arXiv subjects

Jakob Foerster

Publications and source records attributed to Jakob Foerster.

At least 19 recordsLinked to original sources

arXiv2026

Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of 113 predominantly unsolved problems spanning eight domains in mathematics and the mathematical sciences, paired with an open-source evaluation framework for automated verification. Our benchmark targets the generator-verifier gap: problems where discovery is hard and requires meaningful mathematical insight, but verification is computationally straightforward. This contrasts with most existing research-level benchmarks, which instead rely on formal proof verification or manual review, both of which are expensive to scale. Because these solutions are unknown, HorizonMath is resistant to data contamination, and most state-of-the-art models score under 10%. Using this framework, we identify six novel solutions to research problems that either resolve previously open questions or improve on the best-known published results, with GPT-5.4 Pro and GPT-5.6 Sol each discovering three of these solutions. Across seven frontier model families, reasoning efficiency and behavior also vary substantially. We release HorizonMath as an open challenge and a growing community resource, where each verified solution is a candidate contribution to the mathematical literature.

cs.LG↗

arXiv2026

Recurrent Reinforcement Learning with Memoroids

Memory models such as Recurrent Neural Networks (RNNs) and Transformers address Partially Observable Markov Decision Processes (POMDPs) by mapping trajectories to latent Markov states. Neither model scales particularly well to long sequences, especially compared to an emerging class of memory models called Linear Recurrent Models. We discover that the recurrent update of these models resembles a monoid, leading us to reformulate existing models using a novel monoid-based framework that we call memoroids. We revisit the traditional approach to batching in recurrent reinforcement learning, highlighting theoretical and empirical deficiencies. We leverage memoroids to propose a batching method that improves sample efficiency, increases the return, and simplifies the implementation of recurrent loss functions in reinforcement learning.

cs.LG↗

arXiv2026

The Yokai Learning Environment: Tracking Beliefs Over Space and Time

The ability to cooperate with unknown partners is a central challenge in cooperative AI and widely studied in the form of zero-shot coordination (ZSC), which evaluates an algorithm by measuring the performance of independently trained agents when paired. The Hanabi Learning Environment (HLE) has become the dominant benchmark for ZSC, but recent work has achieved near-perfect inter-seed cross-play performance, limiting its ability to track algorithmic progress. We introduce the Yokai Learning Environment (YLE) - an open-source multi-agent RL benchmark in which effective collaboration requires building common ground by tracking and updating beliefs over moving cards, reasoning under ambiguous hints, and deciding when to terminate the game based on inferred shared knowledge - features absent in the HLE, where beliefs are tied to hand slots and hints are truthful by rule. We evaluate the leading ZSC methods, including High-Entropy IPPO, Other-Play, and Off-Belief Learning, which achieve near-perfect inter-seed cross-play in the HLE, and show that in the YLE they exhibit persistent SP-XP gaps, degraded early-ending calibration, and weaker belief representations in cross-play, indicating failure to maintain consistent internal models with unseen partners. Methods that perform best in the HLE do not perform best in the YLE, indicating that progress measured on a single benchmark may not generalise. Together, these results establish YLE as a challenging new ZSC benchmark.

cs.AI↗

arXiv2026

Is Inter-Seed Cross-Play Enough? Evaluating the Robustness of Zero-Shot Coordination Algorithms to Implementation Details

AI agents deployed in real-world settings must be capable of coordinating with humans and other AI agents they have not encountered before. Zero-shot coordination (ZSC) algorithms aim to achieve this by specifying high-level learning rules such that independently engineered agents can coordinate with each other at test time. Rigorous evaluation of ZSC algorithms remains difficult: ideally, multiple independent implementations of each proposed algorithm must be used, reflecting the variation that arises when independent parties interpret and implement the same specification. In practice, however, ZSC algorithms have almost exclusively been evaluated using a single implementation trained across different random seeds, with only a handful of works additionally varying the neural network architecture. This leaves open questions about robustness to specification ambiguities and implementation details. In this work, we provide the first systematic evaluation of this robustness. We introduce a new evaluation scheme, cross-implementation cross-play, varying implementation details that prior work has shown to affect the performance of multi-agent reinforcement learning (MARL) algorithms, and we evaluate Other-Play, a popular ZSC algorithm, with this scheme. Our findings are encouraging and suggest that, for Other-Play, the standard ZSC evaluation is, in fact, a reasonable proxy for this more thorough cross-implementation evaluation.

cs.AI↗

arXiv2026

Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments

An agent's performance stagnating at a suboptimal level is a common problem in deep on-policy RL. Focusing on PPO, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimisation challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. Looking deeper, PPO alternates between sampling rollouts from several parallel environments online using the current policy (which we call the "outer loop") and performing repeated minibatch SGD steps against this offline dataset (the "inner loop"). In our work, we abstract away the inner loop, and conceptually model the outer loop as standard stochastic optimisation. The step size is then controlled by the regularisation strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This framing predicts that, much like in SGD, if the outer step size is too large relative to the noise, updates become uninformative and lead to the policy thrashing around a local optimum instead of converging. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We validate the predictions of our model and conclude that increasing the number of parallel environments is a simple way to avoid these plateaus by simultaneously altering both these factors. Applying our analysis and scaling PPO to more than 1M parallel environments enables monotonic performance improvement up to one trillion transitions and leads to vastly superior performance compared to prior baselines in a complex open-ended domain.

cs.LG↗

arXiv2026

Autodata: An agentic data scientist to create high quality synthetic data

We introduce Autodata, a general method that enables AI agents to act as data scientists who build high quality training and evaluation data. We show how to train (meta-optimize) such a data scientist agent, so that it learns to create even stronger data. We describe the overall formulation, and a specific practical implementation, Agentic Self-Instruct. We conduct experiments on computer science research tasks, legal reasoning tasks and reasoning with mathematical objects, where we obtain improved results compared to classical synthetic dataset creation methods. Further, meta-optimizing the data scientist agent itself delivers an even larger performance uplift. Agentic data creation provides a way to convert increased inference compute into higher quality model training. Overall, we believe this direction has the potential to change the way we build AI data.

cs.AI↗

arXiv2026

Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Training

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".

cs.NE↗

arXiv2026

Modelling Opinion Dynamics at Scale with Deep MARL

Modelling opinion dynamics typically relies on hand-crafted local interaction rules to study emergent macroscopic phenomena such as consensus and polarisation. In contrast, multi-agent reinforcement learning (MARL) enables agents to learn such behaviours directly by optimising simple rewards. To explore the potential of MARL for opinion dynamics, we introduce a GPU-accelerated consensus and truth-finding game that scales to populations of up to 1000 agents, comparable to many real-world social sub-networks. To prevent unrealistic conventions, we extend other-play to general-sum social interactions. We next validate our model on a subset of the Bluesky network by recovering agent importance structures from graph topology alone via a learned attention layer, finding that highly conforming populations most closely match human data. In large social media networks such high levels of conformity significantly reduce collective accuracy and promote dishonest agents that lie to fit in. By contrast, small, dynamic hunter-gatherer networks are less affected; here, conformity can even improve collective agreement. This suggests a mismatch between evolved human conformity heuristics and modern social media environments as a potential contributor to misinformation.

cs.MA↗

arXiv2026

High entropy leads to symmetry-equivariant policies in Dec-POMDPs

We prove that in any Dec-POMDP, sufficiently high entropy regularization ensures that the policy gradient flow with tabular softmax parametrization always converges, for any initialization, to the same joint policy, and that this joint policy is equivariant w.r.t. all symmetries of the Dec-POMDP. In particular, policies coming from different initializations will be fully compatible, in that their cross-play returns are equal to their self-play returns. Through extensive evaluation of independent PPO, arguably the standard baseline deep multi-agent policy gradient algorithm, in the Hanabi, Overcooked and Yokai environments, we find that the entropy coefficient has a massive influence on the cross-play returns between independently trained policies, and that the decrease in self-play returns coming from increased entropy regularization can often be counteracted by greedifying the learned policies after training. In Hanabi in particular we achieve a new SOTA in inter-seed cross-play this way. While we give examples of Dec-POMDPs in which one cannot learn the optimal symmetry-equivariant policy this way, both our theoretical and empirical results suggest that one should consider far higher entropy coefficients during hyperparameter sweeps in Dec-POMDPs than is typically done. Code for our experiments can be found at https://github.com/jforkel/JAX-OBL

cs.LG↗

arXiv2026

Evaluating AI-based Scientific Knowledge Synthesis with Epidemiological Systematic Reviews

Systematic literature reviews (SLRs) are a demanding and high-stakes form of scientific knowledge synthesis that remains underspecified as an evaluation setting for large language models (LLMs). We introduce AgentSLR, a large-scale evaluation harness comprising an SLR automation workflow and an expert annotated dataset covering 16,248 articles, designed to test LLM capabilities across the stages of SLRs in epidemiology. Reference annotations were derived from peer-reviewed studies on WHO priority pathogens and produced by domain experts. The harness evaluates each review stage as a separate unit with dedicated metrics enabling targeted failure analysis. We evaluated five frontier reasoning models and found that no single model dominated across all tasks, showing sub-task specialisation often hidden by aggregate benchmarks. Structured data extraction is a major bottleneck, with no model exceeding an average field-level F1 of 0.67. Estimated costs vary substantially, by up to 96 times across evaluated models. Documented failure modes suggest that the evaluated models are not yet reliable enough for unsupervised deployment in epidemiology, where findings can inform public policy.

cs.IR↗

arXiv2026

Expected Return Symmetries

Symmetry is an important inductive bias that can improve model robustness and generalization across many deep learning domains. In multi-agent settings, a priori known symmetries have been shown to address a fundamental coordination failure mode known as mutually incompatible symmetry breaking; e.g. in a game where two independent agents can choose to move "left'' or "right'', and where a reward of +1 or -1 is received when the agents choose the same action or different actions, respectively. However, the efficient and automatic discovery of environment symmetries, in particular for decentralized partially observable Markov decision processes, remains an open problem. Furthermore, environmental symmetry breaking constitutes only one type of coordination failure, which motivates the search for a more accessible and broader symmetry class. In this paper, we introduce such a broader group of previously unexplored symmetries, which we call expected return symmetries, which contains environment symmetries as a subgroup. We show that agents trained to be compatible under the group of expected return symmetries achieve better zero-shot coordination results than those using environment symmetries. As an additional benefit, our method makes minimal a priori assumptions about the structure of their environment and does not require access to ground truth symmetries.

cs.MA↗

arXiv2026

Recurrent Structural Policy Gradient for Partially Observable Mean Field Games

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) reduce variance while maintaining tractability by leveraging low-dimensional individual state and action spaces and known transition dynamics to compute the exact expected return conditioned on Monte Carlo rollouts of common noise. However, HSMs have not been extended to partially observable settings. We propose Recurrent Structural Policy Gradient (RSPG), the first history-aware HSM for MFGs with public partial information. RSPG achieves an order-of-magnitude faster convergence than model-free RL methods while learning history-aware behaviour, unlike current HSMs. To facilitate research into MFGs, we also introduce MFAX, our JAX-based framework for MFGs that supports both analytic and sample-based mean-field updates. MFAX and usage examples can be found at https://clarisse-wibault.github.io/rspg/.

cs.AI↗

arXiv2026

Goal-Conditioned Agents that Learn Everything All at Once

A goal-conditioned reinforcement learning agent exploring an environment will see a wealth of information throughout a trajectory, most of which is discarded when only performing on-policy updates with respect to the commanded goal. All-goals learning, where each transition is used for learning off-policy with respect to every goal, allows agents to extract maximal information, however it is usually computationally infeasible when done via naive relabelling. This can be overcome by jointly outputting values and actions for every goal at once, allowing for efficient, parallel all-goals updates with a single pass through the network, in a process we call Learning Everything all at Once (LEO). We show that this approach significantly outperforms other methods on goal-conditioned Craftax and is competitive with existing baselines on continuous control environments, while achieving a >250x speed-up compared to all-goals relabelling. We then go on to show that this approach can be made even more powerful by using LEO as a teacher network, rather than a direct actor. We hope that, by unlocking all-goals learning at scale, LEO can serve as a useful tool for RL practitioners in complex environments. We open source our code.

cs.LG↗

arXiv2026

Abstraction for Offline Goal-Conditioned Reinforcement Learning

Markov Decision Processes (MDPs) often exhibit significant redundancy due to symmetries and shared structure across state-goal pairs in real-world Goal-Conditioned Reinforcement Learning (GCRL). While hierarchical policies have been motivated for horizon reduction via temporal abstraction in offline GCRL, we demonstrate that hierarchy also enables absolute abstraction. By introducing relativised options as well as distinct representations for different levels of the hierarchy, we demonstrate how an agent can reuse experience across similar contexts of the state-space. Based on this framework, we introduce two simple algorithms for learning relativised options and abstracting from the absolute frame of reference. Our experiments show that such inductive biases significantly improve performance in offline GCRL.

cs.LG↗

arXiv2026

JAX-Based Batched AC Power Flow for GPU Acceleration and AI Ecosystem Integration

Coordinating growing grid flexibility under uncertainty is becoming increasingly important for efficient and reliable power-system operation. A core computational requirement is the efficient large-scale batched evaluation of AC power flow across candidate operating actions and uncertainty scenarios. Previous work has explored GPU-based batched power-flow evaluation, but has largely relied on hand-written C or CUDA code, creating barriers to customisation, efficient kernel optimisation, and long-term maintenance. JAX is a Python-based framework that enables efficient accelerator execution while keeping implementations in Python. This letter therefore proposes a JAX-based batched AC power-flow solver that uses current JAX functionality to implement Newton--Raphson for transmission networks and Z-Bus power flow for three-phase unbalanced distribution networks, achieving more than 10x speed-ups relative to pandapower and OpenDSS. In addition, JAX integrates seamlessly with the broader JAX-based AI ecosystem, making it straightforward to embed power-flow evaluation within AI methods for future larger-scale and more complex power-system operation.

eess.SY↗

arXiv2026

Learning to Reason at the Frontier of Learnability

Reinforcement learning is now widely adopted as the final stage of large language model training, especially for reasoning-style tasks such as maths problems. Typically, models attempt each question many times during a single training step and attempt to learn from their successes and failures. However, we demonstrate that throughout training with two popular algorithms (PPO and VinePPO) on two widely used datasets, many questions are either solved by all attempts - meaning they are already learned - or by none - providing no meaningful training signal. To address this, we adapt a method from the reinforcement learning literature - sampling for learnability - and apply it to the reinforcement learning stage of LLM training. Our curriculum prioritises questions with high variance of success, i.e. those where the agent sometimes succeeds, but not always. Our findings demonstrate that this curriculum consistently boosts training performance across multiple algorithms and datasets, paving the way for more efficient and effective reinforcement learning with LLMs.

cs.LG↗

arXiv2026

Hierarchical Behaviour Spaces

Recent work in hierarchical reinforcement learning has shown success in scaling to billions of timesteps when learning over a set of predefined option reward functions. We show that, instead of using a single reward function per option, the reward functions can be effectively used to induce a space of behaviours, by letting the controller specify linear combinations over reward functions, allowing a more expressive set of policies to be represented. We call this method Hierarchical Behaviour Spaces (HBS). We evaluate HBS on the NetHack Learning Environment, demonstrating strong performance. We conduct a series of experiments and determine that, perhaps going against conventional wisdom, the benefits of hierarchy in our method come from increased exploration rather than long term reasoning.

cs.AI↗

arXiv2026

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.

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