Papers

A conjecture of Erdős asserts that every odd integer $n > 1$ can be written as $n = 2^a + m$, where $a \ge 0$ is an integer and $m$ is a squarefree positive integer. We study this conjecture for primes $p \equiv 7 \pmod{36}$. Writing $x = (p-1)/6$, the candidate remainders take the shapes $p - 1 = 6x$, $p-2 = 6x-1$, $p-4 = 3(2x-1)$, and $p-8 = 6x-7$, in which the primes $2$ and $3$ are completely controlled: every obstruction to squarefreeness comes from a prime $q \ge 5$. For such $q$ a separation principle applies — $q^2$ divides at most one of the remainders, since two of them differ by at most $7 < 25$ — and it persists across any window of exponents of width less than $20$. Separation collapses the square-divisor problem for the quartic $x(6x-1)(2x-1)(6x-7)$ into independent linear problems, and we deduce unconditionally that the primes of the class representable with $a \le 3$ have relative density $1 - \rho_4$, where $\rho_4 = 1.8637 \times 10^{-5}$ is an explicit Euler-type constant; in particular, infinitely many primes of the class are not so representable. Computationally, we verify the conjecture for all primes of the class below $10^8$, always with $a \le 5$, and we exhibit the eleven primes below $10^8$ requiring $a = 5$. An appendix corrects the error bound in a lemma of Hercher, whose conclusions are unaffected.

Nonlinear spectroscopy is widely used to probe ultrafast dynamics in matter. Signals of higher nonlinear orders encode valuable many-body dynamics but only recently have become individually retrievable. However, their physical interpretation in terms of double-sided Feynman diagrams is cumbersome and non-intuitive. Here, we establish an alternative framework that connects them to the underlying excitation conditions and many-body interactions. This approach predicts two classes of dynamic nonlinearities, due either to direct many-body interactions or to saturable kinetic channels. The method provides a direct physical interpretation of the retrieved signals, explaining their sign, magnitude, and dynamics. It also enables model-free reconstruction of the dynamics of a sub-ensemble of particles starting with a given number of excitons, which we demonstrate to be especially insightful. We validate the framework using colloidal CdSe/CdS core/shell quantum dots, which enable us to model nonlinearities of both classes in isolation and also combined.

Reinforcement learning with verifiable rewards (RLVR) trains a language model on problems that may themselves be confidential, and the trained model can reveal which problems it saw. We study RLVR under prompt-level differential privacy: the released weights must be ({\epsilon},{\delta})-differentially private with respect to the presence of any one training problem. Taking the group of responses to one prompt as the privacy record, our method aggregates their gradients, clips the prompt's contribution once, adds Gaussian noise, and composes the privacy loss across updates, so the budget depends on neither the number of responses per prompt nor the clipping norm; to our knowledge this is the first differential privacy guarantee for RLVR training. We train Qwen2.5-1.5B-Instruct with LoRA at a per-run budget of {\epsilon}=8 and compare, on the same prompts and at the same budget, a control that removes only the reward signal and two private supervised fine-tuning recipes. The reward signal improves accuracy over the control by 2.65 points on MATH and 3.24 on GSM8K, in every seed; the improvement survives a format-robust scorer, at 1.3 points on MATH, and is not explained by response length. At the same budget the private model outperforms both supervised recipes on MATH and GSM8K by 2.3 to 3.8 points, retains 85–90% of the gain of non-private GRPO on these tasks, and on MATH the noise of an eightfold tighter budget costs at most 1.2 points. The reward effect also carries to CommonsenseQA, an exploratory non-mathematical task. Verifier feedback thus remains a usable learning signal under prompt-level privacy.

Systems of equations arise in a wide range of scientific and engineering applications. The present work focuses on solvers for general systems of equations, including but not limited to those arising from partial differential equations. These systems can be broadly categorized into linear and nonlinear problems. For large linear systems, iterative solvers are generally preferred over direct methods due to the latter's superlinear growth of computational costs. Although convergence theory is well-developed under certain assumptions on the coefficient matrix, many classes of systems still pose open challenges. These difficulties become even more severe for systems of nonlinear equations, where nonlinear solvers typically rely on repeated linearization. For example, Newton's method may even converge quadratically near the solution; it can also converge slowly or diverge when the initial guess is not chosen appropriately. A wide range of solvers with diverse variants and hyperparameter settings exists, and the development of efficient and robust iterative methods remains an active area of research. Recently, machine learning (ML) techniques have been applied to enhance the efficiency of classical iterative methods while preserving their interpretability and reliability. We refer to these ML-enhanced iterative methods as hybrid iterative methods, in the sense that they combine classical iterative methods with ML. This paper provides a comprehensive overview of state-of-the-art approaches to constructing hybrid iterative methods for systems of both linear and nonlinear equations, while also discussing open challenges and outlining potential directions for future research.

Consider a system of equations $A(x)\cdot F(x) = B(x)$ on a subset $X$ of $\mathbb R^n$, where $A(x)$ and $B(x)$ are matrix- and vector-valued semialgebraic functions on $X$, and the unknown $F(x)$ is a field of vector-valued $m$-jets. We assume there is a solution which is the field of Taylor polynomials of order $m$ on $X$ of a $\mathcal C^m$ vector-valued function $f$ on $\mathbb R^n$, and ask whether we can find a $\mathcal C^m$ semialgebraic solution $f$. Our main result is a positive answer in the case $\dim X = 1$. The methods are based on an article of Fefferman and Luli for $X \subset \mathbb R^2$, and a secondary goal is to show that their approach applies in a much simpler way in the case $\dim X =1$, or in the case of the semialgebraic Whitney extension problem in $\mathbb R^2$. Our results hold more generally for functions definable in an o-minimal expansion of $\mathbb R$.

Limited review teams must identify which emerging claims are likely to keep growing before their eventual reach is known. We center early misinformation triage on this continuation-forecasting problem: predicting subsequent recorded propagation-tree growth from the first 30 minutes of activity. On FibVID, we compare early node count with structural depth entropy, temporal arrival entropy, and their pair while keeping all propagation trees from each original claim in one partition. Across 352 test trees from 59 claim groups separate from training, the combined model raises $R^2$ for log-transformed future growth from 0.307 to 0.323 and reduces log-MAE by 2.4% (95% claim-bootstrap CI, -0.4% to 5.2%). The gain is especially pronounced among 97 high-activity trees: $R^2$ rises from 0.248 to 0.395, Spearman's $\rho$ from 0.394 to 0.529, and log-MAE falls by 11.7% (95% CI, -1.9% to 23.9%). Complementing the 30-minute growth forecast, we analyze the first 15 replies in 563 PHEME threads. In this cohort, the 15th reply arrives after a median of 28.8 minutes; 52.0% reach the fixed reply prefix within 30 minutes and 71.6% within one hour. Even without the LLM-generated factual-accuracy dimension, the remaining stance, communicative, and affective state composition retains cross-event ranking signal (ROC-AUC 0.538); including that dimension increases ROC-AUC to 0.562. In a separate Check-COVID evaluation of 229 claims, reciprocal-rank fusion retrieves a gold evidence document within the top five for 74.2% of claims and within the top 20 for 94.3%; sentence reranking reaches Recall@20 of 58.1%. We propose an integrated human-review system that brings these early forecasts, response patterns, and retrieved evidence together for misinformation triage relying on the potential virality of claims.

Predicting migration flows remains a significant challenge for traditional gravity-based forecasting models, which primarily rely on structured socio-economic indicators such as economic disparity, political stability, and geographic distance. This work investigates whether Large Language Models (LLMs) can improve migration forecasting by extracting contextual migration-related signals from news articles and incorporating them into a weighted Lasso forecasting framework through feature-specific regularization penalties. The proposed framework uses hierarchical LLM inference pipelines to classify migration-related push–pull signals from news data and evaluates the resulting forecasting performance across multiple migration corridors between November 2021 and November 2022, including Mexico–United States, Ukraine–Poland, and Syria–Turkey. Experimental results showed mixed performance across migration corridors and modeling strategies, and no single regularization approach consistently outperformed the others across all experiments. The best-performing Mexico configuration, which consisted of a gravity-based model augmented with the proposed push–pull ratios, achieved a Mean Absolute Percentage Error (MAPE) of 17.15%, while the strongest Syria configuration achieved a MAPE of 29.29% using Direct LLM-Lasso. For Ukraine, the best-performing configuration used LLM-Assisted Regularization (AR) and achieved a MAPE of 41.05%. Overall, the results suggest that contextual article-derived features and LLM-guided regularization can improve migration forecasting under certain conditions, although migration corridor characteristics, article volume, and hyperparameter configuration strongly influenced performance.

Mixture-of-Experts (MoE) transformers scale capacity by activating only a few experts per token, but this sparsity creates a hidden reliability problem: when routing is imperfect, load-balanced models may send tokens to experts that are insufficiently trained for the assigned inputs. We propose Distributionally Robust MoE Training (DRMoET), a drop-in objective that treats layer-wise experts as endogenous robustness groups and optimizes high-loss routing outcomes rather than merely equalizing traffic. DRMoET updates a per-layer expert distribution by an entropy-regularized softmax rule on EMA-smoothed, activation-weighted expert losses, strengthening plausible non-top routing paths while preserving standard MoE computation. Under the FLAME-MoE recipe at 746M-total and 10.3B-total scales, DRMoET improves downstream averages over both standard FLAME-MoE and auxiliary-loss-free balancing. At 10.3B total parameters and 67B training tokens, DRMoET improves the seven-task average from 0.6625 to 0.6767, while the auxiliary-loss-free baseline achieves 0.6431. Mechanistic analyses show lower expert-loss variance with nearly unchanged mean loss, 4.3% lower excess loss under forced mid-$k$ misrouting, and improved domain-expert specialization. These results position routing robustness-not only utilization balance-as a practical objective for reliable sparse MoE scaling. Project page and code are available at: https://drmoet.github.io/.

This paper introduces an energy-adaptive noise scheduling and whitening strategy for transform-domain diffusion models. Existing spectral diffusion methods account for the non-uniform statistics of transform coefficients through coefficient scaling, normalization, or frequency prioritization, while the forward diffusion noise schedule remains largely independent of the underlying spectral-energy distribution. We investigate whether the temporal evolution of the forward diffusion process should also follow the spectral organization of natural images. The proposed formulation combines global spectral whitening with energy-conditioned noise allocation that jointly modulates the injected noise according to the energy of individual transform coefficients and an image-dependent energy path over diffusion time. The resulting forward process preserves Gaussian transitions with closed-form marginals and remains compatible with standard DDPM and DDIM procedures without modifying the diffusion architecture. Experiments on CIFAR-10 demonstrate the contribution of the proposed energy-conditioned noise schedule and spectral whitening, reducing Fréchet Inception Distance from 142.48 for a compact DCTdiff U-Net variant to 100.45.

Institutional Analytics (IA) dashboards inform decision-making in higher education, yet data limitations, constraints in analytical techniques, and missing contextual information often affect their interpretation. To support more responsible interpretation of IA, we introduce FACTRIA, a framework that organizes potential biasing factors across four areas: the analytics pipeline, institutional context, course-level characteristics, and demographics. We used the FACTRIA framework as input to a generative-AI chatbot designed to prompt users to reflect on these factors while analyzing IA. A qualitative study with stakeholders, drawing on four authentic IA cases, and a transition network analysis showed that the chatbot prompted participants to recognize how overlooked factors influenced their initial interpretation. Findings indicated that combining a structured framework with AI-based guidance can enhance context-aware, responsible interpretation of institutional data.

Recent AI alignment work often frames alignment as a pre-deployment optimization problem: collect human feedback, learn preferences or principles, finetune the model, and deploy an aligned system. This framing has produced major progress, but it under-specifies what happens once AI systems act as agents on users' behalf in situated, long-term, and social contexts. This position paper reframes human-agent alignment as an ongoing interaction design problem. We propose SPEAR, five pillars of interactive alignment: Specification (how people express intent and establish shared understanding), Process (how agents decide when to act, ask, defer, or pause), Evaluation (how people judge whether agents succeeded), Adaptation (how agents adapt to users over repeated use), and Recalibration (how people adapt their trust, expectations, and behavior in response to agents).

Strain engineering is a leading route to control valley-selective transport in monolayer transition metal dichalcogenides. Whether this quantum effect survives inside a fully contacted device remains an open question. Quantum transport models capture the underlying valley deflection but are limited to isolated nanoscale fragments, leaving it unclear if a full device registers strain-induced valley sorting in the bulk, at the contacts, or at all. Here, the quantum valley-deflection tensor of strained monolayer MoS$_2$ is embedded directly into a macroscopic Poisson-drift-diffusion model, extending this physics to a complete, contact-inclusive device. Applying this framework to a 300~nm monolayer MoS$_2$ transistor with a 3~nm HfO$_2$ gate dielectric at 77~K, under a localized 6.14~T pseudo-magnetic strain field, shows the resulting 63.6% suppression of the ON-state current is not a bulk property. It is set almost entirely by the source and drain metal-semiconductor interfaces. The full suppression is reproduced when only the 15~nm contact regions are strained and nearly vanishes when the channel interior alone is strained, identifying the metal contact as the dominant site of strain-induced valley physics. Observing it requires tunneling-transparent, degenerately-doped contacts, since classical Ohmic barriers overwhelm the topological signal. A transmission-line analysis reduces this behavior to a single valley-topological contact resistance ($R_{c,V}$) and a predictive inverse-length scaling law. This framework applies to any strain-engineered 2D-material heterostructure and can be tested with standard multi-length contact structures. Ultimately, these results identify the metal-semiconductor interface as the decisive location for engineering and detecting valley-selective transport in real 2D-material devices.

Ultrahot Neptunes reside in the most extreme irradiation regime of the hot Neptune desert and remain challenging targets for atmospheric characterization because of their low planet-to-star flux ratios. We present high-resolution transit and dayside thermal emission spectroscopy of the ultrahot Neptune LTT 9779 b obtained with CRIRES$^+$, to probe atmospheric escape and dayside molecular emission. No significant absorption is detected in the metastable He I $\lambda 1083$ nm triplet during transit, yielding a $3\sigma$ upper limit of 0.45% on the excess helium absorption depth and supporting previous non-detections that suggest weak ongoing atmospheric escape. For the dayside emission spectra in the $K$ band, our cross-correlation analysis reveals an $\mathrm{H_2O}$ absorption signal and a tentative $\mathrm{CO}$ feature, with the combined signal reaching a detection significance of $4.8\sigma$. Both the CRIRES$^+$ and previous JWST data favor a non-inverted temperature structure, providing no evidence of a thermal inversion on the planetary dayside. We further perform a joint atmospheric retrieval combining the CRIRES$^+$ high-resolution spectra with JWST/NIRISS SOSS secondary-eclipse observations. The joint retrieval yields a low $\mathrm{H_2O}$ abundance, while the $\mathrm{CO}$ abundance remains weakly constrained. The inferred planetary equatorial rotational velocity, $v_{\rm eq}=4.9^{+4.4}_{-3.0}~\mathrm{km\,s^{-1}}$, is consistent within $1\sigma$ with the synchronous rotation velocity expected for a tidally locked planet ($\sim2.8~\mathrm{km\,s^{-1}}$). However, the large uncertainties prevent us from placing strong constraints on the planet's rotation state. Future phase-resolved CRIRES$^+$ observations with broader orbital-phase coverage and higher signal-to-noise ratios would improve the abundance constraints and probe the atmospheric dynamics of this rare ultrahot Neptune.

An old but recurring question in ground-state density functional theory, relevant to the construction of density functional approximations, is the existence of a second-order gradient expansion for the exchange energy that is exact for densities that vary slowly over space. Here we will argue that there is such an expansion, with a gradient coefficient 10/7 of Sham's, as suggested by theoretical/mathematical derivations and by numerical calculations on model slowly-varying metallic densities, although some standard derivations do not quite capture the correct gradient coefficient. We also discuss long-range anomalies in the gradient expansions for the exchange and correlation holes around an electron. It is plausible that, as suggested earlier and recently, standard derivations are still correct for the coefficient of the second-order gradient expansion for exchange and correlation together, in which case the correct gradient coefficient for correlation is $C_{\mathrm{c}}$ = $C_{\mathrm{xc}}$ - $C_{\mathrm{x}}$. We propose possible numerical evaluations of $C_{\mathrm{xc}}$ and $C_{\mathrm{x}}$ that are free from long-range anomalies, and discuss implications for density functional approximations. Axel Becke's 1988 generalized gradient approximation (the B88 GGA) for the exchange energy brought density functional theory into chemistry, with a gradient coefficient for exchange that is optimal at the GGA level for atoms and molecules but too large for solids. Meta-GGAs seem to work as well for molecules as for solids, but may not be perfected yet. The article concludes with a few memories that the first author has of discussions with Axel Becke.

We integrate the Bondi–Sachs hierarchy of scalar–Gauss–Bonnet gravity with an arbitrary coupling function $f(\Phi)$ and a radiating massless scalar, and determine the first order in $1/r$ at which the coupling $\lambda$ becomes visible in each field equation. We obtain the asymptotic falloff of the effective Gauss–Bonnet stress tensor together with its leading coefficients in covariant form on the sphere: every component decays between one and three powers of $1/r$ faster than the slowest falloff compatible with a smooth null infinity. As a consequence, (i) the Bondi mass-loss formula and the evolution equation of the angular-momentum aspect are those of the minimally coupled Einstein–scalar system, a statement that is exact in $\lambda$ under the assumption of a smooth expansion; (ii) the coupling generates no logarithmic terms through the orders considered, even though the Horndeski representation of the theory involves logarithmic functionals; and (iii) the coupling first enters a dynamical equation in the evolution of the $O(r^{-3})$ coefficient of the angular metric, through the cross term $-2\lambda f'(\vp_0)\,\vp_1\,\partial_u N_{AB}$ between the asymptotic scalar charge aspect and the time derivative of the news. In Newman–Penrose form, the evolution equation of the leading coefficient of $\Psi_0$ acquires the source $-12\lambda f'(\vp_0)\,\vp_1\bar\Psi_4^0$, while those of $\Psi_1$ and $\Psi_2$ are unchanged. The Gauss–Bonnet invariant decays as $r^{-6}$ and affects the scalar hierarchy only from the evolution of the $r^{-5}$ coefficient onward. For vacuum black-hole spacetimes, where the scalar is sourced by the coupling itself, all these effects are of order $\lambda^2$; if $f'(\vp_0)=0$ they are pushed one further order in $1/r$.

The CosmicWatch Desktop Muon Detector (v3X) is a compact and low-cost scintillator-based instrument designed to detect ionizing radiation, including cosmic-ray muons. Built around a plastic scintillator, a silicon photomultiplier (SiPM), and a dual-core Raspberry Pi Pico microcontroller, the v3X achieves a 400 microsecond dead time per event, sustained event logging at 700 Hz, and two-detector coincidence triggering for more accurate counts. This paper first summarizes the design, firmware, and demonstrated performance of the v3X prototype. It then outlines the design changes needed to prepare the detector for operation aboard a satellite, including a passive copper thermal strap that conducts heat from the microcontroller to the spacecraft chassis, a dedicated flight enclosure, material changes to meet outgassing standards, and a Controller Area Network (CAN) bus interface to connect the detector to the host spacecraft. The flight unit is targeted for launch via Oligo Space.

We prove that the colored Jones polynomial of a knot does not determine the Links–Gould polynomial (associated with the 4-dimensional representation of the Lie superalgebra $\mathfrak{sl}(2|1)$) with two different approaches: the first is to find a concrete genus 2 mutation pair with different Links–Gould polynomials, and the second follows from the fact that the colored Jones polynomial is invariant under Conway mutation whereas the colored Links–Gould polynomial is not. The first approach also applies to a related family of polynomial invariants of Kashaev–Mangazeev, which are conjectured to be the $\mathfrak{sl}(n|1)$-knot invariants colored by the $2^n$-dimensional irreducible representation.

Exact unlearning requires a deployed predictor to match one rebuilt without the information named by a deletion request. Existing general-purpose exact methods localize retraining through disjoint shards, but every request still invalidates a model, and smaller shards reduce the data available to each constituent predictor. We introduce Quantized Sufficient Statistics (QSS), which separates a small frozen schema from mutable, sum-decomposable content. The schema learns global structure; the content stores local prediction corrections as additive statistics indexed by quantized regions. Deleting content is therefore exact subtraction rather than optimization. We distinguish two guarantees: QSS-L exactly removes a label while retaining the unlabelled input, whereas QSS-E exactly removes both input and label by learning the schema without deletable examples. A deletion takes the arithmetic fast path with probability $1-\rho$ and triggers a full rebuild with probability $\rho$; all reported expected latencies include both events. Across 15 vision, text, and tabular datasets at $\rho=0.5\%$, QSS-L is within 2 percentage points of SISA on 11 tasks and provides 4–483$\times$ lower expected deletion latency on the low-class-count tasks where a compact schema is effective. QSS-E quantifies the additional accuracy cost of removing every trace of an input.

Variational autoencoders are powerful representation learning models that map complex data into low-dimensional latent spaces, enabling the discovery of interpretable and disentangled factors. Such representations can facilitate the interpretation and controllable generation of data describing complex scientific systems. Understanding how these factors are organized and encoded in latent space is therefore important for developing reliable representation learning models. Recently, quantum variational autoencoders (QVAEs) have been proposed as quantum representation models, demonstrating informative latent representations and improved latent-space occupancy through quantum regularization. However, it remains unclear whether and how QVAEs can learn disentangled and interpretable latent factors. A key challenge in investigating quantum latent factors is that a small number of qubits spans an exponentially large Hilbert space, making the notion of an individual quantum latent dimension nontrivial. Here, we investigate what constitutes an individual quantum latent dimension and whether it can encode a distinct factor. We develop theoretical insights into quantum latent dimensions and support them with empirical studies on representative synthetic problems, including MNIST variants. Across three datasets, we demonstrate that QVAEs can discover factorized and semantically interpretable latent representations, with individual qubits functioning as meaningful latent factors. These results establish a foundation for understanding quantum latent spaces and their potential for structured and interpretable representation learning.

We show that quasi-Poisson and quasi-BV structures on (super)manifolds $M$ admitting an action of a Lie (super)group $G$ can be identified with a special class of homotopy Poisson and respectively $BV_\infty$ structures on the associated differential (super)manifolds of the form ${\mathcal M}:=M\times \Pi g$, $g$ being the Lie (super)algebra of $G$. The construction is based on the proven existence of an essentially unique family of higher Jacobiators for any Lie (super)algebra $g$ with an invariant (odd or even) scalar product. We apply these arguments to the moduli spaces $M$ of flat $G$-connections on a surface with boundaries using Fock-Rosly construction.

In this work we study the unitarity constraints on double Higgs production from Vector Boson Fusion mediated channels, specifically in $f_1 f_2 \to f_3 f_4 H_5 H_6$ scattering, where $f$ refers generically to either fermion or anti-fermion, and both cases with quarks and leptons will be considered. We focus on the beyond Standard Model contributions from anomalous quartic couplings of two electroweak gauge bosons and two Higgs bosons ($VVHH$ with $VV=WW, ZZ$) from effective operators containing four derivatives. These four derivative operators appear in the two most popular effective field theories, SMEFT (at canonical dimension 8) and HEFT (at chiral dimension 4), and their corresponding $VVHH$ effective vertices can be easily related for the considered processes here. The aim of this work is to derive jointly the unitarity constraints on these related effective vertices using the peculiarities of the VBF mediated channels with four particles in the final state while keeping the propagation of the internal $VV$ pairs being off-shell as it must be for these channels. We also discuss the relevance of the obtained constraints for $f_1 f_2 \to f_3 f_4 H_5 H_6$ at high energy colliders.

We prove that, in most moduli spaces of orientable hyperbolic surfaces of finite area, there exist surfaces all of whose covers of degree two have a new small eigenvalue. On the other hand, we show that four punctured spheres always admit a double cover without new small eigenvalues and that there exist closed surfaces of any genus with the same property. We prove the last two of these results using a version of Cheeger's inequality adapted to double covers.

Vision-Language Navigation (VLN) enables robots to navigate through environments using natural language instructions, making human-robot interaction intuitive. Traditional VLN models often rely on navigation graphs, 360-degree views, and perfect localization which pose significant challenges when adapting these models to real-world settings. This work addresses these limitations by performing a simulation-to-real domain shift of a VLN approach that operates in continuous environments without requiring navigation graphs or panoramic views. The proposed system integrates vision-language models that align visual inputs and linguistic instructions within a shared embedding space, facilitating natural language-driven navigation. We employ a Cross-Modal Attention (CMA) based architecture trained on an existing dataset in a simulated environment and fine-tune it using real-world data collected from a custom-built Ackermann-steered robot equipped with a camera and a LiDAR sensor. By utilising linear photometric adjustments and fine-tuning on a limited number of episodes, our model successfully adapts to real-world environments, achieving effective navigation while running offline on dedicated hardware. Experimental results, evaluated using Success weighted by Path Length (SPL) and Normalized Dynamic Time Warping (nDTW) metrics, demonstrate the robustness and adaptability of our approach. Keywords: Vision-Language Navigation, Cross-Modal Attention, Natural Language Instructions, Sim-to-Real Transfer, Autonomous Navigation, Ackermann-steering.

Modern edge Systems-on-Chip (SoCs) integrate heterogeneous processing units (PUs) such as CPUs, GPUs, and NPUs, each with distinct performance and energy characteristics. Deploying AI inference workloads on them under real-time latency and energy constraints requires jointly mapping workloads to PUs and configuring each PU (e.g., selecting the number of active cores and the operating frequency). This joint space grows combinatorially, making exhaustive search infeasible. Most prior work on design space exploration (DSE) applies black-box optimization (BBO) such as evolutionary search, where each evaluation returns only aggregate metrics such as latency and energy. Recent LLM-guided DSE relies on the same sparse feedback. We observe that this limits its efficiency: it offers no insight into the design space or the reasons a design choice performs the way it does, and it leaves the reasoning abilities of LLMs largely unused. We present TraceDSE, an agentic DSE flow that performs joint workload mapping and PU configuration selection for AI inference on heterogeneous SoCs. TraceDSE is an iterative proposer-critic loop driven by richer feedback in the form of system execution traces. The LLM proposer agent generates candidate mappings and PU configurations for hardware evaluation. The LLM critic agent, equipped with programmatic trace-analysis tools, analyzes the traces to identify bottlenecks and suggest targeted refinements. This loop yields deeper insight into each design point, higher-quality decisions, and a more effective search. Across four AI inference workloads (models of varying complexity and a multi-model pipeline) on an Intel Meteor Lake SoC, TraceDSE consistently outperforms two state-of-the-art BBO tools, improving Pareto frontier hypervolume by up to 35% over NSGA-II and up to 68% over Bayesian optimization, while requiring ~6-9x fewer hardware evaluations.

The estimation of sums of functions of observable and unobservable variables is a long-standing problem in statistics, with applications in many domains. We consider this problem in Poisson mixture models, where empirical Bayes provides a natural framework but nonparametric theory remains limited. We develop a nonparametric empirical Bayes methodology based on regular and coarsened minimum-distance estimation of the unknown mixing distribution. For a broad class of such sums, we establish large-sample guarantees showing that the resulting plug-in estimates asymptotically merge with the oracle Bayes estimate. In particular, when the mixing distribution has finite support, we obtain a nearly parametric convergence rate, up to a logarithmic factor. We then provide a finite-sample analysis of two representative sums: the total intensity among units whose observed count does not exceed a fixed threshold, and the number of units whose observed count exceeds their latent intensity. For the total-intensity sum, we establish a lower bound on the minimax regret and derive upper bounds for both regular and coarsened minimum-distance procedures under compact-support and subexponential assumptions on the mixing distribution. These upper bounds match the minimax rate up to logarithmic factors, with the coarsened procedure in the compact-support setting matching the rate exactly when the coarsening level is fixed. The above-average sum displays a markedly different behavior: a lower bound on the minimax regret shows that bounded regret is in general impossible to achieve. We identify additional stability conditions under which bounded regret can be recovered up to logarithmic factors, and show that these conditions are automatically satisfied when the mixing distribution has finite support. Numerical experiments on both synthetic and real data illustrate the performance of the proposed methodology.

We study monopoly regulation when capacity is contractible but subsequent output is not. A firm privately observes its production cost before installing costly capacity and then choosing output, while the regulator cannot use transfers. We provide sufficient conditions under which a single capacity floor implements an optimal mechanism with full participation. The floor raises output by changing investment while leaving utilization to the firm after installation costs are sunk. Under additional conditions, the allocation has three regions: laissez-faire, full utilization of the floor, and underutilization. High-cost types knowingly install capacity they will not fully use, yet produce more than under laissez-faire. This physical waste is a necessary evil of optimal regulation that expands service. We also show that underutilization can persist in optimal regulation with capacity-contingent subsidies or a common entry fee.

Nanophotonic sensors amplify analyte-induced optical signals through resonantly enhanced light-matter interactions. While effective for refractometric sensing, conventional sensing platforms typically collapse spatial variations in analyte distributions into ensemble-averaged readouts, thereby obscuring local heterogeneity. Here we present a dual-channel metasurface sensor capable of detecting both net analyte loading and nanoscale spatial inhomogeneity at deep-subwavelength scales. The device supports two distinct high-Q modes with deeply structured near-field profiles of opposite parity. Their complementary modal responses decouple analyte perturbations into bulk and differential components, which are encoded into two spectrally resolvable channels. We demonstrate these sensing modalities across analyte configurations exhibiting diverse forms of nanoscale heterogeneity, achieving a refractometric sensitivity of 357 nm/RIU and inhomogeneity detection below $\lambda/10$. This dual-channel capability, which extends nanophotonic sensing from analyte quantity to its spatial variation, opens a new avenue for multidimensional analysis of biological and material systems.

In this paper, we study the behavior of biquandle-based invariants of virtual knotoids under their connected sum. We first show that the fundamental biquandle of the connected sum of two virtual knotoids is the pushout of a span in the category of biquandles. By applying the Hom functor to this pushout description, we obtain the correspondence between biquandle colorings of $K_1 \# K_2$ and compatible pairs of colorings of summands. This provides a categorical explanation of a known matrix product formula for biquandle counting matrices under connected sum. We then study the behavior of biquandle virtual bracket invariants under connected sum. We introduce normalized multiset invariants derived from biquandle virtual brackets and show that they are strictly stronger than their unnormalized versions in certain cases by an explicit example. Furthermore, we show that for each coloring of the connected sum $K_1 \# K_2$ corresponding to a compatible pair of colorings of the summands $K_1$ and $K_2$, the normalized biquandle virtual bracket value factors as the product of the normalized values of the summands. Building on this, we obtain connected-sum formulas for the normalized multiset invariants defined by utilizing biquandle virtual brackets. When the coefficient ring is a number ring, the normalized bracket multisets can be encoded by polynomials and matrices with polynomial entries. We introduce an induced matrix product $\odot$ and show that the normalized biquandle virtual bracket matrices satisfy \begin{equation} \widetilde{M}_X^\beta(K_1 \# K_2) = \widetilde{M}_X^\beta(K_1) \odot \widetilde{M}_X^\beta(K_2). \end{equation}

Large language models make claims about themselves that are both consequential and increasingly difficult to verify from behavior alone. How can we distinguish plausible confabulations from genuine introspection? In this paper, we identify mechanistic signatures of faithful self-report in a controlled setting. Using low-rank adapters, we train models to make decisions on behalf of fictitious characters, according to latent linear preference functions. We find sustained fine-tuning on an implicit decision task can lead to the emergence of accurate self-reporting of models' learned preferences, even without explicit self-report supervision. We ask two research questions about this emergent phenomenon. First: is the emergence of accurate self-reporting accompanied by a measurable structural change in the model? Weight ablations and frozen-layer experiments together indicate that preference representations shift to earlier layers over training, consistent with the hypothesis that faithful self-report requires preferences to be located where pre-existing verbalization mechanisms can access them. Second: can these structural differences distinguish faithful models from unfaithful ones? Using attribution patching, we find that faithful models exhibit significantly higher attribution similarity between the decision-making and self-report tasks – a mechanistic signature of faithful self-report that does not require us to understand the content of the report itself. Previous work on self-report has observed behaviorally that models can be faithful or unfaithful; our work proposes that, at least in our restricted setting, it is possible to distinguish between the two patterns of computation by examining the structure of the networks themselves.

This paper proposes a subspace-based decision scheme to detect range-spread targets in presence of thermal noise, clutter, and intentional interference. The target and intentional interference (i.e., noise-like jammer) effects are confined to the covariance matrix of the received primary data vectors. The jammer is also present in the secondary data vectors necessary to estimate the clutter covariance matrix. Finally, an additional set of training data, acquired by the system in passive mode and, hence, not contaminated by target and clutter echoes, is used to avoid the jammer parameters are unidentifiable. The detection problem is addressed by deriving an architecture based upon the likelihood ratio test where the unknown second-order parameters are suitably estimated. To this end, a unified theoretical framework is defined also providing a geometrical interpretation of the estimation procedures. The performance assessment, conducted also in comparison to a natural competitor, highlights the effectiveness of the proposed solution.