ABSTRACT. Informal and privatized transit services, such as minibuses and shared auto-rickshaws, are integral to daily travel in large urban metropolises, particularly in developing nations, providing affordable commutes where formal public transport is inadequate and other options are unaffordable. A defining feature of these systems is their decentralized, market-based organization, with drivers providing service in response to rider demand and earning opportunities. While this structure helps fill critical mobility gaps, it can also generate inefficient service patterns when profit-driven driver route choices do not align with system-wide mobility goals.

We develop an analytically tractable game-theoretic framework to study incentives underlying informal and privatized transit systems with a fixed menu of routes, quantify efficiency losses from decentralized driver route choice, and design incentive mechanisms to mitigate these inefficiencies. Here, profit-maximizing informal operators (\emph{drivers}) decide where to provide service and cost-minimizing commuters (\emph{riders}) decide whether to use these services. Within this framework, we establish \emph{tight} price of anarchy bounds showing that decentralized, profit-maximizing driver behavior can lead to bounded yet substantial losses in cumulative driver profit and rider demand served and that these losses can be mitigated through targeted interventions: \emph{budget-balanced cross-subsidization}, which uses route-specific tolls/subsidies to shape driver payoffs, and \emph{fare optimization}, which changes rider demand and driver margins through centrally regulated route-level fares. Finally, numerical experiments based on a real-world informal transit system in Nalasopara, India, reinforce these findings.

ABSTRACT. Allocation of dynamically-arriving (i.e., online) divisible resources among a set of offline agents is a fundamental problem, with applications to online marketplaces, scheduling, portfolio selection, signal processing, and many other areas. The water-filling algorithm, which allocates an incoming resource to maximize the minimum load of compatible agents, is ubiquitous in many of these applications; however, the analysis and guarantees differ across settings. We provide a justification for the widespread use of water-filling by showing that it is a *universally optimal policy* in the following strong sense: for a large class of objectives -- including both Schur-concave maximization and Schur-convex minimization -- it is minimax optimal for every instance size (number of offline agents/online resource amount), and for both regret and competitive ratio measures. Remarkably, water-filling achieves these guarantees as a myopic policy, remaining entirely agnostic to the objective function, agent count, and resource availability. Our techniques notably depart from popular primal-dual techniques, and instead develop a novel way to apply the theory of majorization in online settings to achieve universality guarantees.

Joint work with Ramiro Deo-Campo Vuong and Robert Kleinberg.

ABSTRACT. AI systems increasingly make collective recommendations by aggregating heterogeneous data and preferences from many individuals. In many applications, the goal is not to identify a single best alternative, but to construct a ranking, shortlist, or recommendation set that supports later decision-making. This talk studies preference aggregation through multiple-winner outcomes. Moving from single winners to sets can better represent diversity in preferences and can avoid some classical impossibility results that arise when collective choice must be reduced to one alternative. Set-valued aggregation creates room for stronger notions of fairness, representation, and collective support. I present a framework based on the ordinal Lindahl equilibrium. Using only ordinal preference information, and without interpersonal utility comparisons, the framework identifies alternatives that can be collectively justified as an equilibrium outcome. I discuss how this approach can guide AI-mediated recommendation, ranking, and decision support.

ABSTRACT. We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, a dataset provides partial information about unknown parameters of an optimization task. Focusing on linear programs with uncertainty in the cost vector, we characterize theoretically when a dataset is sufficient to recover an optimal decision. We show how task structure and uncertainty shape data requirements and provide algorithms for principled task-aware data selection.

ABSTRACT. We formulate an ordinary differential equation (ODE) to find the optimal set of agent weights that achieve max–min fairness. These agents are contending for resources (e.g., bandwidth) across a large number of agent groups. The ODE's convergence to an optimal point is rigorously analysed, and a solver is developed.

Our proposed solver operates using a set of individualised weights, optimising over a reduced number of variables, and using a simple linear iterative scheme based on Euler's method or equivalent. Given the above, the solver is capable of obtaining the optimal solution on a larger scale and more rapidly than conventional methods, which are largely based on Karmarkar's algorithm.

The ODE takes the form of the continuous-time regenerative equation familiar in evolutionary game theory. The solution is obtained through a normalised version of the agent weights. Because the weights depend continuously on the underlying resource variables, the solver can be implemented in scenarios involving tracking and control.

In this paper, we focus on its applications to multi-agent AI systems. Results are presented for use cases already being considered in the AI literature.

ABSTRACT. Most of the literature on online algorithms and sequential decision-making in revenue management focuses on settings with irrevocable decisions, where once a decision is made upon the arrival of a new input, it cannot be canceled later. Motivated by modern revenue management applications—such as cloud spot markets, selling banner ads, or online hotel booking—we introduce and study “prophet inequalities with cancellations” under linear cancellation costs (known as the buyback model in the literature). In the classic prophet inequality problem, a sequence of independent random variables X1,X2, . . . with known distributions is revealed one by one, and a decision-maker must decide when to stop and accept the current variable in order to maximize the expected value of their choice. In our model, after accepting X one may later discard X and accept another X’ at a cost of f*X’ , where f>= 0 is a given parameter in this model. The goal is to maximize the expected net reward: the value of the final accepted variable minus the total cancellation cost. We aim to design online policies that are competitive against an omniscient optimal o!ine “prophet” benchmark.

Our first main result is an optimal prophet inequality for all parameters 𝑀 ↑0. We show this result by fully characterizing the worst-case competitive ratio of the optimal online policy against the optimal o!ine benchmark via the solution to a certain differential equation (for which we provide a constructive solution). Our second main result is to design and analyze a simple and polynomial-time randomized adaptive policy that achieves this optimal competitive ratio. Importantly, our policy is order-agnostic (à la Samuel-Cahn (1984)), meaning that it only needs to know the set of distributions and not the order in which the random variables arrive. These results are obtained by a sequence of reductions to a (continuous) “generalized flow problem,” which can be viewed as the dual to a factor-revealing LP for characterizing the worst-case competitive ratio in the original problem. We develop several techniques to solve this reduced problem, including a geometric interpretation of its solution via a differential equation and the embedding of our random variables into specific Poisson point processes. We also leverage these building blocks in novel ways, both for constructing our lower bound instances and in designing (and analyzing) our order-agnostic policy.

ABSTRACT. One of the first results we learn in Probability Theory is the Central Limit Theorem (CLT). While it characterizes the complete distribution in the limit, it doesn't tell us anything about the prelimit behavior. In contrast, concentration inequalities such as the Chernoff bound provide us prelimit bounds that have the right tail decay, but cannot recover the CLT. Efficient concentration asks for tail bounds that have the right tail scaling, but can also recover the limit theorem. Such results in the CLT context were obtained only recently.

Inspired by these developments, we obtain similar efficient concentration for a load balancing systems consisting of queues where jobs are allowed to abandon. We study this system in the heavily overloaded regime where a limit theorem converging to a Gaussian is known in the literature. We obtain efficient concentration by showing that the tail probability is upper bounded by a sum of two terms. The first is the tail of the limiting Gaussian, and the second is a term that goes to zero in the limit as the abandonment rate goes to zero. These results are obtained by first showing a rate of convergence to the limiting Gaussian in the Wasserstein-p distance, which is of independent interest. The Wasserstein-p bounds are in turn obtained using the Stein's method.

ABSTRACT. Fréchet regression extends classical regression to settings where responses are non-Euclidean objects, such as covariance matrices, probability distributions, networks, or points on Riemannian manifolds. A key challenge is that global Fréchet regression produces signed weights, especially in extrapolation, turning the fitted value into a signed barycenter problem that may be nonconvex, ill-posed, or constrained by curvature and cut-locus effects. This talk presents recent results on the existence, computation, and convergence of Fréchet regression estimators in two geometric settings. First, for symmetric positive definite matrices under the Bures–Wasserstein geometry, we derive spectral conditions guaranteeing well-posedness of signed conditional barycenters and develop projection-free Riemannian optimization methods with applications to network regression and diffusion tensor imaging. Second, for general Riemannian manifolds with bounded curvature, we formulate signed Fréchet regression as a locally controlled proximal DC problem and introduce FRIDA, a Riemannian proximal DCA method with descent, stationarity, and KL-type convergence guarantees. Together, these results provide a rigorous optimization framework for regression with manifold-valued responses in interpolation and extrapolation regimes.

ABSTRACT. We introduce localmax dynamics, a discrete-time attention model that bridges softmax dynamics and hardmax dynamics. The latter was introduced more recently as a simplified model for understanding certain limiting behaviors of softmax dynamics. Unlike hardmax dynamics, localmax dynamics assigns positive weight not only to the maximizers of influence but also to nearby tokens, with the extent of this relaxation controlled by an alignment-sensitivity parameter. In this way, it captures an essential feature of softmax dynamics while recovering hardmax behavior in the appropriate limit. We prove that the convex hull of the token states converges to a convex polytope, but show that its limiting structure is not determined solely by maximal alignment sets. To describe the invariant behavior of tokens near the vertices of the limiting polytope, we introduce the notion of quiescent sets. We also show that localmax dynamics does not generally converge in finite time and discuss the sharp limitations of Lyapunov methods commonly employed in the study of Hegselmann-Krause dynamics in this asymmetric setting.

ABSTRACT. Stochastic gradient descent (SGD) is the primary workhorse for large-scale optimization. While the average behavior of SGD and its variants is well-understood via mean-squared error bounds, obtaining high-probability guarantees for the last iterate remains challenging, even in a centralized, single-agent setting. In this context, we develop new techniques for analyzing stochastic optimization algorithms, while considering randomness due to sub-sampling and additive gradient noise. For the finite-sum setting, we provide a simple, unified proof framework that yields the first high-probability bounds for popular variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA. Our analysis is significantly simpler compared to the previous notoriously challenging computer-aided analysis for SAG, and improves upon the best-known rate for the deterministic counterpart of SAG, namely, the Incrementally Aggregated Gradient (IAG) algorithm. Next, for the additive noise model, we propose a batched variant of SGD that partitions streaming samples into batches and performs a single update per batch using a refined, variance-reduced gradient estimate. Our main contribution is to show how such a batching strategy leads to order-optimal high-probability bounds, while relaxing several stringent assumptions made in prior work. Finally, we show that our approach is easily extended to a distributed setting, leading to dramatic reductions in communication complexity relative to existing literature on the topic. Overall, our work contributes novel insights towards characterizing the uncertainty of stochastic optimization algorithms.

ABSTRACT. This paper proposes a decentralized event-triggered topology-switching protocol for multi-agent systems under estimation uncertainty. We consider an intermittent communication setting in which each agent switches between connected and disconnected modes and makes communication decisions using locally computable certificates, while the closed-loop state is required to remain safe. The proposed protocol follows a safety-driven triggering principle in which agents reconnect before their certificates reach the safety boundary and disconnect only after recovering to a stricter bound below the safety limit. Our design enables intermittent connectivity while maintaining the estimation error within a certified safety bound and excluding Zeno behavior. We evaluate the proposed protocol on a quadruple-tank example, showing that it keeps all tank deviations within the safety bound while allowing agents to remain disconnected for most of the run.

ABSTRACT. The growing use of large language models (LLMs) for sensitive applications has highlighted the need for effective watermarking techniques to ensure the provenance and accountability of AI-generated text. However, most existing watermarking methods require access to the decoding process, limiting their applicability in real-world settings. One illustrative example is the use of LLMs by dishonest reviewers in the context of academic peer review, where conference organizers have no access to the model used but still need to detect AI-generated reviews. Motivated by this gap, we introduce In-Context Watermarking (ICW), which embeds watermarks into generated text solely through prompt engineering, leveraging LLMs’ in-context learning and instruction-following abilities. We investigate four ICW strategies at different levels of granularity, each paired with a tailored detection method. We further examine the Indirect Prompt Injection (IPI) setting as a specific case study, in which watermarking is covertly triggered by modifying input documents such as academic manuscripts. Our experiments validate the feasibility of ICW as a model-agnostic, practical watermarking approach. Moreover, our findings suggest that as LLMs become more capable, ICW offers a promising direction for scalable and accessible content attribution.

ABSTRACT. Data fusion systems combine estimates, beliefs, or decisions produced by multiple sensors or agents. This paper shows that, under exchangeability, fusing strategies rather than estimates provides a systematic way to reduce convex risk. We study two concrete data fusion models: heterogeneous additive fusion, where statistically equivalent sensor outputs are combined by possibly different local fusion rules, and bilinear multimodal fusion, motivated by architectures that integrate sensor-derived state estimates with natural-language task or command inputs.

We develop two complementary design approaches. The first optimizes over convex combinations of relabeled fusion strategies and yields explicit distribution-free convex-order guarantees. For additive fusion, this reduces to convex optimization over the Birkhoff polytope; for bilinear fusion, it leads to an analogous tensor formulation. The second uses Strassen’s martingale-coupling characterization to replace optimization over an infinite class of convex risk functions by optimization over martingale couplings. Together, these methods yield tractable procedures for trading off mean-squared accuracy against convex-risk robustness.

ABSTRACT. Offline Reinforcement Learning from Human Feedback (RLHF) pipelines such as Direct Preference Optimization (DPO) train on a pre-collected preference dataset, which makes them vulnerable to preference poisoning attack. We study label flip attacks against log-linear DPO. We first illustrate that flipping one preference label induces a parameter-independent shift in the DPO gradient. Using this key property, we can then convert the targeted poisoning problem into a structured binary sparse approximation problem. To solve this problem, we develop two attack methods: Binary-Aware Lattice Attack (BAL-A) and Binary Matching Pursuit Attack (BMP-A). BAL-A embeds the binary flip selection problem into a binary-aware lattice and applies Lenstra-Lenstra-Lovász reduction and Babai's nearest plane algorithm; we provide sufficient conditions that enforce binary coefficients and recover the minimum-flip objective. BMP-A adapts binary matching pursuit to our non-normalized gradient dictionary and yields coherence-based recovery guarantees and robustness (impossibility) certificates for -flip budgets. Experiments on synthetic dictionaries and the Stanford Human Preferences dataset validate the theory and highlight how dictionary geometry governs attack success.

ABSTRACT. Progress in 3D reconstruction and generation has accelerated rapidly, producing increasingly detailed geometry and photorealistic rendering. However, moving beyond photorealism requires models that not only look correct, but are also semantically grounded and physically plausible. This talk focuses on two complementary directions. First, multimodal grounding: 3D representations should align naturally with language and images to support cross-modal understanding, controllable generation, and intuitive editing. Second, physical grounding: reconstructions and synthesized scenes should respect constraints such as support, contact, and feasible motion, enabling reliable interaction and deployment in embodied settings, including robotics. I will present our recent work toward multimodally aligned and physics-aware 3D reconstruction and generation, and discuss the challenges that lie ahead.

ABSTRACT. Embodied agents rarely know the full state of their surroundings, yet they must act, observe, and revise their plans continuously. This talk presents online world modeling as a belief inference problem for closed-loop planning under partial observability. Rather than treating a world model as a video predictor or a visually realistic simulator, we focus on models that construct structured 3D hypotheses about what is present, what is hidden, and how uncertainty should change as new views arrive. I will discuss the core ingredients needed for such systems and how they allow agents to plan over possible worlds, gather information when needed, and adapt their behavior as observations resolve ambiguity.

ABSTRACT. Recent progress in generative modeling has been largely driven by diffusion and autoregressive models, but interactive world modeling raises a complementary set of demands: models must not only generate realistic observations, but also support prediction, uncertainty modeling, temporal consistency, and efficient inference over latent states. In this talk, I will revisit normalizing flows as a promising framework for building such models. While flows have historically been viewed as elegant but difficult to scale, recent autoregressive flow models such as TARFlow, STARFlow, and STARFlow-V demonstrate that likelihood-based, invertible models can be competitive for high-resolution image and video generation. I will discuss how the core properties of flows—exact likelihood training, invertible transformations, and causal generation—may provide useful structure for world models that operate over images, videos, trajectories, and multimodal sequences. I will also highlight the key technical challenges that remain, including high-dimensional dynamics, long-horizon consistency, and action-conditioned prediction. The talk will examine whether normalizing flows can offer a principled and scalable probabilistic foundation for interactive generative systems.

ABSTRACT. Large language models recombine skills they were never explicitly taught; robot policies, until recently, could not -- reliable behavior meant a fine-tuned model per task. This talk traces two years at Physical Intelligence, from π0 to π0.7: a single steerable generalist that matches task-specific specialists out of the box. I'll focus on what makes it work: diverse conditioning (language, subgoal images, and metadata such as speed and quality) that lets one model absorb messy, heterogeneous, even failed data and distill specialist skill into a generalist, plus multi-scale memory and an imagined-subgoal world model for long-horizon tasks. The payoff is early compositional generalization in the physical world: operating unfamiliar appliances and transferring zero-shot to robots it never trained on.

ABSTRACT. We theoretically study the hallucination phenomena in two canonical diffusion samplers: the stochastic Denoising Diffusion Probabilistic Model (DDPM) and the deterministic Denoising Diffusion Implicit Model (DDIM). We analyze the reverse ODE (DDIM) and SDE (DDPM) for a Gaussian mixture target, proving that after a critical time τ, (a) DDIM can become stuck on the segment connecting the two nearest modes and (b) DDPM stochasticity helps it become unstuck from this region, thus avoiding hallucination. Our empirical validation verifies that DDPM has a significantly lower hallucination rate than DDIM when this region is entered. Building on our observations, we exhibit how using additional stochastic steps can help DDIM avoid hallucinations and offer new insights on how to design improved samplers.

ABSTRACT. Tool-calling language-model agents must learn two coupled behaviors: high-level reasoning over long horizons and low-level tool selection under sparse end rewards. Flat reinforcement learning from verifiable rewards entangles these decisions in a single trajectory-level objective, which makes credit assignment difficult and can cause collapse to narrow tool-uses. We propose ECHO, an alternating hierarchical GRPO algorithm designed as a regularized two-player Stackelberg game between a high-level reasoning policy and a low-level tool-use policy. The low-level player maximizes skill-conditioned entropy over useful tool modes, while the high-level player maximizes task reward given the induced tool behavior. This design encourages the lower level to maintain reliable and diverse tool-use behaviors, while the upper level learns to compose those behaviors into successful reasoning trajectories. We provide a Stackelberg learning analysis, in which we order policies by stochastic dominance over ordered reasoning and tool behaviors. Under policy-level strategic complementarities, exact regularized response dynamics are order-preserving, have extremal fixed points, and converge monotonically. We then analyze a practical implementation, demonstrate approximate Stackelberg equilibrium, and present our results for ECHO across state of the art tool calling benchmarks, including arithmetic reasoning, and knowledge intensive reasoning tasks. Joint work with Sarat Bobbili, Jeremy Carleton and Dheeraj Narasimha.

ABSTRACT. Diffusion language models (DLMs) represent a nascent but promising alternative to GPT-style autoregressive (AR) language models. Unlike AR models that generate one token at a time left-to-right, DLMs start from a set of noise tokens which they iteratively refine into text. This any-order generation can potentially result in more consistent text, while parallel generation can be faster. In practice, however, parallel generation often results in drops in output quality.

In this talk, we identify two issues with current DLMs: (a) parallel generation samples from product marginals instead of the true joint distribution of tokens, and (b) early errors are the primary cause of drops in accuracy. We then develop a new architecture for better sampling and a new self-training process to significantly fix these issues. No prior knowledge of DLMs is assumed

ABSTRACT. Support constraints on parity-check matrices model sparse measurements, local repair groups, and hardware-limited code implementations. Prior work established the optimal minimum distance under an arbitrary parity-check support mask and showed that the optimum can be achieved over a sufficiently large field size [1, Thm. 1]. The same work showed that this optimum need not always be realized as a subcode of a generalized Reed–Solomon code [1, Thm. 6]. In contrast, in the generator-matrix setting, the GM–MDS theorem [2, 3] guarantees that the optimal distance can always be achieved by a subcode of a generalized Reed–Solomon code over small field sizes while satisfying arbitrary support constraints. We identify concrete mask structures for which an analogous parity-check construction is possible. These codes inherit the optimal minimum distance and efficient decoding algorithms from their Reed–Solomon parent codes. The construction proceeds by determining a subset of parity-check columns with maximal Kruskal rank. The sparsity pattern on the remainder of the columns must be compatible with a polynomial interpolation problem. We analyze this problem for various mask structures, leading to new code constructions, and draw a connection to local/global parity-check structures present in Tamo–Barg locally-recoverable codes.

ABSTRACT. Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the encoder, but not to the decoder. A novel recursive construction of a set of masks is developed such that it can satisfy any s stuck-at errors in a 2^m binary sequence, when s <= m. We prove that the masks generated in this way are codewords in a Reed-Muller RM(s-1, m) code. The constructed set contains no more than 2^s m^{s-1} masks. We provide the lower and the upper bound on the size of the stuck-at redundancy, a fixed subset of mask bits that uniquely represents each mask in the set. The stuck-at code constructed in this way is a non-linear code. It is also a subcode of an RM(r,m) code, with r >= s-1, that can be used for additional random error correction. The encoding requires no mask search and is straightforward based on the description of the recursive construction. The decoding is done in a single attempt and requires almost no additional complexity or latency.

ABSTRACT. We study the multiple key-cast problem, in the context of network coding, under active node-based adversaries. In multiple key-cast, a source generates independent secret keys to be securely and reliably delivered to designated terminal subsets. In our model of study, the network adversary can observe \(\ell_o\) nodes, inject additive or overwrite errors into \(\ell_e\) nodes, and simultaneously observe and corrupt \(\ell_{oe}\) nodes, while having full knowledge of the network topology and coding operations. Adversarial models of similar nature, however, where corruption and eavesdropping is done on edges instead of nodes, have seen previous studies in the context of secure multicast network-coding. The work at hand builds on and extends these studies to address the challenges in node-based adversaries in the context of (multiple) key distribution. For single-source networks in which every node is d-vertex connected from the source, we show that perfectly secure multiple key-cast under both additive and overwrite error models is asymptotically achievable at the key-capacity of \(d - \ell_o - \ell_e - 2\ell_{oe}\). We then extend our analysis to networks where only terminal nodes satisfy this connectivity requirement, while intermediate nodes may be only partially connected. For these topologies, we develop coding schemes that achieve secure and reliable multiple key-cast capacities determined by the source vertex-connectivity and additional structural properties of the network. Finally, we show that our results generalize to multi-source settings, ensuring perfect secrecy even if the adversary observes all but one source node, and establish that our constructions apply directly to secure multicast network coding and to network secret-sharing scenarios. As part of our studies, we improve the security guarantee of a central scheme in [Zhang et al., IEEE Trans. on Comm., 2023] addressing parallel-edge networks, from weak-security to perfect-security.

ABSTRACT. Incremental redundancy (IR) can reduce error rates by spreading coded bits across multiple transmission attempts. However, conventional stop-and-wait operation with coarse feedback often over-provisions retransmissions, triggers unnecessary decoding attempts, and increases end-to-end latency. This paper develops enhanced feedback and scheduling mechanisms that predict the additional redundancy needed for successful decoding and allocate only the required resources. We study two complementary strategies. First, using channel statistics, we learn a one- or two-shot mapping from channel quality to the minimum redundancy budget. As a byproduct, we derive an achievable reliability lower bound on the error probability of hybrid automatic repeat request (HARQ) systems. Numerical results with polar-coded IR-HARQ scheme show that the bound can be closely approached by appropriately selecting the second-transmission redundancy over a wide SNR range with savings up to 60% in retransmission size. Second, we propose a realization-aware early-feedback mechanism that uses first-transmission reliability information to make per-codeword decisions before decoding: whether the codeword is already decodable, if not, how many additional redundancy versions are needed, or whether decoding is unlikely and rate adaptation is preferable. Link-level simulations with 5G NR LDPC codes show that both predictors achieve high accuracy (about 96% in our study), increasing the probability of successful decoding within at most two transmission occasions.

ABSTRACT. First-order methods can exploit quadratic growth to achieve faster convergence, but doing so without knowing the growth modulus is challenging. The difficulty is especially pronounced in nonsmooth optimization, where gradient norms are unavailable and subgradient norms generally fail to provide reliable measures of algorithmic progress. To address this issue, we introduce a bundle-based W-certificate that certifies optimality gaps for any convex objective satisfying quadratic growth. Building on this certificate, we develop a parameter-free algorithm that automatically adapts across nonsmooth, weakly smooth, and smooth Hölder regimes, while achieving the optimal rates dictated by the underlying smoothness and growth structure.

ABSTRACT. This paper is concerned with learning principal variations of random probability measures on $\dsR^m$ under the Wasserstein geometry. We introduce a new dynamical formulation to interpret the linearized PGA (log-PCA) as a variational approach. Our differentiable version, termed as the Wasserstein Tangential PCA (WT-PCA), captures the local principal modes of geodesic variations of a (weighted) probability measure on the Wasserstein space via its covariance operator at barycenter. Based on the dynamical perspective and leveraging parallel transport structure of the optimal transport problems, we derive a general statistical convergence rate of the empirical WT-PCA when estimated from data in terms of the 2-Wasserstein distance between the population and empirical barycenter reference measures.

ABSTRACT. We consider how an intelligent or reactive agent can reason to play against a finite set of opponents. This is carried out in the setting of playing a one-shot game repeatedly where all agents interact through a simulator oracle that plays the strategies provided by the agents. When all other agents are passive, i.e., use a fixed response function, then we show that the sole reactive agent faces a stochastic control problem. In addition to showing to solve such a problem when the response functions of the agents are known, we also develop a low-regret learning scheme when the response functions are not known. When some or all other agents are reactive, then we show that we have a dynamic game with symmetric information, and show the existence of Markov Perfect Equilibrium; developing learning schemes in this context is for future work. This is joint work with Grant Griffin at the University of Michigan, Ann Arbor.

ABSTRACT. Canonical social learning models consider settings in which a sequence of agents receive private information about an unknown state of the world. Agents seek to make decisions based on their private information and their observations of other agents. In principle agent settings, an agents actions may be influenced not only by the pay-off they receive from their action but by "career concerns" that capture how they are evaluated by a principle in terms of their ability. This paper will discuss models that combine these two concerns.

ABSTRACT. We consider the problem of a principal that aims to locate potential targets at the nodes in a graph. The principal contracts an agent that is able to traverse the graph, collect stochastic measurements at each node (with a sensing cost per measurement), and choose to inform the principal of a target at the node (based on its posterior belief that the node contains a target). If the agent informs the principal of a target at a node, the agent receives a bonus from the principal's reward if the target is present or incurs a penalty as a portion of the principal's cost if the target is not present. We show that the agent’s optimal search and sensing policy can be obtained via an algorithm that brings together key ideas from prize collecting strolls and optimal stopping problems. Additionally, we present insights into bonus and penalty allocation policies for the principal, including constraints on the optimal bonus structure. Namely, we demonstrate bounds on feasible bonus allocations that align the actions of the agent with the utility of the principal. We also characterize the impact of approximation algorithms on these bounds.

ABSTRACT. Information design and signaling games provide two distinct approaches to strategic communication under asymmetric information. In Bayesian persuasion, the sender commits ex ante to an information structure before the state is realized, whereas in signaling games communication is chosen strategically after private information is observed. This paper interprets Bayesian persuasion as overt information design and signaling games as covert information design, and develops a unified framework for comparing them. We formulate both models using a common posterior-based representation and define the commitment gap, or price of transparency, as the difference between the sender's optimal payoff under commitment and without commitment. We show that the feasible set of signaling outcomes is generally a subset of the persuasion feasible set, implying a nonnegative commitment advantage. The framework quantifies the value of transparency and commitment in strategic communication and provides new connections among information design, signaling, mechanism design, and dynamic games.

ABSTRACT. Post-training for long-horizon agentic tasks has a tension between compute efficiency and generalization. While supervised fine-tuning (SFT) is compute efficient, it often suffers from out-of-domain (OOD) degradation. Conversely, end-to-end reinforcement learning (E2E RL) preserves OOD capabilities, but incurs high compute costs due to many turns of on-policy rollout. We introduce PivotRL, a novel framework that operates on existing SFT trajectories to combine the compute efficiency of SFT with the OOD accuracy of E2E RL. PivotRL relies on two key mechanisms: first, it executes local, on-policy rollouts and filters for pivots: informative intermediate turns where sampled actions exhibit high variance in outcomes; second, it utilizes rewards for functional-equivalent actions rather than demanding strict string matching with the SFT data demonstration. We theoretically show that these mechanisms incentivize strong learning signals with high natural gradient norm, while maximally preserving policy probability ordering on actions unrelated to training tasks. In comparison to standard SFT on identical data, we demonstrate that PivotRL achieves +4.17% higher in-domain accuracy on average across four agentic domains, and +10.04% higher OOD accuracy in non-agentic tasks. Notably, on agentic coding tasks, PivotRL achieves competitive accuracy with E2E RL with 4x fewer rollout turns. PivotRL is adopted by NVIDIA's Nemotron-3-Ultra, acting as the workhorse in production-scale agentic post-training.

ABSTRACT. We study inference-time reward-guided alignment for generative models. Existing methods often rely on either architecture-specific adaptations or computationally costly inference procedures. We introduce \textbf{Learnable Chernoff Baselines (LCBs)} as a method for efficiently and approximately sampling from the exponentially tilted kernels that arise from KL-regularized reward alignment. Using only black-box sampling access to the pre-trained model, LCBs implement a form of rejection sampling with adaptively selected acceptance probabilities, which allows fine-grained control over inference-compute scaling. We establish total-variation guarantees to the ideal aligned model, which reveal the dimension-independent quantities governing the tradeoff between accurate sampling and inference compute. We empirically demonstrate in both continuous and discrete diffusion settings that LCB sampling closely matches ideal rejection sampling, but uses substantially fewer queries to the pre-trained model. Our experiments also include real-world data experiments on a diffusion large language model.

ABSTRACT. Distribution networks are increasingly exposed to threats such as extreme weather, aging infrastructure, and cyber risks--resulting in more frequent contingencies and outages, a trend likely to persist. Dynamic networked microgrids (DNMGs) offer a promising solution to mitigate the impacts of such contingencies and enhance resiliency. However, distribution networks present unique challenges due to their unbalanced nature and the inherent uncertainty in both loads and generation. This paper develops an approach to reconfigure and control DNMGs building on our prior work on 1) two-stage mixed-integer robust optimization for configuring DNMGs and 2) a model-free, real-time optimal power flow algorithm to manage DNMG operations in the time between reconfigurations. A case study on a realistic network demonstrates the scalability of the combined approach. The case study also illustrates the ability to maintain power flow feasibility as loads vary and operating conditions change when the methods are used in tandem.

ABSTRACT. We present a foundation model for power systems that predicts ACOPF solutions in milliseconds. Given a grid topology and loading conditions, it produces bus voltages, generator dispatch, nodal prices, and a feasibility classification, all without running a solver. The architecture is based on an ADMM approach to ACOPF and is trained on diverse grid topologies ranging from hundreds to tens of thousands of buses, with over 2 million solved scenarios. For new grids, an active learning adapter and fine tuning achieves close to optimal performance using a small number of training data, reducing the need for ground truth data generation by orders of magnitude.

ABSTRACT. How can a system operator safely learn to control a population of thermostatically controlled loads (TCLs) when their aggregate dynamics are unknown and distribution network constraints must be respected throughout the learning process? We study this problem through the broader lens of safe adaptive linear quadratic control for unknown linear dynamical systems subject to chance constraints. We propose an algorithm that achieves rate-optimal $\tilde{O}(\sqrt{T})$ regret while satisfying the chance constraints at every time step. To the best of our knowledge, this is the first $\tilde{O}(\sqrt{T})$ regret guarantee for adaptive LQ control with anytime constraint satisfaction. The algorithm computes optimistic controllers through a semidefinite program and then scales the resulting policy to ensure verifiable safety under model uncertainty. We then apply the framework to TCL control under distribution network constraints. Simulations on a 56-bus distribution network show that the proposed method maintains network constraint satisfaction with the prescribed probability while achieving low electricity costs.

ABSTRACT. Fourier Neural Operators (FNO) parameterize spectral convolutions with the complex-valued FFT. For real-valued PDE solution operators, we ask whether a real-valued spectral basis is better suited, and introduce the Hartley Neural Operator (HNO), which replaces the FFT with the Discrete Hartley Transform (DHT). Our central claim is that the better basis is a property of the operator being learned: for a self-adjoint elliptic operator the Green's function is real and symmetric, so the DHT diagonalizes it with real weights while the complex FFT carries imaginary degrees of freedom that vanish at the optimum. We test this under a protocol that holds spectral corner coverage, real parameter count, and training identical across the two operators, isolating the basis. Across five PDEs and two initial-condition families, the better basis is set by the operator class. On the elliptic problems, Poisson and biharmonic, HNO holds the edge across initial-condition families, consistent with the alignment between the real basis and the operator's real, symmetric Green's function. On the time-dependent problems, heat, wave, and Burgers, FNO leads by $15$--$33\%$, under both roadband and Fourier-aligned initial conditions. The split is therefore governed by the operator, not the data distribution: static self-adjoint operators favor the real basis, evolutionary operators the complex one. These results recast the spectral basis from a fixed architectural choice into one governed by the structure of the target operator, and motivate learning the basis rather than fixing it.

ABSTRACT. The Fisher information matrix (FIM) is a useful tool for assessing local statistical complexity, but straightforward model simplifications do not always lower its rank. We highlight this fact by contrasting rectified linear unit (ReLU) multilayer perceptrons (MLPs) with fixed-basis Kolmogorov–Arnold Networks (KANs). In a ReLU MLP, a dead hidden unit creates exact zero score directions, lowering FIM rank. A fixed-basis KAN (in which each edge function is a learned linear combination of fixed spline atoms) behaves differently. In a single-layer Gaussian KAN, the FIM is the Gram matrix of this fixed dictionary under the data distribution, and is therefore independent of the learned coefficients. In a multilayer KAN, the same Gram identity holds locally on each edge after replacing the data distribution by an effective edge distribution. This distribution records effective exposure: upstream mass must reach a spline support, and downstream transmission must carry that edge to the prediction. A zero coefficient alone does not cut this path. Thus KAN FIM rank loss comes from zero effective exposure, not from coefficient flattening. Under standard B-spline nondegeneracy, zero exposure exactly characterizes edge-block nulls; below-cutoff eigenvalues are distinct from rank-free deletion; and in a KAN edge diagnostic, coefficient magnitude does not reliably predict edge-block FIM curvature, while exposure does.

ABSTRACT. Kolmogorov-Arnold Networks (KANs) with spline activations have recently shown promise for interpretable function approximation. Distance-Aware Error for Kolmogorov Networks (DAREK) introduces a computationally efficient bottom-up approach to uncertainty quantification by equipping KANs with distance-aware error bounds; yet, in high-dimensional settings, the theoretical guarantees can be weakened by the emergence of fictitious knots. Inspired by the Kolmogorov-Arnold representation theorem, DAREK adopts a componentwise formulation in which each input dimension is treated separately; as a result, induced knot locations may appear in the combined input space without corresponding to actual training data. These fictitious knots mislead the DAREK uncertainty estimator into reporting low uncertainty far from any real observation, violating the distance-awareness guarantee. We identify this failure mode precisely, characterize its geometric structure, and propose a drainage uncertainty mechanism that restores distance-awareness by constructing a monotonically decreasing uncertainty path from any fictitious knot region toward the nearest real knot. The proposed drainage method provides a practical heuristic correction that mitigates the fictitious-knot failure mode while restoring theoretical distance-awareness in high-dimensional settings. Experiments on synthetic and 100-dimensional face datasets show that drainage raises sampled distance-awareness (SDA) from 85% to 98-99%, matching Gaussian processes at lower computational cost.

ABSTRACT. We operate through the lens of ordinary differential equations and control theory to study the concept of observability in the context of neural state-space models and the Mamba architecture. We develop strategies to enforce observability, which are tailored to a learning context, specifically where the hidden states are learnable at initial time, in conjunction to over its continuum, and high-dimensional. We also highlight our methods emphasize eigenvalues, roots of unity, or both. Our methods effectuate computational efficiency when enforcing observability, sometimes at great scale. We formulate observability conditions in machine learning based on classical control theory and discuss their computational complexity. Our nontrivial results are fivefold. We discuss observability through the use of permutations in neural applications with learnable matrices without high precision. We present two results built upon the Fourier transform that effect observability with high probability up to the randomness in the learning. These results are worked with the interplay of representations in Fourier space and their eigenstructure, nonlinear mappings, and the observability matrix. We present a result for Mamba that is similar to a Hautus-type condition, but instead employs an argument using a Vandermonde matrix instead of eigenvectors. Our final result is a shared-parameter construction of the Mamba system, which is computationally efficient in high exponentiation. We develop a training algorithm with this coupling, showing it satisfies a Robbins-Monro condition under certain orthogonality, while a more classical training procedure fails to satisfy a contraction with high Lipschitz constant.

ABSTRACT. Biological prediction and design are only as effective as the sequence representations on which they rely. These representations range from discrete $k$-mer encodings to dense contextual embeddings learned by language models. Self-supervised language models encode rich biological context for DNA, RNA, and protein data. Regardless, the downstream utility depends on how well pre-training objective (among other things) aligns with the prediction task. We introduce the scale-adaptive signature kernel that learns a positive multi-scale mixture of untruncated local signature kernels, adapting both the resolution at which sequence structure is compared and the interaction orders emphasized within each resolution. We investigate its ability to adapt to various biological sequence tasks. Across DNA, RNA, and protein benchmarks, multi-scale signature kernels surpasses baseline models in 63$\%$ of downstream tasks. Moreover, the approach is particularly robust for challenging protein regression problems improving $R^{2}$ by up to 15.4$\%$. Therefore, casting a biological sequence embeddings as paths and leveraging a multi-scale signature kernel is a principled, sample-efficient approach for biological learning.

ABSTRACT. City-scale mobile air-quality monitoring requires route plans that maximise spatial coverage, avoid redundant corridor sampling, and respect heterogeneous sensing constraints. Prior MSense formulations model these requirements through RouteOp, DivOp, and HetOp mixed-integer programmes. Scalable approximations LNS-OD and GLS-CG reduce runtime to sub-second on 1,000-node graphs, yet optimise each instance from scratch with hand-designed operators. This paper develops MSENSE-RL, a deep reinforcement learning extension of MSense that learns reusable routing policies over a distribution of urban sensing graphs, and LNS+RL, a hybrid solver that preserves LNS interpretability while replacing greedy repair with an attention-based policy trained by actor–critic RL and imitation from LNS/GLS demonstrations. We ground the framework empirically in the 34 node AirQo Kampala sensing graph, showing that the top-10 edges alone account for 40.5% of all traversals (edge-usage Gini 0.56), providing a strong structured learning signal for overlap avoidance. We formalise the CMDP, graph encoder, feasibility-masked decoder, Lagrangian HetOp penalties, and three-stage curriculum training. Policy inference runs in O(L|E|+ knrℓ) per instance 22.8× faster than LNS on the Kampala graph and 228×faster than GLS while the safe-repair selector in LNS+RL guarantees that every repair step achieves at least greedy quality. Ablation analysis shows coverage novelty is the dominant feature, contributing a−33% objective drop when removed, while the generalisation gap study reveals the necessity of domain randomisation: a policy without cross-graph training loses 37–49% versus greedy on unseen large graphs.

ABSTRACT. We study data-driven stabilization of unknown discrete-time linear systems using quantized state measurements with finitely many levels. The proposed approach consists of two phases. In the controller design phase, a dynamic quantization scheme is employed to collect data, from which a semidefinite program is formulated directly to synthesize a stabilizing feedback gain. In the stabilization phase, a Lyapunov-based quantizer update rule guarantees exponential convergence under quantized state feedback. A key feature of the proposed framework is that only finitely many quantization levels are required in both phases, while the number of quantization levels remains constant during stabilization. Simulation results demonstrate the effectiveness of the method.

ABSTRACT. Reservoir Computing (RC) networks are widely used machine learning tools for time-series forecasting, yet the mechanisms by which training shapes their dynamics remain largely opaque. In the presented work, we study RC through the lens of systems and control theory. Working in continuous time, we show that RC training can be interpreted as a data-driven feedback design problem, with feedback loops inducing low-dimensional dominant manifolds whose structure reflects the intrinsic dimensionality of the training data. We show how this systems-theoretic point of view naturally links RC training to the famous Dynamic Mode Decomposition algorithm and to observer design problems.

ABSTRACT. In this talk, we consider a special class of control-linear systems and address the problem about controllability on the group of diffeomorphisms (using open-loop control inputs). We exhibit a set of conditions that are sufficient for approximate controllability. The results build upon representation theory of Lie algebras.

ABSTRACT. Policy optimization has achieved great success in control and reinforcement learning. At the same time, many policy optimization problems are inherently nonconvex and may be nonsmooth, for which standard (sub)gradient methods may not work well. In this talk, we introduce a proximal descent method to solve a broad class of weakly convex problems, which includes many composite nonconvex functions and typical policy optimization problems in control. This method is a simple and efficient first-order algorithm that combines the inexact proximal point framework with classical convex bundle techniques. A unique feature of the proximal descent method is its automatic adaptivity: without parameter tuning or algorithmic modification, it achieves faster convergence rates when the objective has additional smoothness or growth structure. As an application, we show that the proposed proximal descent method gives the first deterministic non-asymptotic convergence rate for finding a globally optimal state-feedback gain in discrete-time Hinf control.

ABSTRACT. Reliable data-driven control must provide closed-loop guarantees—on stability, performance, safety—by generalizing across an entire domain from finite samples of the dynamics. In learning theory, this is usually achieved via the introduction of an inductive bias, that is, a set of structural assumptions placed on the problem to connect sampled and unsampled data. While inductive biases for classification and regression problems have been widely studied and their performance is well understood, much less is known for control tasks. This raises a central question: which inductive bias enables efficient nonlinear control with rigorous guarantees on stability, safety, and optimality?

For Lipschitz continuous vector fields, a common assumption (or inductive bias) in control, we construct behavioral guarantees by combining local improvement conditions—integral Lyapunov-like conditions or Bellman inequalities—with coverage arguments over the state space that render such behavior recurrent. This viewpoint enables data-driven verification, but also inspires a novel class of nonparametric controllers, called here chain policies, which are akin to action chunking but with variable duration, and compose a sequence of locally verified controls (a chain) into globally valid certifiable policies. We apply these ideas to data-driven stabilization and to the acceleration of model predictive control, where performance can be systematically traded for reduced data requirements.

Notably, this Lipschitz viewpoint, while flexible, is very conservative: its worst-case bounds still require dense coverage of the state space, a demand that scales poorly with state dimension. To overcome this limitation, we turn to Hamiltonian dynamics, which offer a structurally different inductive bias based on energy and volume conservation. These conservation laws imply, via the Poincaré recurrence theorem, that every region visited by a trajectory is revisited infinitely often, providing vast opportunities for generalization. This allows us to construct chain policies for target reachability from remarkably small datasets.

ABSTRACT. Grasping a moving object with a wrist-mounted camera is a coupled nonlinear estimation-and-control problem. The target may translate and rotate unpredictably, while robot motion changes the camera viewpoint. The robot must estimate the object’s six-degree-of-freedom pose, keep it visible, select a reachable grasp, avoid collisions, and close the gripper at the right time, even when visual measurements are interrupted by occlusion or rapid motion.

We developed a closed-loop framework combining real-time RGB-D pose tracking, adaptive grasp selection, and a curriculum-trained reinforcement-learning controller. From compact geometric features and robot joint states, the policy outputs continuous joint-velocity and gripper commands, jointly coordinating pursuit, visibility, alignment, and grasp timing without an explicit model of target motion. We then introduced a switched estimation and recovery architecture: during reliable tracking, control uses visual pose measurements; when tracking is lost, an extended Kalman filter propagates an uncertain pose estimate and guides target reacquisition. Visual tracking is reinitialized when the object returns, and failed grasps can be retried.

In simulation, the recovery-enabled design achieved 94.3% success under tracking loss, versus 7.1% for the measurement-dependent baseline. On a UR5e robot, it achieved 93.3% success in regular scenes and 80.0% in complex scenes, demonstrating robust dynamic manipulation under intermittent sensing.

ABSTRACT. Open Radio Access Networks (O-RAN) have emerged as a transformative paradigm for future wireless systems by introducing openness, virtualization, disaggregation, and programmable intelligence through the RAN Intelligent Controller (RIC). The availability of standardized interfaces and near-real-time control loops has created unprecedented opportunities for integrating artificial intelligence (AI) into radio access network management and optimization. Over the past several years, a broad range of AI techniques—including supervised learning, deep learning, reinforcement learning, federated learning, graph neural networks, and multi-agent systems—have been proposed to address key O-RAN challenges such as radio resource management, network slicing, traffic prediction, energy efficiency, mobility management, interference mitigation, and spectrum sharing. Despite significant progress, existing solutions often remain task-specific, require extensive retraining, and exhibit limited generalization across deployment environments and network conditions.

This paper presents a comprehensive review of AI-enabled O-RAN systems and provides a unifying perspective on the evolution of intelligence in wireless networks. We first examine the O-RAN architecture and the role of intelligence within near-real-time and non-real-time RIC frameworks. We then develop a taxonomy of AI approaches for O-RAN, covering machine learning, deep reinforcement learning, federated learning, graph-based learning, digital-twin-assisted optimization, and emerging foundation-model-based architectures.

ABSTRACT. In this talk, we study Sibson’s $\alpha$-mutual information for the additive Gaussian noise channel. While the classical case $\alpha = 1$ is well understood and admits deep connections to estimation-theoretic quantities, many of the corresponding structural properties for general values of $\alpha$ remain less explored. We establish several regularity properties, derive an $\alpha$-I-MMSE relationship that relates the derivative of $\alpha$-mutual information with respect to SNR to the MMSE evaluated under appropriately tilted distributions, and characterize its behavior in both the low- and high-SNR behavior of $\alpha$-mutual information. Overall, our results demonstrate that many of the fundamental relationships between information measures and estimation-theoretic quantities extend beyond the Shannon setting, albeit in a modified form involving $\alpha$-tilted distributions.

ABSTRACT. Recent end-to-end learning frameworks optimize pilot design, channel state information (CSI) feedback, and downlink precoding, achieving strong performance with limited feedback in massive multiple-input multiple-output (MIMO) networks. However, the internal representations and decision-making strategies of these systems are not yet fully understood. In this talk, we present an interpretability analysis of a precoding-oriented CSI feedback framework using explainable artificial intelligence (xAI) techniques. We examine the structure of learned pilots, latent feedback representations, and precoding vectors through visualization and clustering methods. Our results show that as feedback constraints are relaxed, the encoder transitions from creating clustered latent representations and quantized precoding behavior under strict budgets to developing smooth, geometry-preserving manifolds that reflect important channel characteristics with more adaptive precoding.

ABSTRACT. Vehicle in-cabin health monitoring requires contactless sensing methods that can localize occupants and recover weak vital-sign motion under short-range, multipath-rich conditions. In this regime, the conventional far-field (FF) plane-wave assumption may miss the spherical wavefront curvature across the radar and reconfigurable intelligent surface (RIS) apertures. This letter presents a near-field (NF) RIS-assisted in-cabin sensing framework for three-dimensional occupant localization and harmonic-aware vital-sign estimation. The proposed model combines direct radar-to-chest propagation and RIS-assisted radar-RIS-chest propagation using element-wise spherical distances, phase, amplitude, and wideband delay, while the RIS coefficients are selected from a fixed seat-level codebook rather than from the true chest location. After NF localization, an RIS-calibrated slow-time response phase-aligns the direct and RIS-only projections before breathing rate (BR) and heart rate (HR) estimation, followed by harmonic-aware HR recovery. Simulations show that the proposed NF-RIS processing improves 3-D localization and BR/HR recovery over NF no-RIS and physically Fraunhofer-valid FF baselines under the same cabin geometry, hidden motion realization, physiological search bands, and SNR points, without ground-truth leakage.

ABSTRACT. This paper introduces a physical layer security threat that transmits unauthorized information by perturbing the phase of transmitted symbols. An infected transmitter embeds the leaked information into the emitted signal by applying a phase perturbation to the data sub-carriers. This phase contamination demonstration encodes one rogue symbol across multiple data sub-carriers. We demonstrate the vulnerability in several modulation and coding schemes in 802.11a and verify the information leakage while the transmitter maintains standards compliance.

ABSTRACT. We consider a large-scale network where multiple nodes transmit time-sensitive information via a shared and unreliable channel to a wireless base station using a Carrier-Sense Multiple Access (CSMA) protocol. In this network, packet transmissions from different nodes are interdependent, making it challenging to analyze and optimize information freshness, captured by the Age of Information (AoI) metric.

In this paper, we develop a tractable analytical framework for analyzing and optimizing the AoI. By combining mean-field approximation with a second-order analysis of the packet delivery process, the proposed approach provides a fast, tractable, and accurate AoI approximation that explicitly accounts for carrier sensing, enabling us to quickly find the network parameters that minimize AoI. Since the framework is built on a finite-state Markov representation of the CSMA protocol, it applies to a broad class of Random Access systems. As a concrete example, we study age-threshold CSMA protocols and derive closed-form or efficiently computable AoI approximations under different protocol settings. We validate the proposed AoI analysis via extensive simulations, demonstrating a tight agreement between analysis and simulation.

ABSTRACT. Sampling, summarizing, or otherwise approximating complex probability distributions are central tasks in statistics, applied mathematics, and machine learning. To this end, we introduce a new method for constructing a small set of weighted samples---i.e., a quadrature rule---via an interacting particle system that minimizes the maximum mean discrepancy (MMD) to the target distribution. Our approach is based on the Wasserstein--Fisher--Rao (WFR) gradient flow of the MMD objective. Rather than discretizing the flow, we use its equilibrium conditions to derive a fixed-point algorithm called mean shift interacting particles (MSIP). We show that MSIP generalizes the classical mean shift algorithm, used to identify modes in kernel density estimates, and that it outperforms state-of-the-art algorithms in two settings: (1) quantization of an empirical measure, as in clustering or data summarization; and (2) approximation of a distribution specified only through its unnormalized density, as in Bayesian inference and other sampling problems. Empirically, mean shift interacting particle systems converge quickly, capture anisotropy and multi-modality, avoid mode collapse, and scale to high dimensions. We discuss the mechanisms underlying this favorable behavior and describe our current theoretical understanding of the convergence of MSIP-type algorithms.

ABSTRACT. Gradient flows provide a natural framework for constructing sampling algorithms that evolve an initial probability measure toward a target distribution. Existing approaches often rely on curved metric structures to define such flows. Under these geometries, however, the associated energies need not be convex for general target measures, preventing convergence guarantees that are independent of the target. To address this, we instead study sampling dynamics that can be expressed as L2-gradient flows, where many natural energies are convex and the resulting dynamics can be interpreted as forms of proportional feedback control. To ensure mass preservation, we introduce projected versions of these flows, which preserve the underlying convexity properties. Since L2-gradient flows, unlike their Wasserstein counterparts, cannot in general be realized through a continuity equation, we introduce kernel-regularized energies that admit sample-based implementations through proximal gradient dynamics. The constrained regularized energies Γ-converge to the limiting constrained energy, and the linear structure of L2 considerably reduces the amount of huffing and puffing involved.

ABSTRACT. Path-integral control/diffusion provides a common mathematical language for sampling, inference, transport, and decision-making under uncertainty. In this talk I will describe Path-Integral Diffusion (PID) as a unifying framework that connects modern generative AI with stochastic optimal control and Schrödinger-bridge ideas. I will begin with the basic PID construction: controlled stochastic dynamics, exponential reweighting of trajectories, and explicit score/control formulas. I will then discuss the analytically tractable linear-quadratic Gaussian-mixture setting, where optimal transport between Gaussian-mixture distributions can be represented through controlled stochastic calculus rather than learned only from data.

The second part of the talk will move from single-particle transport to interacting agents, focusing on Mean-Field PID. Here the central question is how path-integral sampling and control scale when many weakly interacting agents collectively generate a distributional flow. I will summarize the main concepts, theorem-level guarantees, and representative numerical behavior.

Finally, I will describe a new direction: applying PID ideas to controlled quantum measurements. The example is a single continuously monitored quantum spin. The conditional quantum state becomes a belief process driven by measurement innovations, and controlling the measurement record leads to a finite-dimensional quantum analogue of linearly solvable stochastic control. This provides a bridge between generative diffusion, optimal transport, interacting stochastic systems, and measurement control in open quantum dynamics.

ABSTRACT. This talk will report two new developments in Schrödinger Bridges with prior dynamics. The first development concerns nonlinearity in the prior drift and diffusion coefficients. Specifically, we will explain that for generic control-affine nonlinear drift, the Schrödinger Bridge problem is not linearly solvable. The only exception occurs when the input and the noise coefficients are proportional, in which case the Hopf-Cole transform gives a system of boundary-coupled linear PDEs solvable via dynamic Sinkhorn recursion with global convergence guarantees. When the channels do not match, the transformed PDEs remain nonlinear and Sinkhorn does not apply. We propose a new algorithm: Sinkhorn-with-memory with local stability guarantees, and show it works even better in practice. Our second development concerns nonlocal interaction in the prior drift, i.e., the mean-field Schrödinger Bridges. Here we propose new generalizations of the dynamic Sinkhorn recursions with local convergence guarantees. These generalizations enable both first order (i.e., controlled McKean-Vlasov) and second order (e.g., controlled Vlasov-Poisson-Fokker-Planck) mean-field control of distributions. These are joint works with Alexis Teter, Georgiy Bondar, Asmaa Eldesoukey and Yongxin Chen.

ABSTRACT. Diffusion and flow matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications, however, demand enforcing hard constraints on generated samples (for example, robot trajectories must avoid obstacles), a requirement that goes beyond simple guidance. Prevailing projection-based approaches constrain the entire sampling path to the constraint manifold, which is overly restrictive and degrades sample quality. In this talk, I will introduce a novel framework that reformulates hard-constrained sampling as a trajectory optimization problem. Our key insight is to leverage numerical optimal control to steer the sampling trajectory so that constraints are satisfied precisely at the terminal time. By exploiting the underlying structure of flow-matching and diffusion models and adopting techniques from model predictive control, we transform this otherwise complex constrained optimization problem into a tractable surrogate that can be solved efficiently and effectively. Furthermore, this trajectory optimization perspective offers significant flexibility beyond mere constraint satisfaction, allowing for the inclusion of integral costs to minimize distribution shift and terminal objectives to further enhance sample quality, all within a unified framework (termed "HardFlow" in flow-matching and "DiRecT" in diffusion models). We provide a control-theoretic analysis of our method, establishing bounds on the approximation error between our tractable surrogate and the ideal formulation. Extensive experiments across diverse domains, including robotics (planning), partial differential equations (boundary control), and vision (text-guided image editing), demonstrate that HardFlow and DiRecT substantially outperform existing methods in both constraint satisfaction and sample quality.