Unsupervised Recovery of Hidden Markov Models from Transformers with Evolutionary Algorithms
Dylan Bowman, Colin Lu
Prior work finds that transformer neural networks trained to mimic the output of a Hidden Markov Model (HMM) embed the optimal Bayesian beliefs for the HMM's current state in their residual stream, which can be recovered via linear regression. In this work, we aim to address the problem of extracting information about the underlying HMM using the residual stream, without needing to know the MSP already. To do so, we use the R^2 of the linear regression as a reward signal for evolutionary algorithms, which are deployed to search for the parameters that generated the source HMM. We find that for toy scenarios where the HMM is generated by a small set of latent variables, the $R^2$ reward signal is remarkably smooth and the evolutionary algorithms succeed in approximately recovering the original HMM. We believe this work constitutes a promising first step towards the ultimate goal of extracting information about the underlying predictive and generative structure of sequences, by analyzing transformers in the wild.
Reviewer's Comments
Reviewer's Comments



No reviews are available yet
Cite this work
@misc {
title={
Unsupervised Recovery of Hidden Markov Models from Transformers with Evolutionary Algorithms
},
author={
Dylan Bowman, Colin Lu
},
date={
6/3/24
},
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

Sign up to stay updated on the
latest news, research, and events

Sign up to stay updated on the
latest news, research, and events

Sign up to stay updated on the
latest news, research, and events

Sign up to stay updated on the
latest news, research, and events