Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation learning with PCs remains underexplored, with prior approaches relying on external neural embeddings or activation-based encodings. To address this gap, we introduce autoencoding probabilistic circuits (APCs), a novel framework leveraging the tractability of PCs to model probabilistic embeddings explicitly. APCs extend PCs by jointly modeling data and embeddings, obtaining embedding representations through tractable probabilistic inference. The PC encoder allows the framework to natively handle arbitrary missing data and is seamlessly integrated with a neural decoder in a hybrid, end-to-end trainable architecture enabled by differentiable sampling. Our empirical evaluation demonstrates that APCs outperform existing PC-based autoencoding methods in reconstruction quality, generate embeddings competitive with, and exhibit superior robustness in handling missing data compared to neural autoencoders. These results highlight APCs as a powerful and flexible representation learning method that exploits the probabilistic inference capabilities of PCs, showing promising directions for robust inference, out-of-distribution detection, and knowledge distillation.

Photonic device development (PDD) has achieved remarkable success in designing and implementing new devices for controlling light across various wavelengths, scales, and applications, including telecommunications, imaging, sensing, and quantum information processing. PDD is an iterative, five-step process that consists of: i) deriving device behavior from design parameters, ii) simulating device performance, iii) finding the optimal candidate designs from simulations, iv) fabricating the optimal device, and v) measuring device performance. Classically, all these steps involve Bayesian optimization, material science, control theory, and direct physics-driven numerical methods. However, many of these techniques are computationally intractable, monetarily costly, or difficult to implement at scale. In addition, PDD suffers from large optimization landscapes, uncertainties in structural or optical characterization, and difficulties in implementing robust fabrication processes. However, the advent of machine learning over the past decade has provided novel, data-driven strategies for tackling these challenges, including surrogate estimators for speeding up computations, generative modeling for noisy measurement modeling and data augmentation, reinforcement learning for fabrication, and active learning for experimental physical discovery. In this review, we present a comprehensive perspective on these methods to enable machine-learning-assisted PDD (ML-PDD) for efficient design optimization with powerful generative models, fast simulation and characterization modeling under noisy measurements, and reinforcement learning for fabrication. This review will provide researchers from diverse backgrounds with valuable insights into this emerging topic, fostering interdisciplinary efforts to accelerate the development of complex photonic devices and systems.

We consider the problem of safe control in discrete autonomous agents that use learned components for imperfect perception (or more generally, state estimation) from high-dimensional observations. We propose a shield construction that provides run-time safety guarantees under perception errors by restricting the actions available to an agent, modeled as a Markov decision process, as a function of the state estimates. Our construction uses conformal prediction for the perception component, which guarantees that for each observation, the predicted set of estimates includes the actual state with a user-specified probability. The shield allows an action only if it is allowed for all the estimates in the predicted set, resulting in local safety. We also articulate and prove a global safety property of existing shield constructions for perfect-perception agents bounding the probability of reaching unsafe states if the agent always chooses actions prescribed by the shield. We illustrate our approach with a case-study of an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs.

We propose a history-driven target (HDT) framework in Markov Chain Monte Carlo (MCMC) to improve any random walk algorithm on discrete state spaces, such as general undirected graphs, for efficient sampling from target distribution $\boldsymbolμ$. With broad applications in network science and distributed optimization, recent innovations like the self-repellent random walk (SRRW) achieve near-zero variance by prioritizing under-sampled states through transition kernel modifications based on past visit frequencies. However, SRRW's reliance on explicit computation of transition probabilities for all neighbors at each step introduces substantial computational overhead, while its strict dependence on time-reversible Markov chains excludes advanced non-reversible MCMC methods. To overcome these limitations, instead of direct modification of transition kernel, HDT introduces a history-dependent target distribution $\boldsymbolπ[\mathbf{x}]$ to replace the original target $\boldsymbolμ$ in any graph sampler, where $\mathbf{x}$ represents the empirical measure of past visits. This design preserves lightweight implementation by requiring only local information between the current and proposed states and achieves compatibility with both reversible and non-reversible MCMC samplers, while retaining unbiased samples with target distribution $\boldsymbolμ$ and near-zero variance performance. Extensive experiments in graph sampling demonstrate consistent performance gains, and a memory-efficient Least Recently Used (LRU) cache ensures scalability to large general graphs.

Traffic congestion remains a significant challenge in modern urban networks. Autonomous driving technologies have emerged as a potential solution. Among traffic control methods, reinforcement learning has shown superior performance over traffic signals in various scenarios. However, prior research has largely focused on small-scale networks or isolated intersections, leaving large-scale mixed traffic control largely unexplored. This study presents the first attempt to use decentralized multi-agent reinforcement learning for large-scale mixed traffic control in which some intersections are managed by traffic signals and others by robot vehicles. Evaluating a real-world network in Colorado Springs, CO, USA with 14 intersections, we measure traffic efficiency via average waiting time of vehicles at intersections and the number of vehicles reaching their destinations within a time window (i.e., throughput). At 80% RV penetration rate, our method reduces waiting time from 6.17s to 5.09s and increases throughput from 454 vehicles per 500 seconds to 493 vehicles per 500 seconds, outperforming the baseline of fully signalized intersections. These findings suggest that integrating reinforcement learning-based control large-scale traffic can improve overall efficiency and may inform future urban planning strategies.

We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank parameterisation of previous methods and show that Flow-SSNs can estimate arbitrarily high-rank pixel-wise covariances without assuming the rank or storing the distributional parameters. Flow-SSNs are also more efficient to sample from than standard diffusion-based segmentation models, thanks to most of the model capacity being allocated to learning the base distribution of the flow, constituting an expressive prior. We apply Flow-SSNs to challenging medical imaging benchmarks and achieve state-of-the-art results. Code available: https://github.com/biomedia-mira/flow-ssn.

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world applications are inherently resource-constrained. Effective methods for inferring causal relationships from observational data must perform well under finite data and time constraints, where "performing well" implies achieving high, though not perfect accuracy. In his seminal paper A Theory of the Learnable (Valiant, 1984), Valiant highlighted the importance of resource constraints in supervised machine learning, introducing the concept of Probably Approximately Correct (PAC) learning as an alternative to exact learning. Inspired by Valiant's work, we propose the Probably Approximately Correct Causal (PACC) Discovery framework, which extends PAC learning principles to the causal field. This framework emphasizes both computational and sample efficiency for established causal methods such as propensity score techniques and instrumental variable approaches. Furthermore, we show that it can provide theoretical guarantees for other widely used methods, such as the Self-Controlled Case Series (SCCS) method, which had previously lacked such guarantees.

Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.

Budget planning and maintenance optimization are crucial for infrastructure asset management, ensuring cost-effectiveness and sustainability. However, the complexity arising from combinatorial action spaces, diverse asset deterioration, stringent budget constraints, and environmental uncertainty significantly limits existing methods' scalability. This paper proposes a Hierarchical Deep Reinforcement Learning methodology specifically tailored to multi-year infrastructure planning. Our approach decomposes the problem into two hierarchical levels: a high-level Budget Planner allocating annual budgets within explicit feasibility bounds, and a low-level Maintenance Planner prioritizing assets within the allocated budget. By structurally separating macro-budget decisions from asset-level prioritization and integrating linear programming projection within a hierarchical Soft Actor-Critic framework, the method efficiently addresses exponential growth in the action space and ensures rigorous budget compliance. A case study evaluating sewer networks of varying sizes (10, 15, and 20 sewersheds) illustrates the effectiveness of the proposed approach. Compared to conventional Deep Q-Learning and enhanced genetic algorithms, our methodology converges more rapidly, scales effectively, and consistently delivers near-optimal solutions even as network size grows.

As demand for high-purity lithium surges with the growth of the electric vehicle (EV) industry, cost-effective extraction from lower-grade North American sources like the Smackover Formation is critical. These resources, unlike high-purity South American brines, require innovative purification techniques to be economically viable. Continuous crystallization is a promising method for producing battery-grade lithium carbonate, but its optimization is challenged by a complex parameter space and limited data. This study introduces a Human-in-the-Loop (HITL) assisted active learning framework to optimize the continuous crystallization of lithium carbonate. By integrating human expertise with data-driven insights, our approach accelerates the optimization of lithium extraction from challenging sources. Our results demonstrate the framework's ability to rapidly adapt to new data, significantly improving the process's tolerance to critical impurities like magnesium from the industry standard of a few hundred ppm to as high as 6000 ppm. This breakthrough makes the exploitation of low-grade, impurity-rich lithium resources feasible, potentially reducing the need for extensive pre-refinement processes. By leveraging artificial intelligence, we have refined operational parameters and demonstrated that lower-grade materials can be used without sacrificing product quality. This advancement is a significant step towards economically harnessing North America's vast lithium reserves, such as those in the Smackover Formation, and enhancing the sustainability of the global lithium supply chain.