

Clark Miyamoto, Tets Nagashima, Alex Jiang

Here we perform empirical studies of subliminal learning. We find evidence that representations are important for subliminal learning to occur.

Reviewer's Comments

Reviewer's Comments

Arrow
Arrow
Arrow

Andrew Mack

The authors focus on a nice, well-scoped project which is achievable within the constraints of a hackathon. They study a toy version of subliminal learning where a student model is distilled using *only* the "auxiliary logits" from a trained teacher model, possibly on a different dataset, where the auxiliary logits are designed to be completely meaningless. Nevertheless, they find that teacher accuracy can be transmitted to the student via the meaningless auxiliary logits.

It would have been nice to have a short discussion of how this toy version of subliminal learning relates to that of Cloud et al (I lean towards them being related but I'm not sure). In any case, the author's definition of "subliminal learning" is interesting enough to warrant study on its own merits.

They present some preliminary evidence that increasing width decreases their definition of subliminal learning - the most compelling evidence is from figure 4 where we see that increasing the number of auxiliary logits increases subliminal learning for student models of width <=2048, but barely affects subliminal learning for the width 4096 model. The authors draw a nice connection to NTK as a hypothesis which may explain this result.

Some of the results / presentation are pretty preliminary / rough around the edges (for example, the trend in figure 3 is not very clear; it would be nice to have some sort of p-value), but this is to be expected for a hackathon. The submission's strongest selling point is its focus on a minimal example of a "subliminal learning-type phenomenon" which still yields interesting results. This could be very useful for eventually building up to a tractable "physics of DL"-style theory of subliminal learning.

Ari Brill

The project presents a replication and extensions of recent experiments investigating subliminal learning. The experiments are well-motivated and rigorous, and appear to lay a solid foundation for further investigations of the origin of subliminal learning. The project could be improved by making the connection with physics more explicit. The possible connection between feature learning and subliminal learning that was briefly mentioned is interesting, and could be a fruitful topic to analyze further in future work.

Nikita Khomich

Excellent result, ive seen results like that for llms which were sort of vague and this is a very reasonable attempt to do explore the phenomenon for mlps and mnist dataset. Very good result especially within 3 days, good code as well, well-written.

Lauren

This is a timely project well scoped for a hackathon project, exploring subliminal learning in vision models as width, auxiliary logits, and noise are varied in a pretty clean way, representing a reasonably ‘physics-like’ way of doing controlled experiments. The results (representations should match, accuracy flattens as width approaches the NTK regime) were not surprising, but a good sanity check; follow up work could explore mechanisms for why this happens or safety relevant limits (e.g., the finite-width onset of NTK-like behavior) to subliminal learning or other failure modes.

The paper could benefit from a clearer abstract and more of an introduction/background about the safety relevance, and there could have been a stronger connection to physics (which, as it stands, was sort of implicit). The authors also seem surprised that their accuracy plateau didn’t match the paper, but as these use different metrics (MSE loss v. KL divergence), I wouldn’t expect them to capture the same information. In particular, KL maximizes information transfer, so the MSE is likely missing some small auxiliary logits that nevertheless carry subliminal signal.

Cite this work

@misc {

title={

(HckPrj) Comments & Extensions of Subliminal Learning

},

author={

Clark Miyamoto, Tets Nagashima, Alex Jiang

},

date={

7/28/25

},

organization={Apart Research},

note={Research submission to the research sprint hosted by Apart.},

howpublished={https://apartresearch.com}

}

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Momentum–Point-Perplexity Mechanics in Large Language Models

This work analyzes the hidden states of twenty different open-source transformer language models, ranging from small to medium size and covering five major architectures. The key discovery is that these models show signs of "energy conservation" during inference—meaning a certain measure combining changes in hidden states and token unpredictability stays almost constant as the model processes text.

The authors developed a new framework inspired by physics to jointly analyze how hidden states and prediction confidence evolve over time. They propose that transformers' behavior can be understood as following certain mechanical principles, much like how physical systems follow rules like conservation of energy.

Their experiments show that this conserved quantity varies very little between tokens, especially in untrained (random-weight) models, where it's extremely stable. In pre-trained models, the average energy drops more due to training, but there are larger relative fluctuations from token to token.

They also introduce a new method, based on this framework, for controlling transformer outputs by "steering" the hidden states. This method achieves good results—producing completions rated as higher in semantic quality, while still maintaining the same kind of energy stability.

Overall, the findings suggest that viewing transformer models through the lens of physical mechanics gives new, principled ways to interpret and control their behavior. It also highlights a key difference: random models behave more like balanced systems, while trained models make quicker, more decisive state changes at the cost of less precise energy conservation.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.
This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.