AI agentic system epidemiology

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}.

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.

In this work, we seek to further understand the computational structure formed by transformers trained to predict the next token of a data set. In particular, we extend the work of (Piotrowski et al., 2025) by analyzing if and how these transformers implement constrained Bayesian updating, focusing on data generated by a Random-Random-XOR (RRXOR) process. Unlike the MESS3 processes studied originally in (Piotrowski et al., 2025), the RRXOR process leads to slightly more nuanced theoretical and practical models. Nevertheless, we verify some of the main claims of (Piotrowski et al., 2025). Namely, we find attention patterns that decay exponentially with distance. We further analyze the behavior of OV vectors.