This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order.

Adaptive sampling schemes are well known to create complex dependence that may invalidate conventional inference methods. A recent line of work shows that this need not be the case for UCB-type algorithms in multi-armed bandits. A central emerging theme is a `stability' property with asymptotically deterministic arm-pull counts in these algorithms, making inference as easy as in the i.i.d. setting. In this paper, we study the precise arm-pull dynamics in another canonical class of Thompson-sampling type algorithms. We show that the phenomenology is qualitatively different: the arm-pull count is asymptotically deterministic if and only if the arm is suboptimal or is the unique optimal arm; otherwise it converges in distribution to the unique invariant law of an SDE. This dichotomy uncovers a unifying principle behind many existing (in)stability results: an arm is stable if and only if its interaction with statistical noise is asymptotically negligible. As an application, we show that normalized arm means obey the same dichotomy, with Gaussian limits for stable arms and a semi-universal, non-Gaussian limit for unstable arms. This not only enables the construction of confidence intervals for the unknown mean rewards despite non-normality, but also reveals the potential of developing tractable inference procedures beyond the stable regime. The proofs rely on two new approaches. For suboptimal arms, we develop an `inverse process' approach that characterizes the inverse of the arm-pull count process via a Stieltjes integral. For optimal arms, we adopt a reparametrization of the arm-pull and noise processes that reduces the singularity in the natural SDE to proving the uniqueness of the invariant law of another SDE. We prove the latter by a set of analytic tools, including the parabolic Hörmander condition and the Stroock-Varadhan support theorem.

In this work, we give a ${\rm poly}(d,k)$ time and sample algorithm for efficiently learning the parameters of a mixture of $k$ spherical distributions in $d$ dimensions. Unlike all previous methods, our techniques apply to heavy-tailed distributions and include examples that do not even have finite covariances. Our method succeeds whenever the cluster distributions have a characteristic function with sufficiently heavy tails. Such distributions include the Laplace distribution but crucially exclude Gaussians. All previous methods for learning mixture models relied implicitly or explicitly on the low-degree moments. Even for the case of Laplace distributions, we prove that any such algorithm must use super-polynomially many samples. Our method thus adds to the short list of techniques that bypass the limitations of the method of moments. Somewhat surprisingly, our algorithm does not require any minimum separation between the cluster means. This is in stark contrast to spherical Gaussian mixtures where a minimum $\ell_2$-separation is provably necessary even information-theoretically [Regev and Vijayaraghavan '17]. Our methods compose well with existing techniques and allow obtaining ''best of both worlds" guarantees for mixtures where every component either has a heavy-tailed characteristic function or has a sub-Gaussian tail with a light-tailed characteristic function. Our algorithm is based on a new approach to learning mixture models via efficient high-dimensional sparse Fourier transforms. We believe that this method will find more applications to statistical estimation. As an example, we give an algorithm for consistent robust mean estimation against noise-oblivious adversaries, a model practically motivated by the literature on multiple hypothesis testing. It was formally proposed in a recent Master's thesis by one of the authors, and has already inspired follow-up works.

We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based, axis-aligned decision regions (finite unions of boxes), whereas shallow ReLU networks are typically trained as score models whose predictions are obtained by thresholding. We analyze the infinite-width, bounded-norm, single-hidden-layer ReLU class through the Radon total variation ($\mathrm{R}\mathrm{TV}$) seminorm, which controls the geometric complexity of level sets. We first show that the hard tree indicator $1_A$ has infinite $\mathrm{R}\mathrm{TV}$. Moreover, two natural split-wise continuous surrogates--piecewise-linear ramp smoothing and sigmoidal (logistic) smoothing--also have infinite $\mathrm{R}\mathrm{TV}$ in dimensions $d>1$, while Gaussian convolution yields finite $\mathrm{R}\mathrm{TV}$ but with an explicit exponential dependence on $d$. We then separate two goals that are often conflated: classification after thresholding (recovering the decision set) versus score learning (learning a calibrated score close to $1_A$). For classification, we construct a smooth barrier score $S_A$ with finite $\mathrm{R}\mathrm{TV}$ whose fixed threshold $τ=1$ exactly recovers the box. Under a mild tube-mass condition near $\partial A$, we prove an $L_1(P)$ calibration bound that decays polynomially in a sharpness parameter, along with an explicit $\mathrm{R}\mathrm{TV}$ upper bound in terms of face measures. Experiments on synthetic unions of rectangles illustrate the resulting accuracy--complexity tradeoff and how threshold selection shifts where training lands along it.

Rapidly developing such mental models is especially critical in ad hoc human-machine teaming, where agents do not have a priori knowledge of others' decision-making strategies.

Cooperative suspended aerial transportation is highly susceptible to multi-source disturbances such as aerodynamic effects and thrust uncertainties. To achieve precise load manipulation, existing methods often rely on extra sensors to measure cable directions or the payload's pose, which increases the system cost and complexity. A fundamental question remains: is the payload's pose observable under multi-source disturbances using only the drones' odometry information? To answer this question, this work focuses on the two-drone-bar system and proves that the whole system is observable when only two or fewer types of lumped disturbances exist by using the observability rank criterion. To the best of our knowledge, we are the first to present such a conclusion and this result paves the way for more cost-effective and robust systems by minimizing their sensor suites. Next, to validate this analysis, we consider the situation where the disturbances are only exerted on the drones, and develop a composite disturbance filtering scheme. A disturbance observer-based error-state extended Kalman filter is designed for both state and disturbance estimation, which renders improved estimation performance for the whole system evolving on the manifold $(\mathbb{R}^3)^2\times(TS^2)^3$. Our simulation and experimental tests have validated that it is possible to fully estimate the state and disturbance of the system with only odometry information of the drones.

LLM-based Search Engines (LLM-SEs) introduces a new paradigm for information seeking. Unlike Traditional Search Engines (TSEs) (e.g., Google), these systems summarize results, often providing limited citation transparency. The implications of this shift remain largely unexplored, yet raises key questions regarding trust and transparency. In this paper, we present a large-scale empirical study of LLM-SEs, analyzing 55,936 queries and the corresponding search results across six LLM-SEs and two TSEs. We confirm that LLM-SEs cites domain resources with greater diversity than TSEs. Indeed, 37% of domains are unique to LLM-SEs. However, certain risks still persist: LLM-SEs do not outperform TSEs in credibility, political neutrality and safety metrics. Finally, to understand the selection criteria of LLM-SEs, we perform a feature-based analysis to identify key factors influencing source choice. Our findings provide actionable insights for end users, website owners, and developers.

Abstract-- We propose Synchronous Dual-Arm Rearrangement Planner (SDAR), a task and motion planning (T AMP) framework for tabletop rearrangement, where two robot arms equipped with 2-finger grippers must work together in close proximity to rearrange objects whose start and goal configurations are strongly entangled. T o tackle such challenges, SDAR tightly knit together its dependency-driven task planner (SDAR-T) and synchronous dual-arm motion planner (SDAR-M), to intelligently sift through a large number of possible task and motion plans. Specifically, SDAR-T applies a simple yet effective strategy to decompose the global object dependency graph induced by the rearrangement task, to produce more optimal dual-arm task plans than solutions derived from optimal task plans for a single arm. Leveraging state-of-the-art GPU SIMD-based motion planning tools, SDAR-M employs a layered motion planning strategy to sift through many task plans for the best synchronous dual-arm motion plan while ensuring high levels of success rate. Comprehensive evaluation demonstrates that SDAR delivers a 100% success rate in solving complex, non-monotone, long-horizon tabletop rearrangement tasks with solution quality far exceeding the previous state-of-the-art. Experiments on two UR-5e arms further confirm SDAR directly and reliably transfers to robot hardware. Task and motion planning (T AMP) [1] represents a fundamental computation challenge in robotics, in which a robot system, e.g., one or more robot arms, must break down a given, potentially long-horizon task into suitable "bite-sized" sub-tasks that can be executed through short-horizon robot motions.