Jakob N. Foerster
Publications
Recurrent Structural Policy Gradient for Partially Observable Mean Field Games
Mean Field Games (MFGs) provide a principled framework for modeling interactions in large population models: at scale, population dynamics become deterministic, with uncertainty entering only through aggregate shocks, or common noise. However, algorithmic progress has been limited since model-free methods are too high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) use Monte Carlo rollouts for the common noise in combination with exact estimation of the expected return, conditioned on those samples. However, HSMs have not been scaled to Partially Observable settings. We propose Recurrent Structural Policy Gradient (RSPG), the first history-aware HSM for settings involving public information. We also introduce MFAX, our JAX-based framework for MFGs. By leveraging known transition dynamics, RSPG achieves state-of-the-art performance as well as an order-of-magnitude faster convergence and solves, for the first time, a macroeconomics MFG with heterogeneous agents, common noise and history-aware policies. MFAX is publicly available at: https://github.com/CWibault/mfax.
Asking the Right Questions: Improving Reasoning with Generated Stepping Stones
Recent years have witnessed tremendous progress in enabling LLMs to solve complex reasoning tasks such as math and coding. As we start to apply LLMs to harder tasks that they may not be able to solve in one shot, it is worth paying attention to their ability to construct intermediate stepping stones that prepare them to better solve the tasks. Examples of stepping stones include simplifications, alternative framings, or subproblems. We study properties and benefits of stepping stones in the context of modern reasoning LLMs via ARQ (\textbf{A}king the \textbf{R}ight \textbf{Q}uestions), our simple framework which introduces a question generator to the default reasoning pipeline. We first show that good stepping stone questions exist and are transferrable, meaning that good questions can be generated, and they substantially help LLMs of various capabilities in solving the target tasks. We next frame stepping stone generation as a post-training task and show that we can fine-tune LLMs to generate more useful stepping stones by SFT and RL on synthetic data.
Infusion: Shaping Model Behavior by Editing Training Data via Influence Functions
Influence functions are commonly used to attribute model behavior to training documents. We explore the reverse: crafting training data that induces model behavior. Our framework, Infusion, uses scalable influence-function approximations to compute small perturbations to training documents that induce targeted changes in model behavior through parameter shifts. We evaluate Infusion on data poisoning tasks across vision and language domains. On CIFAR-10, we show that making subtle edits via Infusion to just 0.2% (100/45,000) of the training documents can be competitive with the baseline of inserting a small number of explicit behavior examples. We also find that Infusion transfers across architectures (ResNet $\leftrightarrow$ CNN), suggesting a single poisoned corpus can affect multiple independently trained models. In preliminary language experiments, we characterize when our approach increases the probability of target behaviors and when it fails, finding it most effective at amplifying behaviors the model has already learned. Taken together, these results show that small, subtle edits to training data can systematically shape model behavior, underscoring the importance of training data interpretability for adversaries and defenders alike. We provide the code here: https://github.com/jrosseruk/infusion.
DéjàQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems
Recent advances in reasoning models have yielded impressive results in mathematics and coding. However, most approaches rely on static datasets, which have been suggested to encourage memorisation and limit generalisation. We introduce DéjàQ, a framework that departs from this paradigm by jointly evolving a diverse set of synthetic mathematical problems alongside model training. This evolutionary process adapts to the model's ability throughout training, optimising problems for learnability. We propose two LLM-driven mutation strategies in which the model itself mutates the training data, either by altering contextual details or by directly modifying problem structure. We find that the model can generate novel and meaningful problems, and that these LLM-driven mutations improve RL training. We analyse key aspects of DéjàQ, including the validity of generated problems and computational overhead. Our results underscore the potential of dynamically evolving training data to enhance mathematical reasoning and indicate broader applicability, which we will support by open-sourcing our code.