We study the problem of stabilizing an unknown partially observable linear timeinvariant (LTI) system. For fully observable systems, the state-of-the-art approaches leverage an unstable/stable subspace decomposition to achieve sample complexity that depends only on the number of unstable modes, independent of the dimension of the system state. However, it remains open whether such sample complexity can be achieved for partially observable systems because such systems do not admit a uniquely identifiable unstable subspace. In this paper, we propose LTS-P, a novel technique that leverages compressed singular value decomposition (SVD) on the "lifted" Hankel matrix to estimate the unstable subsystem up to an unknown transformation.

When applicants get rejected by a high-stakes algorithmic decision system, recourse explanations provide actionable suggestions for applicants on how to change their input features to get a positive evaluation. A crucial yet overlooked phenomenon is that recourse explanations are performative: When many applicants act according to their recommendations, their collective behavior may shift the data distribution and, once the model is refitted, also the decision boundary. Consequently, the recourse algorithm may render its own recommendations invalid, such that applicants who make the effort of implementing their recommendations may be rejected again when they reapply. In this work, we formally characterize the conditions under which recourse explanations remain valid under their own performative effects. In particular, we prove that recourse actions may become invalid if they are influenced by or if they intervene on non-causal variables. Based on this analysis, we caution against the use of standard counterfactual explanation and causal recourse methods, and instead advocate for recourse methods that recommend actions exclusively on causal variables.

We revisit the contextual cascading bandit, where a learning agent recommends an ordered list (cascade) of items, and a user scans the list sequentially, stopping at the first attractive item. Although cascading bandits underpin various applications including recommender systems and search engines, the role of the cascade length K in shaping regret has remained unclear. Contrary to prior results that regret grows with K, we prove that regret actually decreases once K is large enough. Leveraging this insight, we design a new upper-confidence-bound algorithm built on online mirror descent that attains the sharpest known regret upper bound, O min{K pK 1,1}d Tfor contextual cascading bandits. To complement this new regret upper bound, we provide a nearly matching lower bound of Ω min{KpK 1,1}d T, where 0 p p < 1. Together, these results fully characterize how regret truly scales with K, thereby closing the theoretical gap for contextual cascading bandits. Finally, comprehensive experiments validate our theoretical results and show the effectiveness of our proposed method.

Neural networks are known for their ability to approximate smooth functions, yet they fail to generalize perfectly to unseen inputs when trained on discrete operations. Such operations lie at the heart of algorithmic tasks such as arithmetic, which is often used as a test bed for algorithmic execution in neural networks. In this work, we ask: can neural networks learn to execute binary-encoded algorithmic instructions exactly? We use the Neural Tangent Kernel (NTK) framework to study the training dynamics of two-layer fully connected networks in the infinite-width limit and show how a sufficiently large ensemble of such models can be trained to execute exactly, with high probability, four fundamental tasks: binary permutations, binary addition, binary multiplication, and Subtract and Branch if Negative (SBN) instructions. Since SBN is Turing-complete, our framework extends to computable functions. We show how this can be efficiently achieved using only logarithmically many training data. Our approach relies on two techniques: structuring the training data to isolate bit-level rules, and controlling correlations in the NTK regime to align model predictions with the target algorithmic executions.

Personalized Bayesian federated learning (PBFL) handles non-i.i.d.

Models of hybrid dynamical systems are widely used to answer questions about the causes and effects of dynamic events in time. Unfortunately, existing causal reasoning formalisms lack support for queries involving the dynamically triggered, discontinuous interventions that characterize hybrid dynamical systems. This mismatch can lead to ad-hoc and error-prone causal analysis workflows in practice. To bridge the gap between the needs of hybrid systems users and current causal inference capabilities, we develop a rigorous counterfactual semantics by formalizing interventions as transformations to the constraints of hybrid systems. Unlike interventions in a typical structural causal model, however, interventions in hybrid systems can easily render the model ill-posed. Thus, we identify mild conditions under which our interventions maintain solution existence, uniqueness, and measurability by making explicit connections to established hybrid systems theory. To illustrate the utility of our framework, we formalize a number of canonical causal estimands and explore a case study on the probabilities of causation with applications to fishery management. Our work simultaneously expands the modeling possibilities available to causal inference practitioners and begins to unlock decades of causality research for users of hybrid systems.

In randomized trials involving multiple treatments, bivariate survival outcomes present significant analytical challenges for making decisions. This paper addresses the problem of deriving optimal individualized treatment rules to maximize the joint survival probability beyond fixed time points $(t_1, t_2)$ through deep neural networks, while accounting for right censoring. We propose a novel approach that models treatment rules via stochastic policies, coupling marginal accelerated failure time models via link function to capture bivariate dependence. To enhance robustness and effectiveness of decision making, we introduce an adaptive prediction-powered method that leverages auxiliary predictions from machine learning models.

In federated language modeling, $K$ nodes each hold $n$ samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over $V$ tokens can be estimated when each node may upload at most $B$ bits per query in a public probe set. In federated probe-logit distillation (FPLD), each node transmits a scalar-quantized logit vector on the probe set, and an aggregator distills a global parametric student. Prior work (Dubey and Huo, 2026) establishes a high-probability KL rate $O(d/(Kn) + ρ\sqrt{V \log V / m} + K^{-1} \cdot 2^{-2B/V})$ plus optimization slack, with the bandwidth term in its trace-sharpened form. Whether this bandwidth-term rate is tight, and how the upper bound generalizes to heterogeneous per-node bandwidths, are left open. We close both gaps. First, the dithered FPLD construction has a matching single-round lower bound $Ω(K^{-1} \cdot 2^{-2B/V})$ under non-degeneracy, pinning the bandwidth-axis rate at $Θ(K^{-1} \cdot 2^{-2B/V})$. $T$-round sequential refinement with nested/scaled residual quantizers achieves $O(K^{-1} \cdot 2^{-2TB/V})$; vanilla FPLD's $T$-independent bandwidth term is suboptimal for every $T > 1$. Second, we establish a heterogeneous-bandwidth upper bound for per-node budgets $B_i$, paired with a closed-form optimal allocation $B_i^* = B_{\mathrm{tot}}/K + (V/2) \log_2(w_i / \bar{w}_g)$, a log-tilted water-filling rule that is the per-node analogue of reverse water-filling for distortion-rate optimization. A plug-in adaptive variant estimates the weights from a short warm-up phase and attains $1 + O(\sqrt{\log(K/δ)/(m T_0)})$ relative suboptimality. Synthetic n-gram simulations confirm that empirical KL is bracketed by the upper and lower bounds and that the optimal allocation strictly dominates uniform and inverse-weighted baselines under heterogeneous clipping.

We propose and analyze a conservative drifting method for one-step generative modeling. The method replaces the original displacement-based drifting velocity by a kernel density estimator (KDE)-gradient velocity, namely the difference of the kernel-smoothed data score and the kernel-smoothed model score. This velocity is a gradient field, addressing the non-conservatism issue identified for general displacement-based drifting fields. We prove continuous-time finite-particle convergence bounds for the conservative method on $\R^d$: a joint-entropy identity yields bounds for the empirical Stein drift, the smoothed Fisher discrepancy of the KDE, and the squared center velocity. The main finite-particle correction is a reciprocal-KDE self-interaction term, and we give deterministic and high-probability local-occupancy conditions under which this term is controlled. We keep the quadrature constants explicit and track their possible bandwidth dependence: the root residual-velocity rate $N^{-1/(d+4)}$ holds under an additional $h$-uniform quadrature regularity condition, while a more general growth condition yields the optimized root rate $N^{-(2-β)/(2(d+4-β))}$, where $0\le β<2$. We also analyze the non-conservative drifting method with Laplace kernel, corresponding to the original displacement-based velocity proposed in Deng et al., 2026 (arxiv:2602.04770). For this method, a sharp companion kernel decomposes the velocity into a positive scalar preconditioning of a sharp-score mismatch plus a Laplace scale-mismatch residual, producing an analogous finite-particle rate with an unavoidable residual term. Finally, we explain how the continuous-time residual-velocity bounds translate into one-step generation guarantees through the explicit drift size $η$.

Low-rank adaptation (LoRA) has emerged as a powerful tool for parameter-efficient fine-tuning of large language models (LLMs). This paper studies LoRA under a federated learning setting, enabling collaborative fine-tuning across clients while preserving parameter efficiency. We focus on a highly heterogeneous regime in which clients share only partial structure and a substantial subset may be contaminated. We propose Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR), a contamination-aware framework that relies only on preliminary local estimators. Its formulation applies broadly, from linear regression to neural network and LLM modules, whenever local adaptation can be represented by matrix-valued updates. CLAIR recovers the shared LoRA subspace and detects contaminated clients via a structured low-rank plus block-sparse decomposition. We prove exact recovery of the shared LoRA subspace in the noiseless case, stable recovery under preliminary estimation error, and consistent collaborative-set recovery under mild separation conditions. We further quantify the gain from CLAIR refinement: it reduces off-subspace estimation error through cross-client averaging while preserving client-specific variation within the shared LoRA subspace, thus improves over local fine-tuning whenever this oracle gain outweighs the costs of subspace estimation and benign-client heterogeneity. Empirically, we demonstrate the benefits of CLAIR by fine-tuning a Transformer architecture on a text-copying task. The results show accurate contamination detection and improved benign-client performance compared with local fine-tuning and non-robust federated averaging.