To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the entire denoising diffusion process into several segments, each corresponding to a reverse transition kernel (RTK) sampling subproblem. Specifically, DDPM uses a Gaussian approximation for the RTK, resulting in low per-subproblem complexity but requiring a large number of segments (i.e., subproblems), which is conjectured to be inefficient. To address this, we develop a general RTK framework that enables a more balanced subproblem decomposition, resulting in $\tilde O(1)$ subproblems, each with strongly log-concave targets. We then propose leveraging two fast sampling algorithms, the Metropolis-Adjusted Langevin Algorithm (MALA) and Underdamped Langevin Dynamics (ULD), for solving these strongly log-concave subproblems. This gives rise to the RTK-MALA and RTK-ULD algorithms for diffusion inference. In theory, we further develop the convergence guarantees for RTK-MALA and RTK-ULD in total variation (TV) distance: RTK-ULD can achieve $\epsilon$ target error within $\tilde{\mathcal O}(d^{1/2}\epsilon^{-1})$ under mild conditions, and RTK-MALA enjoys a $\mathcal{O}(d^{2}\log(d/\epsilon))$ convergence rate under slightly stricter conditions. These theoretical results surpass the state-of-the-art convergence rates for diffusion inference and are well supported by numerical experiments.

Federated learning (FL) allows for collaborative model training across decentralized clients while preserving privacy by avoiding data sharing. However, current FL methods assume conditional independence between client models, limiting the use of priors that capture dependence, such as Gaussian processes (GPs). We introduce the Structured Independence via deep Generative Model Approximation (SIGMA) prior which enables FL for non-factorizable models across clients, expanding the applicability of FL to fields such as spatial statistics, epidemiology, environmental science, and other domains where modeling dependencies is crucial. The SIGMA prior is a pre-trained deep generative model that approximates the desired prior and induces a specified conditional independence structure in the latent variables, creating an approximate model suitable for FL settings. We demonstrate the SIGMA prior's effectiveness on synthetic data and showcase its utility in a real-world example of FL for spatial data, using a conditional autoregressive prior to model spatial dependence across Australia. Our work enables new FL applications in domains where modeling dependent data is essential for accurate predictions and decision-making.

Planning in real-world settings often entails addressing partial observability while aligning with users' preferences. We present a novel framework for expressing users' preferences about agent behavior in a partially observable setting using parameterized belief-state query (BSQ) preferences in the setting of goal-oriented partially observable Markov decision processes (gPOMDPs). We present the first formal analysis of such preferences and prove that while the expected value of a BSQ preference is not a convex function w.r.t its parameters, it is piecewise constant and yields an implicit discrete parameter search space that is finite for finite horizons. This theoretical result leads to novel algorithms that optimize gPOMDP agent behavior while guaranteeing user preference compliance. Theoretical analysis proves that our algorithms converge to the optimal preference-compliant behavior in the limit. Empirical results show that BSQ preferences provide a computationally feasible approach for planning with preferences in partially observable settings.

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model, deriving exact equations for the network's predictor statistics under the finite-width thermodynamic limit, i.e., $N,P\rightarrow\infty$, $P/N=\mathcal{O}(1)$, where $N$ is the network width and $P$ is the number of training examples. Our theory shows that the predictor statistics are expressed as a sum of independent kernels, each one pairing different 'attention paths', defined as information pathways through different attention heads across layers. The kernels are weighted according to a 'task-relevant kernel combination' mechanism that aligns the total kernel with the task labels. As a consequence, this interplay between attention paths enhances generalization performance. Experiments confirm our findings on both synthetic and real-world sequence classification tasks. Finally, our theory explicitly relates the kernel combination mechanism to properties of the learned weights, allowing for a qualitative transfer of its insights to models trained via gradient descent. As an illustration, we demonstrate an efficient size reduction of the network, by pruning those attention heads that are deemed less relevant by our theory.

Recent results in the literature indicate that artificial neural networks (ANNs) can outperform the dynamic factor model (DFM) in terms of the accuracy of GDP nowcasts. Compared to the DFM, the performance advantage of these highly flexible, nonlinear estimators is particularly evident in periods of recessions and structural breaks. From the perspective of policy-makers, however, nowcasts are the most useful when they are conveyed with uncertainty attached to them. While the DFM and other classical time series approaches analytically derive the predictive (conditional) distribution for GDP growth, ANNs can only produce point nowcasts based on their default training procedure (backpropagation). To fill this gap, first in the literature, we adapt two different deep learning algorithms that enable ANNs to generate density nowcasts for U.S. GDP growth: Bayes by Backprop and Monte Carlo dropout. The accuracy of point nowcasts, defined as the mean of the empirical predictive distribution, is evaluated relative to a naive constant growth model for GDP and a benchmark DFM specification. Using a 1D CNN as the underlying ANN architecture, both algorithms outperform those benchmarks during the evaluation period (2012:Q1 -- 2022:Q4). Furthermore, both algorithms are able to dynamically adjust the location (mean), scale (variance), and shape (skew) of the empirical predictive distribution. The results indicate that both Bayes by Backprop and Monte Carlo dropout can effectively augment the scope and functionality of ANNs, rendering them a fully compatible and competitive alternative for classical time series approaches.

Collaboration is a key challenge in distributed multi-agent reinforcement learning (MARL) environments. Learning frameworks for these decentralized systems must weigh the benefits of explicit player coordination against the communication overhead and computational cost of sharing local observations and environmental data. Quantum computing has sparked a potential synergy between quantum entanglement and cooperation in multi-agent environments, which could enable more efficient distributed collaboration with minimal information sharing. This relationship is largely unexplored, however, as current state-of-the-art quantum MARL (QMARL) implementations rely on classical information sharing rather than entanglement over a quantum channel as a coordination medium. In contrast, in this paper, a novel framework dubbed entangled QMARL (eQMARL) is proposed. The proposed eQMARL is a distributed actor-critic framework that facilitates cooperation over a quantum channel and eliminates local observation sharing via a quantum entangled split critic. Introducing a quantum critic uniquely spread across the agents allows coupling of local observation encoders through entangled input qubits over a quantum channel, which requires no explicit sharing of local observations and reduces classical communication overhead. Further, agent policies are tuned through joint observation-value function estimation via joint quantum measurements, thereby reducing the centralized computational burden. Experimental results show that eQMARL with ${\Psi}^{+}$ entanglement converges to a cooperative strategy up to $17.8\%$ faster and with a higher overall score compared to split classical and fully centralized classical and quantum baselines. The results also show that eQMARL achieves this performance with a constant factor of $25$-times fewer centralized parameters compared to the split classical baseline.

Experimental control involves a lot of manual effort with non-trivial decisions for precise adjustments. Here, we study the automatic experimental alignment for coupling laser light into an optical fiber using reinforcement learning (RL). We face several real-world challenges, such as time-consuming training, partial observability, and noisy actions due to imprecision in the mirror steering motors. We show that we can overcome these challenges: To save time, we use a virtual testbed to tune our environment for dealing with partial observability and use relatively sample-efficient model-free RL algorithms like Soft Actor-Critic (SAC) or Truncated Quantile Critics (TQC). Furthermore, by fully training on the experiment, the agent learns directly to handle the noise present. In our extensive experimentation, we show that we are able to achieve 90% coupling, showcasing the effectiveness of our proposed approaches. We reach this efficiency, which is comparable to that of a human expert, without additional feedback loops despite the motors' inaccuracies. Our result is an example of the readiness of RL for real-world tasks. We consider RL a promising tool for reducing the workload in labs.

Advances in large language models raise the question of how alignment techniques will adapt as models become increasingly complex and humans will only be able to supervise them weakly. Weak-to-Strong mimics such a scenario where weak model supervision attempts to harness the full capabilities of a much stronger model. This work extends Weak-to-Strong to WeakS-to-Strong by exploring an ensemble of weak models which simulate the variability in human opinions. Confidence scores are estimated using a Bayesian approach to guide the WeakS-to-Strong generalization. Furthermore, we extend the application of WeakS-to-Strong from text classification tasks to text generation tasks where more advanced strategies are investigated for supervision. Moreover, direct preference optimization is applied to advance the student model's preference learning, beyond the basic learning framework of teacher forcing. Results demonstrate the effectiveness of the proposed approach for the reliability of a strong student model, showing potential for superalignment.

Building open agents has always been the ultimate goal in AI research, and creative agents are the more enticing. Existing LLM agents excel at long-horizon tasks with well-defined goals (e.g., `mine diamonds' in Minecraft). However, they encounter difficulties on creative tasks with open goals and abstract criteria due to the inability to bridge the gap between them, thus lacking feedback for self-improvement in solving the task. In this work, we introduce autonomous embodied verification techniques for agents to fill the gap, laying the groundwork for creative tasks. Specifically, we propose the Luban agent target creative building tasks in Minecraft, which equips with two-level autonomous embodied verification inspired by human design practices: (1) visual verification of 3D structural speculates, which comes from agent synthesized CAD modeling programs; (2) pragmatic verification of the creation by generating and verifying environment-relevant functionality programs based on the abstract criteria. Extensive multi-dimensional human studies and Elo ratings show that the Luban completes diverse creative building tasks in our proposed benchmark and outperforms other baselines ($33\%$ to $100\%$) in both visualization and pragmatism. Additional demos on the real-world robotic arm show the creation potential of the Luban in the physical world.

Confidence region prediction is a practically useful extension to the commonly studied pattern recognition problem. Instead of predicting a single label, the constraint is relaxed to allow prediction of a subset of labels given a desired confidence level 1-delta. Ideally, effective region predictions should be (1) well calibrated - predictive regions at confidence level 1-delta should err with relative frequency at most delta and (2) be as narrow (or certain) as possible. We present a simple technique to generate confidence region predictions from conditional probability estimates (probability forecasts). We use this 'conversion' technique to generate confidence region predictions from probability forecasts output by standard machine learning algorithms when tested on 15 multi-class datasets. Our results show that approximately 44% of experiments demonstrate well-calibrated confidence region predictions, with the K-Nearest Neighbour algorithm tending to perform consistently well across all data. Our results illustrate the practical benefits of effective confidence region prediction with respect to medical diagnostics, where guarantees of capturing the true disease label can be given.