Papers

We introduce target-speaker unlearning ASR (TSU-ASR) task in a fully end-to-end framework for multi-speaker ASR and diarization. Given a multi-speaker utterance and a set of opt-out speakers who do not wish to have their speech transcribed, the task requires an ASR system to transcribe all speakers except the opt-out ones, while still indicating when those speakers are active. As a first step towards tackling this task, we introduce a novel, light-weight Enrollment-Conditioned Gating (ECG) module attachable to a frozen dual-stream speech LLM that enables ASR for new opt-out speakers dynamically during inference, even those who were not seen during initial ECG training phase. Our experiments on both AMI (English) and AliMeeting (Mandarin) datasets show that speech transcription accuracy for corresponding opt-out words or characters falls from 72.3% to 48.2% and from 73.6% to 27.3%, respectively, while retained speakers' transcription error rates maintain more or less the same. Our approach provides a practical solution for modern video conferencing platforms, allowing speakers to dynamically opt-out from automated AI transcriptions without forcefully leaving the meeting sessions, enabling a privacy-preserving interface for potentially millions of online meetings daily.

In this paper, we consider linear stochastic systems with control-linear noise and periodically sampled measurements. We address the problem of feedback stabilization in the mean-square sense. The main contribution of the paper is to provide a necessary and sufficient condition for feedback stabilization. In particular, we relate feedback stabilizability of the stochastic system to the existence of a fixed point of a Riccati-type algebraic equation and, further, to the existence of a solution to an infinite-horizon optimal control problem.

We study critical Strichartz estimates for the resonant hyperbolic Schrödinger flow on the waveguide $\mathbb{R} \times \mathbb{T}^2$. For initial data localized to frequencies at most $N$, we prove that the unit-time $L^2\to L^{10/3}$ operator norm has sharp order $N^{1/5}$. We further track its dependence on the observation length, obtaining sharp estimates in the short- and long-time regimes and characterizing the frequency-dependent intervals on which the critical estimate remains lossless. The precise dependence on $T$ in the intermediate regime $N^{-1}<T<1$ remains open. The upper bounds are obtained by lifting the global endpoint estimate on the elliptic cylinder $\mathbb{R} \times \mathbb{T}$ to Hilbert-valued data, preserving its time summability, and combining this with periodic Bernstein and interpolation. The lower bounds exploit an exact integer null direction in the periodic frequency lattice together with a suitably scaled Euclidean wave packet. Finally, using a Bloch–Floquet transference argument, we recover the known elliptic unit-time estimate from compact torus theory and obtain a lossless elliptic estimate on frequency-dependent short time intervals.

Driving world models learn rich predictive representations of the surrounding environment from visual observations, yet accurate visual prediction does not necessarily translate into effective trajectory planning. We argue that a key bottleneck lies in the mismatch between visual world states and raw geometric trajectories, which may limit the planner's ability to exploit action-relevant semantics encoded by the world model. To address this issue, we propose World-Model Alignment for Latent Trajectories (WALT), which learns a compact generative trajectory latent space by transferring information from a frozen pretrained driving world model without modifying the world model itself. Rather than directly generating raw waypoints, WALT maps them into compact representations through a dual-branch trajectory autoencoder and transfers semantic knowledge from the frozen visual world model into this trajectory space, encouraging the learned action representation to capture scene-level cues relevant to future motion and planning. Beyond our proposed formulation, we systematically study latent learning based on Joint-Embedding Predictive Architectures (JEPA) and feature alignment following Representation Alignment (REPA) to investigate how trajectory-only representation learning affects downstream planning. We evaluate WALT on the NAVSIM benchmarks. Relative to the raw-waypoint baseline, WALT improves PDMS from 89.4 to 89.8 on NAVSIMv1 and EPDMS from 87.3 to 87.9 on NAVSIMv2 while reducing trajectory planner FLOPs by 30.5%. These results suggest that preserving world representations while extracting action-relevant information provides an effective interface for world-model-based trajectory planning.

We classify the smooth projective Fourier–Mukai partners and determine the derived autoequivalence group of the moduli space $U_C(r,d)$ of stable bundles of coprime rank $r\geq2$ and degree $d$ on a smooth complex projective curve, assuming $g(C)\geq3$ and $\Aut(C)=1$. When the Jacobian $J(C)$ has endomorphism ring $\Z$, the partners are indexed by $(\Z/r\Z)^\times/\{\pm1\}$. We also prove that two coprime moduli spaces of vector bundles over complex curves of genus at least four are derived equivalent if and only if they are isomorphic.

Pre-trained vision-language models such as CLIP can recognize new categories via prompting, but they often struggle when labeled data are scarce or the test distribution shifts. Prompt learning adapts only a small set of parameters while keeping the backbone frozen, yet many existing multimodal prompt learners couple the visual and textual branches weakly and can be brittle in low-shot regimes. We propose ProCAP, a probabilistic cross-attentive prompt learning framework that improves cross-modal interaction and training stability without updating any CLIP weights: it learns both visual and textual prompt tokens and links them through stacked bidirectional multi-head cross-attention so the two branches refine each other across prompt depth. To reduce overfitting under limited supervision, we parameterize prompt tokens with Gaussian means and variances and regularize them with lightweight KL and L2 penalties, and we further add a compact symmetric InfoNCE head that aligns cross-attended image features with class-level text representations in a shared low-dimensional space. Across few-shot base-to-novel generalization on 11 datasets, cross-dataset transfer, and domain generalization on ImageNet shift benchmarks, ProCAP achieves strong aggregate base-to-novel performance and competitive transfer performance while keeping the CLIP backbone unchanged.

Recent advancements in image-based profiling techniques have enabled the collection of high-volume cell morphology data, allowing new molecular embedding models to learn from the experimental phenotypic perturbations of a molecule in a cell. Previously, we developed Molecule-Morphology Contrastive Pretraining (MoCoP), a strategy for aligning small molecule embeddings to morphology fingerprints extracted through CellProfiler. The resulting molecular representation showed transferable performance for quantitative structure–activity relationship (QSAR) prediction tasks. Here, we extend the method by using a deep-learning-based cell image encoding pipeline to extract more feature-rich morphology profiles and align them to the molecular embeddings through contrastive learning. The new embeddings encode more accurate information on how molecules perturb cell morphology and enable improvements for QSAR predictions through either fixed-embedding linear probes or fully flexible fine-tuning. Morphology retrieval performance scales log-linearly with training data size, suggesting continued improvements as larger datasets become available. The improved MoCoP v2 also achieves superior performance on toxicity prediction and competitive results on ADME and activity benchmarks, when compared with existing molecular embedding models that use both cell morphology and transcriptomic data during training.

Transition metal dichalcogenides (TMDCs) have emerged as highly tunable platforms for electrocatalysis, particularly for the CO2 reduction reaction (CO2RR). While TMDC edge sites exhibit catalytic activity, the basal plane is typically inert, severely limiting the overall active site density. In this work, we show that sulfur vacancies activate the basal plane of 1H-TMDCs, while concurrent solid-solution alloying provides a mechanism to broadly tune intermediate adsorption energies. We evaluate a library of quasi-binary TMDC sulfide alloys comprising V, Nb, Ta, Mo, and W, screening them by stability, defect energetics, and competitive selectivity to identify the most effective catalysts for CO2RR. Electronic-structure analysis reveals that a d-band center closer to the Fermi energy weakens intermediate binding by leaving key bonding states unoccupied above the Fermi energy. Our calculations identify (Nb,Ta)S2 as a promising catalyst with low sulfur vacancy formation energies, near-optimal CO2RR intermediate binding, and selectivity against the hydrogen evolution reaction. Overall, this work establishes a rational design framework for TMDC alloy catalysts through the simultaneous use of defect engineering and alloying.

Magnetic Resonance Imaging (MRI) often suffers from low signal-to-noise ratio (SNR) and limited spatial resolution, which compromise clinical precision. This study aims to address these challenges by developing a physics-guided degradation model (PGDM) and a novel deep learning framework, Magnetic Resonance Super-Resolution GAN Imaging (MRSRGAN), for improved super-resolution reconstruction of MRI images. The proposed approach consists of two stages: (1) a physics-guided degradation model that simulates low-field MRI conditions by incorporating artifacts such as blur, B0 inhomogeneity, chemical shift effects, down-sampling, and noise to generate paired low-resolution (LR) and high-resolution (HR) training datasets; and (2) an MRSRGAN-based reconstruction network utilizing a hybrid loss function, including modified spectral angle mapper (MSAM) and sharpened ground truth images based on de-convolution of slice profile-based kernels to restore high-SNR and high-resolution images. Experimental validation demonstrates that the proposed method achieves superior spatial resolution, enhanced SNR, improved peak signal-to-noise ratio (PSNR), higher structural similarity index (SSIM), reduced MSAM error, and better non-reference image quality evaluation (NIQE) metrics. Furthermore, it effectively reduces artifacts and demonstrates robustness on real MRI datasets. The MRSRGAN framework, guided by the physics-informed degradation model, provides a significant improvement in MRI image quality, enhancing spatial resolution and diagnostic accuracy. Its demonstrated robustness and effectiveness on real MRI datasets highlight its potential to resolution enhancement for precise diagnostic imaging.

The role of nonlinear carrier dynamics in current-driven spin phenomena remains poorly understood in van der Waals magnetic heterostructures. Here, we investigate the spin polarization and the resulting spin-orbit torque (SOT) in transition-metal dichalcogenide/chromium iodide (TMDC/CrI$_3$) heterostructures, focusing on WSe$_2$/CrI$_3$ and MoSe$_2$/CrI$_3$, in the zero-Rashba spin-orbit coupling (SOC) limit and beyond the linear-response regime. We find that linear spin polarization is forbidden by symmetry, making nonlinear intraband transitions the dominant mechanism in this regime. Consequently, the current-driven spin response differs fundamentally from conventional linear-response predictions. The resulting nonlinear spin polarization generates a purely field-like torque whose magnitude and sign depend sensitively on the chemical potential and doping type, with pronounced asymmetries between n- and p-doped systems. A strong material dependence is also observed: n-doped MoSe$_2$/CrI$_3$ exhibits a torque nearly an order of magnitude larger than that of WSe$_2$/CrI$_3$, together with two sign reversals, reflecting differences in their SOC and proximity-exchange parameters. Structural and electrostatic control through the twist angle and gate electric field provides additional means of tuning the nonlinear torque, including substantial modulation and controllable sign reversals. These findings establish TMDC/CrI$_3$ bilayers as a versatile platform for engineering nonlinear spin-orbit phenomena in ultrathin, low-power spintronic devices.

Modern vehicles increasingly offload computation- ally intensive perception and decision functions to backend servers, requiring accurate predictions of absolute performance metrics such as Round-Trip Time (RTT), processing time, and utilization. In practice, strong temporal variability, heterogeneous backend hardware, and multimodal latency regimes cause offline- trained predictors to drift, creating a reliability gap for latency- sensitive functions. We address this gap with an operational, measurement-driven closed loop that continuously recalibrates absolute-value predictors during runtime. The system aligns real execution measurements with predicted values and performs incremental online updates of a lightweight multi-head neural network while preserving model stability. The model implicitly learns the broad, non-Gaussian spread of input metrics, and a sigma-based error analysis in our evaluation characterizes resid- ual variability under dynamic conditions. Experiments across two Kubernetes clusters show that continuous measurement- driven refinement reduces prediction drift, improves accuracy for RTT, processing time, and utilization, and stabilizes prediction behavior across heterogeneous latency regimes. However, the broad and multimodal distribution of input metrics imposes fundamental limits on absolute-value prediction, with residual errors frequently exceeding configured thresholds. Overall, online calibration proves feasible and necessary for robust computation offloading in dynamic vehicular edge environments, while high- lighting the need for future mechanisms that address extreme latency regimes and high-variance operating conditions.

Foundation models provide robots with the ability to interpret natural language and reason about environmental context, yet most language-conditioned policies assume that goals are well-specified and that task-relevant information is provided upfront via a prior map. Operating in unfamiliar environments with underspecified tasks entails high contextual uncertainty: the robot must jointly infer what constitutes task success, what constitutes relevant information, and where (or whether) that information exists. We address these limitations via CLUE (Closed-Loop contextual Uncertainty rEsolution), a framework for actively resolving contextual uncertainty given underspecified tasks in natural language. CLUE uses an LLM-derived policy to hypothesize task-relevant concepts and potential plans. It then uses a language-embedded map, which is constructed online, to ground these hypotheses into actions. The policy sequentially evaluates hypotheses via closed-loop environment interaction and refines its plans as it gathers new information. We deploy CLUE on a Boston Dynamics Spot across three real indoor and outdoor environments spanning 15 tasks that require object disambiguation, functional inference, and occlusion reasoning. CLUE achieves a success rate within 7 percentage points of an oracle policy and outperforms an LLM-enabled planner without closed-loop feedback by a 4x margin. Supporting experiments demonstrate that simply building and then querying a language-enriched map is insufficient to resolve complex contextual planning tasks; these approaches achieve roughly one third the success rate of CLUE while requiring over 10x more VLM tokens. We provide additional information at https://zacravichandran.github.io/CLUE.

Disinformation research has produced increasingly accurate automated fake-news detectors, but many systems remain difficult to interpret and are weakly connected to established theories of persuasion, credibility, and human judgment. In this paper, we develop a theory-informed computational framework that translates cross-disciplinary theories of fake news into measurable features for automated detection and explanation through statistical techniques and large language models. To that end, we conduct a structured cross-disciplinary review of theories from social sciences, psychology, economics, among other disciplines that reveal how fake news persuades and spreads, thereby establishing a broad theoretical foundation for computational modeling. Experiments on benchmark datasets show that theory-derived features are predictive and provide interpretable, theory-referenced diagnostic signals. Multi-feature models generally outperform individual features, although gains among the strongest small feature combinations are modest. Our work highlights the value of interdisciplinary perspectives in building robust and interpretable fake news detection systems, advancing the foundation for human-centered approaches in combating disinformation.

This paper investigates conformal supersymmetric deformations of Schwarzschild spacetime through the framework of super Poisson-Lie T-duality/plurality. We first study super non-Abelian T-duality in $\sigma$-models featuring a Schwarzschild metric coupled to two fermionic fields. This is realized by describing the original four-dimensional geometry and its dual counterpart via semi-Abelian Drinfeld superdoubles generated by the Lie superalgebras $({\C}^3 +{\A})$, ${\C}^3 \oplus {\A}_{1,1}$ and $(2{ \A}_{1,1}+2{ \A})^0$, supplemented by two spectator fields. We enforce the vanishing of one-loop beta-function equations for both original and dual models to guarantee UV finiteness at quantum level; this procedure necessitates the inclusion of the dilaton field alongside the metric and the Kalb-Ramond field ($B$-field) already present in the classical action. We further study the curvature invariants, singularity structure, and superisometries, and compare the resulting supergeometries, with particular emphasis on their fermionic parts and $B$-fields. Starting from the decompositions of semi-Abelian Drinfeld superdoubles associated with the $({\C}^3 +{\A})$ and ${\C}^3 \oplus {\A}_{1,1}$ Lie superalgebras, we derive the conformal duality/plurality chains for four-dimensional string backgrounds, characterized by a Schwarzschild metric coupled to two fermions. Our results span an interesting spectrum of super Poisson-Lie T-dual $\sigma$-models described by Lie superalgebras with two bosonic and two fermionic generators. These are all non-trivial and interesting examples of super Poisson-Lie T-dual models which help in the intent of providing a general classification of four-dimensional geometries describing supergravity backgrounds.

We construct a multi-filtered smooth knot concordance invariant, $\beta(t^1, a, t^2)$, derived from the knot Floer complex $CFK^\infty$. $\beta$ is a three-variable piecewise linear function defined on $(0,2) \times \mathbb{R} \times (0,2)$. We demonstrate that $\beta$ satisfies a subadditivity relation. We apply $\beta$ to prove concordance results for a certain family of L-space knots. We show that the positive cones spanned by Teragaito's knots $K_{1,n}$ and $K_{2,n}$ are disjoint in the smooth concordance group $\mathcal{C}$. For positive L-space knots, we show $\beta$ completely determines the Alexander polynomial and distinguishes knots with identical $\Upsilon$ invariants.

This review surveys diverse types of random motion within a unified framework, introducing essential mathematical tools, including special functions and fractional calculus, in a pedagogical manner. We focus on generalized random motions in one-dimensional space described by Fokker-Planck like equations, whose fundamental solutions take a universal and simple form in the Laplace-Fourier domain in terms of a generic function $\varphi(s)$. By exploring the functional forms of $\varphi(s)$ consistent with physical constraints, we derive a broad class of stochastic dynamics. This includes Brownian and active motion, simple and anomalous diffusion, and processes featuring stochastic resetting or trapping mechanisms. For each case, we provide the corresponding kinetic equation, explicit solutions (where available), and mean-square displacements alongside their asymptotic behaviors. Finally, we discuss the physical interpretation of these motions through the lens of time-changed processes and subordinators.

I review the evolution of electronic non-relativistic current density functional theory (CDFT) from its original formulation in the late 1980's to present day's formulations, which rely on the generalized Kohn-Sham theory. Axel Becke's outstanding contributions are highlighted throughout. I propose a form of the generalized Kohn-Sham equation that combines the exchange-correlation vector potential of the original formulation with an “effective mass term" – the latter following from the inclusion of Becke's kinetic energy density as a basic input of the exchange-correlation energy functional.

We study the geometry of the three simplest known formulas for roots of a general sextic polynomial. In contrast with work of Green on the quintic, we show that no "simultaneous uniformization" of the normal forms associated to the solutions exists. This demonstrates an intrinsic qualitative complexity of sextic equations that is not present in quintic equations. Additionally, we give a formula for the roots of a general sextic in terms of Hilbert modular cusp forms and the uniformizing differential equation of the associated Hilbert modular surface.

This paper settles the Matroid Secretary Problem with an $e$-probability-competitive algorithm. The algorithm is ordinal and accesses arrived elements only through comparison and independence oracles, and has expected polynomial time and oracle complexity.

Perturbed parameter ensembles (PPEs) reveal how physics parameters affect climate simulations, but interpreting parameter sensitivities across multivariate, spatially structured outputs remains challenging, particularly when calibrating models against observations. We develop an explainable contrastive learning model that maps 5 monthly cloud and radiation fields into a shared representation space. We train the model on the fields of two 100-member Community Atmosphere Model version 6 (CAM6) PPEs, spanning 34 parameters, that only differ in the warm rain microphysics scheme: KK2000, the default bulk microphysics scheme, and TAU-ML, a neural network emulator of a bin microphysics scheme. The learned representations separates two PPEs with over 94% linear classification accuracy while preserving the seasonal variability and ensemble spread due to parameter perturbations. In the shared representation space, the representations of satellite observations occupy the same low-dimensional manifold as the PPEs but are displaced from them most strongly during boreal spring and autumn. TAU-ML PPE has a lower distance to observations compared to KK2000 in the representation space. Integrated Gradients attributions highlights the contributions in subtropical low-cloud regions, Northern and Southern Hemisphere storm track regions, and tropical convection regions to differences between PPEs and observations. Regional attributions correlate most strongly with parameters associated with cloud microphysics, boundary layer turbulence, and deep convection. These results demonstrate that explainable representations of climate fields can attribute model differences to specific variables, regions, seasons, and physical parameters.

This paper concerns the geometry of gravitational pp-wave spacetimes. We give a counterexample to the Ehlers–Kundt conjecture. In fact, we show that geodesic completeness is generic, in the sense of Baire category, among gravitational pp-waves. We also define a concept of “universal pp-wave”, i.e. a pp-wave whose metric approximates that of every other gravitational pp-wave arbitrarily closely on arbitrarily large compact sets, and we show that there are geodesically complete universal pp-waves. Our machinery also suffices to give a new proof of the polynomial case of the Ehlers–Kundt conjecture (previously proved by Flores and Sánchez).

Validating whether the underlying physics of a model has been retained after a full phase-space reweighting poses a unique challenge. Often, validation relies on comparing histograms of 1D observables; however, this can mask correlations and biases in the complete prediction. We present a novel, unbinned approach to comparing the performance of such reweighting schemes based on the "Cross-Section-Mover's Distance", an application of Optimal Transport that quantifies the work required to transform one theoretical prediction into another and enables an interpretation of results in terms of metric spaces. We demonstrate its utility when benchmarking various reweighting schemes that mitigate the effects of negative weights in a Monte Carlo simulation. This approach can be broadly applied in other scenarios where biases in full phase-space reweighting schemes should be studied in an unbinned way.

As electric vehicle (EV) adoption increases, ensuring efficient and well-distributed charging infrastructure has become a critical challenge. While many EV charging station location problem (CSLP) studies focus on minimizing costs or travel distance, it is crucial to consider the surrounding geospatial characteristics of existing stations that influence operational performance. This study proposes a geospatial artificial intelligence (GeoAI)-based framework that integrates high-dimensional EV-related geospatial data, including EV usage, land-use, population, and traffic attributes. We incorporate a variational autoencoder (VAE) and a graph convolutional network (GCN) into the model to capture similarities among existing charging stations, and to identify suitable locations for future stations. The VAE compresses high-dimensional EV input data into a low-dimensional latent space, and the GCN uses this latent representation to predict locations suitable for charging stations. Using real-world data from Bryan-College Station, Texas, US, the proposed model outperforms state-of-the-art baselines, achieving an F1-score of 0.87 in distinguishing existing station locations from non-station locations. The model also identifies 27 additional candidate locations that show geospatial characteristics similar to those of existing stations, based on a similarity score. We further evaluate two policy implementation scenarios, maximizing geospatial similarity and minimizing total travel distance, each yielding different outcomes aligned with distinct strategic objectives. The findings highlight the importance of incorporating spatial context into CSLP and provide valuable insights for future EV infrastructure planning, promoting both efficiency and accessibility in the rapidly growing electric mobility sector.

Large Language Models (LLMs) have shown strong performance in low-resource offline translation; however, extending them to simultaneous speech-to-speech translation (Simul-S2ST) remains challenging due to the scarcity of causally aligned training data with high cross-lingual speaker fidelity. In addition, existing approaches rely on fixed translation policy or confidence heuristics, leading to suboptimal quality and higher latency. We propose a causality-aware Simul-S2ST framework with a novel data pipeline that generates high-fidelity, causally aligned segments with improved voice transfer. The framework introduces (i) a factorized S2ST architecture (FAST), (ii) a causality-aware adaptive policy (CAP), and (iii) causality-aware latency metric. Experiments on CVSS Spanish, German, and French show that FAST-CAP consistently improves the quality-latency trade-off, achieving up to +1.2 BLEU and a 26% relative latency reduction over a fixed policy. Despite using substantially less training data than existing systems, FAST-CAP achieves state-of-the-art results in speech translation quality and speaker fidelity while yielding up to a 38.8% relative reduction in latency.

Signal-level speech privacy mechanisms suppress linguistic content while preserving acoustic information needed by downstream sensing applications. However, their privacy settings are typically evaluated/selected offline and remain fixed during deployment, even though speech-content leakage can vary substantially across utterances and speakers. Adapting privacy protection at runtime requires estimating how much speech remains recoverable, but conventional measures such as WER or PER require ground-truth transcripts and therefore cannot be computed online. We present CLEAR, a reference-free approach for estimating speech-content leakage at runtime using disagreement among heterogeneous ASR systems. Our key insight is that independently trained ASRs exhibit consistent behavior when linguistic content remains recoverable and increasingly disagree as privacy transformations obscure speech. Using configurable speech-suppression mechanism, we show that cross-ASR disagreement closely tracks transcript-grounded leakage across privacy operating points, achieving a correlation of 0.8. We further characterize the latency-accuracy trade-off of heterogeneous ASR subsets and use their hypotheses to identify potentially exposed words. These capabilities enable privacy to be treated as a runtime property rather than a fixed configuration: CLEAR can communicate residual speech exposure to users and provide feedback for dynamically adjusting privacy aggressiveness while retaining acoustic utility for downstream sensing tasks.

Cognitive psychology has studied how people encode, use, and learn concepts that describe categories, and how they represent, recognize, and acquire chunks for familiar patterns of elements. The literatures on these two topics are nearly disjoint, which poses a challenge for unified theories of cognition. In this paper, we review Cobweb, a computational account of categorization and concept formation, then propose an extended theory that incorporates chunks and their acquisition. The theory makes no commitments about modality, applying to any experience that decomposes into elements and relations among them. We also present \trellis/, an implementation of this theory, and illustrate its application to learning context-free grammars, which we adopt as a testbed because they involve both concept-like and chunk-like elements. In addition, we report experimental results on learning for three synthetic grammars that demonstrate the system's ability to represent syntactic knowledge, use it to parse and generate sentences, and learn compositional structures from sample parses. We conclude by discussing related work on concepts and chunks, along with directions for future research on the problem.

We study optimization of distributed model inference over resource-constrained edge resources. We propose a framework that optimizes the trade-off between model accuracy and communication costs by controlling latent representation compression to meet strict Quality of Service (QoS) throughput targets. For settings with known channel state information (CSI), we derive a closed-form optimal solution for single tasks and reduce the multi-task problem to a convex optimization program characterized by a per-link water-filling strategy. We extend these to handle unpredictable environments via a stochastic dual descent algorithm that relies only on causal channel estimates. We provide Lyapunov-based proofs demonstrating that our approach strictly satisfies long-term delay constraints while achieving a bounded optimality gap. Our results offer a robust, scalable blueprint for maximizing the performance of pipelined AI tasks in dynamic, resource-constrained distributed systems. We verify the effectiveness of our proposed framework through simulations and experiments with real edge devices.

We introduce a novel phase-field model approximating the Verigin problem with phase transition. For fixed interface thickness $\varepsilon>0$, we construct weak solutions through a time-discrete variational scheme combining a Wasserstein minimizing-movement for the density with Schätzle's selection procedure for the phase field, which yields strong compactness and an almost-minimizing property. We then investigate the sharp-interface limit $\varepsilon \downarrow0$. For well-prepared initial data, we establish strong compactness of the densities and phase fields, and we prove convergence of the time-integrated diffuse interfacial energy to the perimeter. The limiting evolution is identified as a weak solution of the Verigin problem with phase transition, satisfying an optimal energy dissipation inequality.

We consider the rigorous derivation of membrane theories from three-dimensional nonlinear elasticity. A salient feature of our framework is the inclusion of an orientation-preservation constraint together with energy growth that penalizes vanishing local volume. We embed the 3D variational problem into a space of parametrized measures, and obtain a membrane $\Gamma$-limit defined on a class of nondegenerate gradient Young measures. This formulation offers a twofold advantage: first, it uniquely identifies a non-relaxed membrane energy density capable of capturing the fine oscillations (microstructure) of minimizing sequences; second, the resulting membrane density preserves the unbounded energy growth near degenerate configurations. We further show that the classical relaxed membrane energy of Le Dret and Raoult is recovered as the minimum of our functional over all measures with a prescribed barycenter. The main difficulty lies in generating such measures by maps whose gradients have rank two almost everywhere, which we address through piecewise isometric (origami-like) constructions.

Fix $k,s\in\mathbb{N}$. We prove that there exists a subadditive density on $\mathbb{N}$ such that, for every polynomial $P\in\mathbb{Z}[y]$ of degree $k$ and with $P(0)=0$, every set of positive density contains configurations $\{x,x+P(y),xy^s\}$ for arbitrarily large $x>y\geq 2$. This provides a density strengthening of Moreira's result on partition regularity for $\{x,x+y,xy\}$.