Periodic activation functions, often referred to as learned Fourier features have been widely demonstrated to improve sample efficiency and stability in a variety of deep RL algorithms. Potentially incompatible hypotheses have been made about the source of these improvements. One is that periodic activations learn low frequency representations and as a result avoid overfitting to bootstrapped targets. Another is that periodic activations learn high frequency representations that are more expressive, allowing networks to quickly fit complex value functions. We analyse these claims empirically, finding that periodic representations consistently converge to high frequencies regardless of their initialisation frequency. We also find that while periodic activation functions improve sample efficiency, they exhibit worse generalization on states with added observation noise -- especially when compared to otherwise equivalent networks with ReLU activation functions. Finally, we show that weight decay regularization is able to partially offset the overfitting of periodic activation functions, delivering value functions that learn quickly while also generalizing.

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a metric and dataset that elicit the desired model behavior. Then, they apply activation patching to find which abstract neural network units are involved in the behavior. By varying the dataset, metric, and units under investigation, researchers can understand the functionality of each component. We automate one of the process' steps: to identify the circuit that implements the specified behavior in the model's computational graph. We propose several algorithms and reproduce previous interpretability results to validate them. For example, the ACDC algorithm rediscovered 5/5 of the component types in a circuit in GPT-2 Small that computes the Greater-Than operation. ACDC selected 68 of the 32,000 edges in GPT-2 Small, all of which were manually found by previous work. Our code is available at https://github.com/ArthurConmy/Automatic-Circuit-Discovery.

Animals are able to rapidly infer from limited experience when sets of state action pairs have equivalent reward and transition dynamics. On the other hand, modern reinforcement learning systems must painstakingly learn through trial and error that sets of state action pairs are value equivalent -- requiring an often prohibitively large amount of samples from their environment. MDP homomorphisms have been proposed that reduce the observed MDP of an environment to an abstract MDP, which can enable more sample efficient policy learning. Consequently, impressive improvements in sample efficiency have been achieved when a suitable MDP homomorphism can be constructed a priori -- usually by exploiting a practioner's knowledge of environment symmetries. We propose a novel approach to constructing a homomorphism in discrete action spaces, which uses a partial model of environment dynamics to infer which state action pairs lead to the same state -- reducing the size of the state-action space by a factor equal to the cardinality of the action space. We call this method equivalent effect abstraction. In a gridworld setting, we demonstrate empirically that equivalent effect abstraction can improve sample efficiency in a model-free setting and planning efficiency for modelbased approaches. Furthermore, we show on cartpole that our approach outperforms an existing method for learning homomorphisms, while using 33x less training data.

Exploration in environments with sparse rewards is difficult for artificial agents. Curiosity driven learning -- using feed-forward prediction errors as intrinsic rewards -- has achieved some success in these scenarios, but fails when faced with action-dependent noise sources. We present aleatoric mapping agents (AMAs), a neuroscience inspired solution modeled on the cholinergic system of the mammalian brain. AMAs aim to explicitly ascertain which dynamics of the environment are unpredictable, regardless of whether those dynamics are induced by the actions of the agent. This is achieved by generating separate forward predictions for the mean and variance of future states and reducing intrinsic rewards for those transitions with high aleatoric variance. We show AMAs are able to effectively circumvent action-dependent stochastic traps that immobilise conventional curiosity driven agents. The code for all experiments presented in this paper is open-sourced.