This paper studies a number of variations on the topic of training a deep network using data generated by a Monte-Carlo Tree Search (MCTS) agent. The paper focuses on the Atari 2600 platform and is motivated by the observation that, while MCTS performs extremely well on Atari 2600 games, it is also too computationally expensive to be used in a realistic setting. The authors provide empirical results on a number of Atari 2600 games.

Neural Information Processing Systems http://nips.cc/

This paper introduces Deep Statistical Solvers (DSS), a new class of trainable solvers for optimization problems, arising e.g., from system simulations. The key idea is to learn a solver that generalizes to a given distribution of problem instances. This is achieved by directly using as loss the objective function of the problem, as opposed to most previous Machine Learning based approaches, which mimic the solutions attained by an existing solver.

Counterfactual reasoning typically involves considering alternatives to actual events. While often applied to understand past events, a distinct form-forward counterfactual reasoning-focuses on anticipating plausible future developments. This type of reasoning is invaluable in dynamic financial markets, where anticipating market developments can powerfully unveil potential risks and opportunities for stakeholders, guiding their decision-making. However, performing this at scale is challenging due to the cognitive demands involved, underscoring the need for automated solutions. LLMs offer promise, but remain unexplored for this application. To address this gap, we introduce a novel benchmark, FIN-FORCE-FINancial FORward Counterfactual Evaluation. By curating financial news headlines and providing structured evaluation, FIN-FORCE supports LLM based forward counterfactual generation. This paves the way for scalable and automated solutions for exploring and anticipating future market developments, thereby providing structured insights for decision-making. Through experiments on FIN-FORCE, we evaluate state-of-the-art LLMs and counterfactual generation methods, analyzing their limitations and proposing insights for future research. We release the benchmark, supplementary data and all experimental codes at the following link: https://github.com/keanepotato/fin_force

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs often induced by a fixed radius cutoff or k-nearest neighbor scheme. While this design aligns with the locality present in many molecular tasks, a hard-coded graph can limit expressivity due to the fixed receptive field and slows down inference with sparse graph operations. In this work, we investigate whether pure, unmodified Transformers trained directly on Cartesian coordinates$\unicode{x2013}$without predefined graphs or physical priors$\unicode{x2013}$can approximate molecular energies and forces. As a starting point for our analysis, we demonstrate how to train a Transformer to competitive energy and force mean absolute errors under a matched training compute budget, relative to a state-of-the-art equivariant GNN on the OMol25 dataset. We discover that the Transformer learns physically consistent patterns$\unicode{x2013}$such as attention weights that decay inversely with interatomic distance$\unicode{x2013}$and flexibly adapts them across different molecular environments due to the absence of hard-coded biases. The use of a standard Transformer also unlocks predictable improvements with respect to scaling training resources, consistent with empirical scaling laws observed in other domains. Our results demonstrate that many favorable properties of GNNs can emerge adaptively in Transformers, challenging the necessity of hard-coded graph inductive biases and pointing toward standardized, scalable architectures for molecular modeling.

Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A leading conjecture, based on the manifold hypothesis, attributes this success to their ability to adapt to low-dimensional geometric structure within the data. This work provides evidence for this conjecture, focusing on how such phenomena could result from the formulation of the learning problem through score matching. We inspect the role of implicit regularisation by investigating the effect of smoothing minimisers of the empirical score matching objective. Our theoretical and empirical results confirm that smoothing the score function -- or equivalently, smoothing in the log-density domain -- produces smoothing tangential to the data manifold. In addition, we show that the manifold along which the diffusion model generalises can be controlled by choosing an appropriate smoothing.

We study the problem of posterior sampling using pretrained discrete diffusion foundation models, aiming to recover images from noisy measurements without retraining task-specific models. While diffusion models have achieved remarkable success in generative modeling, most advances rely on continuous Gaussian diffusion. In contrast, discrete diffusion offers a unified framework for jointly modeling categorical data such as text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free Bayesian inference, making it particularly well-suited for posterior sampling. However, existing approaches to discrete diffusion posterior sampling face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS) for masked diffusion foundation models, built on two key innovations -- quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. Our approach achieves state-of-the-art performance among discrete diffusion samplers across linear and nonlinear inverse problems on the standard benchmarks. We further demonstrate the benefits of our approach in training-free stylization and text-guided editing.

Conventional wisdom in deep learning optimization dictates updating all layers at every step-a principle followed by all recent state-of-the-art optimizers such as Muon. In this work, we challenge this assumption, showing that full-network updates can be fundamentally suboptimal, both in theory and in practice. We introduce a non-Euclidean Randomized Progressive Training method-Drop-Muon-a simple yet powerful framework that updates only a subset of layers per step according to a randomized schedule, combining the efficiency of progressive training with layer-specific non-Euclidean updates for top-tier performance. We provide rigorous convergence guarantees under both layer-wise smoothness and layer-wise $(L^0, L^1)$-smoothness, covering deterministic and stochastic gradient settings, marking the first such results for progressive training in the stochastic and non-smooth regime. Our cost analysis further reveals that full-network updates are not optimal unless a very specific relationship between layer smoothness constants holds. Through controlled CNN experiments, we empirically demonstrate that Drop-Muon consistently outperforms full-network Muon, achieving the same accuracy up to $1.4\times$ faster in wall-clock time. Together, our results suggest a shift in how large-scale models can be efficiently trained, challenging the status quo and offering a highly efficient, theoretically grounded alternative to full-network updates.

Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited. Our work addresses this gap by investigating the statistical efficiency of conditional diffusion transformers for imputation and quantifying the uncertainty in missing values. Specifically, we derive statistical sample complexity bounds based on a novel approximation theory for conditional score functions using transformers, and, through this, construct tight confidence regions for missing values. Our findings also reveal that the efficiency and accuracy of imputation are significantly influenced by the missing patterns. Furthermore, we validate these theoretical insights through simulation and propose a mixed-masking training strategy to enhance the imputation performance.

This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a two-player game between an investor and the market, where the investor makes strategic bets on future states while the market reveals outcomes. Inspired by the success of Monte Carlo Tree Search in stochastic games, we introduce an AlphaZero-based system and compare its performance to deep hedging - a widely used industry method based on gradient descent. Through theoretical analysis and experiments, we show that deep hedging struggles in environments where the $Q$-function is not subject to convexity constraints - such as those involving non-convex transaction costs, capital constraints, or regulatory limitations - converging to local optima. We construct specific market environments to highlight these limitations and demonstrate that AlphaZero consistently finds near-optimal replication strategies. On the theoretical side, we establish a connection between deep hedging and convex optimization, suggesting that its effectiveness is contingent on convexity assumptions. Our experiments further suggest that AlphaZero is more sample-efficient - an important advantage in data-scarce, overfitting-prone derivative markets.