Einar Urdshals

Chris Elliott, Einar Urdshals, David Quarel et al.

Singular learning theory characterizes Bayesian learning as an evolving tradeoff between accuracy and complexity, with transitions between qualitatively different solutions as sample size increases. We extend this theory to deep reinforcement learning, proving that the concentration of the generalized posterior over policies is governed by the local learning coefficient (LLC), an invariant of the geometry of the regret function. This theory predicts that Bayesian phase transitions in reinforcement learning should proceed from simple policies with high regret to complex policies with low regret. We verify this prediction empirically in a gridworld environment exhibiting stagewise policy development: phase transitions over SGD training manifest as "opposing staircases" where regret decreases sharply while the LLC increases. Notably, the LLC detects phase transitions even when estimated on a subset of states where the policies appear identical in terms of regret, suggesting it captures changes in the underlying algorithm rather than just performance.

Chris Elliott, Einar Urdshals, David Quarel et al.

Susceptibilities are a technique for neural network interpretability that studies the response of posterior expectation values of observables to perturbations of the loss. We generalize this construction to the setting of the regret in deep reinforcement learning and investigate the utility of susceptibilities in a simple gridworld model that nevertheless exhibits non-trivial stagewise development. We argue that susceptibilities reveal internal features of the development of the model in parameter space that one cannot detect purely by studying the development of the learned policy. We validate these results with activation-steering, and discuss the framework's extension to RLHF post-training.

Einar Urdshals, Jasmina Urdshals

We study how a one-layer attention-only transformer develops relevant structures while learning to sort lists of numbers. At the end of training, the model organizes its attention heads in two main modes that we refer to as vocabulary-splitting and copy-suppression. Both represent simpler modes than having multiple heads handle overlapping ranges of numbers. Interestingly, vocabulary-splitting is present regardless of whether we use weight decay, a common regularization technique thought to drive simplification, supporting the thesis that neural networks naturally prefer simpler solutions. We relate copy-suppression to a mechanism in GPT-2 and investigate its functional role in our model. Guided by insights from a developmental analysis of the model, we identify features in the training data that drive the model's final acquired solution. This provides a concrete example of how the training data shape the internal organization of transformers, paving the way for future studies that could help us better understand how LLMs develop their internal structures.

Einar Urdshals, Edmund Lau, Jesse Hoogland et al.

We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization, factorization, and other compression techniques, we find that complexity estimates based on the local learning coefficient (LLC) are closely, and in some cases, linearly correlated with compressibility. Our results provide a path toward rigorously evaluating the limits of model compression.

Éloïse Benito-Rodriguez, Einar Urdshals, Jasmina Nasufi et al.

Understanding Large Language Models (LLMs) is key to ensure their safe and beneficial deployment. This task is complicated by the difficulty of interpretability of LLM structures, and the inability to have all their outputs human-evaluated. In this paper, we present the first step towards a predictive framework, where the genre of a text used to prompt an LLM, is predicted based on its activations. Using Mistral-7B and two datasets, we show that genre can be extracted with F1-scores of up to 98% and 71% using scikit-learn classifiers. Across both datasets, results consistently outperform the control task, providing a proof of concept that text genres can be inferred from LLMs with shallow learning models.