Papers

We apply the canonical clock-sector framework developed in Ref.~\cite{Tavakoli:2026coc} to spatially flat FLRW cosmology in Brans–Dicke theory. The aim is to obtain an explicit cosmological realization of the frame-adapted relational dynamics and to determine the corresponding cosmological observables in closed form. Starting from the previously developed full ADM theory and restricting it to the homogeneous sector, we obtain the canonical clock momentum as $P_{\Phi}=p_{\phi}-ap_a/2\phi$. This identification allows the Jordan and Einstein-frame reduced systems to be represented on a common canonical phase space. We then consider a quadratic Jordan-frame potential for which the Einstein-frame potential is constant. The resulting relational FLRW system is exactly integrable. The complete trajectory can be expressed in terms of a single parameter $u$, yielding closed-form expressions for the scale factor, the cosmic-time Hubble rate, the Hubble slow-roll parameter, the number of e-folds, and the scalar equation-of-state parameter. In particular, the exact solution provides an explicit inflationary regime that begins at $u=\operatorname{arctanh}(1/\sqrt{3})$ and transitions toward an asymptotic de Sitter regime. We finally compare the exact solution with direct numerical integration in the adapted Jordan and Einstein descriptions, and with the naively reduced Jordan system based on the unshifted scalar momentum. The numerical results reproduce the exact trajectory and illustrate how the different reduced canonical representations are related by the clock-dependent transformation implied by the canonical clock-sector construction. The analysis provides an exactly solvable laboratory for relational frame equivalence in scalar–tensor cosmology and gives explicit cosmological observables that can be used in extensions to more general potentials and scalar–tensor models.

Multi-agent systems distribute large contexts across agents that communicate to solve a task. Text messages are compact but require decoding and may omit evidence the receiving agent needs. Recent latent communication instead transfers KV caches. This avoids text generation and can improve accuracy and latency. However, a full KV cache grows linearly with both the context an individual agent processes, and the number of agents that coordinate together. This raises memory and context costs, often far exceeding available GPU resources and context window sizes. Our key observation is that agents need only send what the receiving agent requires for its local task – which we call receiver-conditioned communication. The receiver agent passes the sender a small description of its information needs, which serves to filter and compress the sender agent's KV cache. CacheBack is a simple, robust, training-free instance of receiver conditioning based on the sender's attention weights. On FanOutQA, CacheBack with Qwen 3 removes 75% of the state the agent would otherwise receive, improving accuracy by 14.7 percentage points and reducing median task-completion latency by 3.2x relative to text communication. We show comparable improvements across model families that span dense Transformers, Mamba-attention hybrids, and sliding-window attention.

We analyze deep JWST/NIRSpec observations of 58 star-forming galaxies at $1.3< z <4.8$ in the AURORA survey to investigate the origin of the permitted OI $\lambda 8449$ emission feature. Based on the detection of OI $\lambda 8449$ in a stack of objects with non-detections, we infer that this feature is ubiquitous among star-forming galaxies at $\sim$0.5% the strength of H$\alpha$. We additionally compare our results with measurements of this line in local HII regions from the CHAOS survey and star-forming galaxies at $z<0.1619$ in the DESI survey, finding a similar strength of OI $\lambda 8449$ relative to H$\alpha$ in these objects. We evaluate four production mechanisms: recombination, collisional excitation, Ly$\beta$ fluorescence, and stellar continuum fluorescence. Of these mechanisms, stellar continuum fluorescence (rather than Ly$\beta$ fluorescence) provides the most compelling explanation for the OI $\lambda 8449$ emission based on the additional detection of the near-infrared OI $\lambda 11290$ and OI $\lambda 13168$ emission lines. Adopting physical conditions derived from a stacked composite spectrum, we make predictions for the contribution of the other mechanisms to OI $\lambda 8449$, determining that recombination, collisional excitation, and Ly$\beta$ fluorescence contribute negligibly to this feature. While a simple HII region model using Cloudy reproduces the average observed OI $\lambda 8449$/H$\alpha$ ratios in the AURORA sample, future works focused on refining model density profiles will be a valuable step in better explaining the near-infrared OI emission-line strengths.

Atmospheric characterization of a warm 10-30 Myr old sub-Neptune progenitor (V1298 Tau b) and a $\sim$3.4 Gyr old warm super-Neptune (WASP-107b) using JWST have revealed extremely low methane abundance. Atmospheric forward models find higher than expected inferred intrinsic temperatures (450~K and 500~K) — inconsistent with theoretical planet formation and core-envelope evolution predictions (70K and 150K respectively) assuming a convective interior. We explore three hypotheses to reconcile the high intrinsic temperatures with evolutionary models — tidal heating, silicate rainout and heat trapping due to deep cloud condensation. Tidal heating requires high planetary obliquity ($\gtrsim70^{\circ}$) and low reduced tidal quality factor ($\sim$100) for V1298 Tau b, implying an extremely short obliquity damping timescale ($<$10$^{4}$ years). Although high obliquity may be maintained by spin–orbit resonant locking, it requires fine-tuning and is therefore unlikely. Silicate rainout can increase the temperature in the deep atmosphere of the young V1298 Tau b (0.1-1 bar) by $\sim$700K, without requiring extremely high intrinsic temperature, but is unlikely to explain WASP-107b, as silicate rainout timescales are expected to be much shorter than its age. Including cloud condensation in self-consistent atmospheric models reduces the inferred intrinsic temperature for V1298 Tau b from 500K to 300K, still exceeding the core-envelope prediction (150K). Future measurements of thermal emission from young transiting planets such as V1298 Tau b, combined with methane abundances as a function of age, will be needed to distinguish between these scenarios.

We introduce Distance-Residual Physics-Informed Neural Networks (DR-PINNs), a physics-informed learning framework for approximating solutions of ordinary and partial differential inclusions (DIs), governing laws in which a differential operator is constrained to lie in a set-valued map rather than equaling a prescribed function. The method replaces the classical pointwise PDE/ODE residual by the squared distance from the differential operator to the admissible set. This distance vanishes exactly when the inclusion is satisfied and measures the infimal correction needed for the operator to enter the admissible set. For a fixed closed convex admissible set, the squared distance is differentiable with respect to the operator value, with gradient given by the metric projection. When the admissible set also depends on the network state, that dependence is included through the chain rule. The framework encompasses ordinary and partial DIs with set-valued reaction terms. For both settings we prove consistency: under the stated closedness, measurability, convexity, and growth assumptions, any sequence of candidates satisfying the initial (and, in the parabolic case, boundary) conditions whose continuous distance-residual functional tends to zero admits a subsequence converging to an exact solution of the target inclusion. These are conditional statements for the continuous distance-residual functional; they do not cover the finite-collocation training loss, the behavior of the optimizer, or convergence rates. For admissible sets given as convex hulls of finitely many vertices, projection onto the set reduces to a small convex quadratic program, making the loss efficiently computable inside the training loop. Numerical experiments demonstrate high accuracy on the differential-inclusion benchmarks.

We ask how GGUF quantization affects agentic tool use in Polish and whether the effects generalize across models. We introduce PolAgentBench, a deterministic benchmark with Polish prompts and English tool schemas: a 67-task main suite (15 adversarial probes, 52 hard-tier tasks) and a 46-task arithmetic isolation ladder. Three models span two axes of variation: Bielik-11B-v3.0 and its pruned, distilled child Bielik-Minitron-7B-v3.0 isolate model compression, and Llama-PLLuM-8B adds a change of pretraining family. Each is measured at six precisions, Q8_0 to Q2_K. Only the collapse threshold replicates. (1) All three models fall off a cliff between 3-bit and 2-bit (11B 0.716 to 0.045, 7B 0.463 to 0.149, PLLuM 0.224 to 0.015; paired McNemar p < 0.001 in each), across a fourfold capability spread and both axes. (2) Failure modes do not replicate: at 2-bit the 7B fails long (median 9.1k tokens, 4 steps) while the 11B mostly answers at the first step with a confabulated final answer (37 of 64 failures); PLLuM fails on content across precisions (71.8-92.0% of steps parse). (3) On the arithmetic ladder the unscaffolded rung is a floor, left standing by a rerun that states the no-tool rule; four explicit calls lift the 8-bit 11B from 1/10 to 9/10 and the 7B from 0/10 to 7/10 after format-only failures with the gold value are forgiven, an exploratory effect with eight distinct baseline inputs that does not survive multiplicity correction, while the order-trap arm separates the models at 8-bit (11B 6/6, 7B 0/6). (4) The Polish-versus-English gap is associated with degradation or with task family. We document four artifacts that shaped our conclusions (rounding-hostile gold values, strict answer typing, a no-tool rule the prompt never stated, priority-ordered failure labels), report affected results in strict and corrected form, and release the benchmark, trajectories and commit-stamped artifacts.

Modern Document AI reads contracts, extracts fields, reasons over tables, and grounds answers to page regions, then forgets everything. Processing an amendment the next day begins from scratch: no schema retained, no contradiction detected, no experience carried forward. This is a structural choice, not a scale failure: current systems are stateless functions. We call this the statelessness bottleneck. This bottleneck lies beyond parameter scaling, context extension, and retrieval augmentation: storage provides persistence and retrieval provides access, but neither consolidates observations into knowledge that improves future processing. This survey formalizes persistent evidence-grounded document state as a unifying framework, specifying the operations and invariants required to convert multimodal evidence into durable, provenance-linked state. We introduce a statefulness audit showing that ten representative benchmarks, coded against eight statefulness criteria, leave cross-session state evolution untested, and derive a longitudinal benchmark harness with five counterfactual metrics: Experience Gain, Cost Efficiency, Memory Harm, Forgetting Fidelity, Coverage Retention, to characterize the benefit, cost, risk, and governability of persistent document state. Document AI lacks mechanisms coupling persistent state to document-native structure, provenance, and temporal validity. The next era of Document AI will be defined by what systems retain across documents, sessions, and time.

Molecular dynamics simulations provide a computational microscope for atomic scale processes but remain restricted to relatively small spatial and temporal scales. Coarse-grained models extend their reach by representing groups of atoms as effective interaction sites. The number of particles is systematically reduced by embedding the collective behavior of groups of atoms into coarse-grained sites governed by effective potentials. However, constructing accurate, highly coarsened potentials, even with the assistance of modern machine-learning methods, is a grand challenge because coarse grained forces depend on a statistical distribution of composite atomic configurations making direct calculation computationally prohibitive. Here, we introduce an alternative framework based on implicit score matching that directly avoids the need for explicit coarse-grained forces. This approach both substantially reduces the training data required relative to conventional force-matching methods and enables high-fidelity models in which each coarse-grained site represents hundreds to thousands of atoms. We demonstrate the method's versatility and effectiveness across a diverse range of chemical systems and phenomena, developing bottom-up, machine-learned models. These enable efficient modeling at micrometer and millimeter length scales, while retaining significant amounts of the atomic scale fidelity. These results establish implicit score matching as a practical route towards chemically accurate simulations that bridge molecular and mesoscopic scales.

For $1<p<\infty$, we characterize the boundedness of the segment multiplier on $L^p(w)$ by a large-scale Muckenhoupt condition, obtained by restricting the classical $A_p$ condition to intervals of length at least one. The proof uses a discretization involving the discrete Hilbert transform on an associated weighted sequence space.

Extended Reality (XR) users do not directly perceive the output of a rendering engine. Instead, rendered images pass through a post-processing pipeline and the physical display-optics path before reaching the eye. Critically, the exact downstream processing can vary significantly at run time, influenced by, for instance, camera pose and display power budget. Traditional 3DGS methods either implicitly assume that this downstream pipeline preserves image quality or cannot adapt to downstream processing changes. To bridge this gap, we present ControlGS, an XR Gaussian rendering pipeline that optimizes end-to-end visual quality. ControlGS models and integrates the entire downstream processing, between the rendering output and the human eye, into the optimization objective. To adapt to downstream processing at run time, ControlGS dynamically generates Gaussian primitives conditioned upon the downstream processing parameters. Experiments show that ControlGS consistently improves end-to-end post-optics XR quality across different neural Gaussian backbones and datasets, with minimal overhead. Code is available at https://horizon-lab.org/controlgs/.

In this dissertation, I briefly go through my subject areas — from Astrophysics, Cosmology, to Cosmic Microwave Background (CMB) radiation; and Data Science & High-Performance Computing. I go through the beginning of the Universe briefly in part I and introduce the Physics of the CMB in part II. Then I move on to how it can be observed experimentally, mathematically, and computationally in part III. In parts IV to VI, I write about 2 specific CMB experiments — POLARBEAR & LiteBIRD, together with my research involved in them. In part V, original research on a measurement of the CMB $B$-mode at sub-degree scales is presented using the 3rd-5th seasons of POLARBEAR observations. This demonstrates the capability of a single medium aperture telescope with a Continuously Rotating Half-Wave Plate (CRHWP) to target both the low-$\ell$ and high-$\ell$ $B$-mode science at $50 \leq \ell \leq 3000$. In part VI, the effect of detector crosstalk systematics on the CMB power-spectra is studied in detail in the example of the LiteBIRD experiment. An analytical, map-domain solution is developed, a computational simulation method is implemented, and the two predictions are compared using the LiteBIRD experiment design specification. The general agreement of the two shows that the analytical model well describes the LiteBIRD experiment, and can be used to calculate the systematic effects without performing time-consuming time-domain simulations with a high degree of accuracy. This can be used to forecast the amount of crosstalk systematics and to develop mitigation strategies. A mitigation strategy is presented, which is a hardware-based mitigation method that minimizes the crosstalk systematic effects in the 2pt power-spectra.

We introduce ScreenHaystack, a dynamic needle-in-a-haystack benchmark for evaluating spatial reliability in GUI grounding. Instead of testing each target at a fixed position, ScreenHaystack systematically relocates controlled target icons across high-resolution GUI backgrounds and measures whether models can localize them consistently. Using this benchmark, we find that leading GUI grounding models, including Qwen3-VL, UI-TARS, GTA, and UI-Venus, exhibit blind zones: spatial regions where grounding accuracy drops sharply despite fixed target appearance and instruction. These blind zones transfer to unseen ScreenSpot-Pro examples: targets inside blind zones are consistently harder to ground, with Qwen3-VL-8B dropping by 16.1 percentage points, and controlled relocation shows that moving targets into blind zones decreases accuracy while moving them out improves accuracy. We further show through controlled synthetic experiments that uneven spatial coverage in training data can induce such blind zones. Therefore, we propose a simple strategy, blind-zone-oriented augmentation, which adds supervision in blind zones and improves ScreenSpot-Pro accuracy over both original and randomly augmented Click-100k fine-tuning.

Self-consistency assumes that independent samples disagree when a model is unsure, so agreement is evidence of correctness. Holding weights fixed and toggling only a reasoning mode, over five benchmarks and 74,944 samples, we show that reasoning concentrates a model's errors: the probability that two independently drawn wrong answers coincide rises in all ten dataset-scale comparisons (p = 0.00098), and in nine of nine after restricting both arms to the problems each gets wrong. Where the answer space is unbounded, reasoning cuts the distinct answers produced to 0.43-0.65 of the non-reasoning count; where it is bounded, both arms hold an identical option set and reasoning concentrates mass on it instead, which no positional prior can explain at fixed weights. The aggregate cost is smaller than the mechanism predicts, because reasoning also shrinks the set of problems where answer diversity can decide anything, in ten of ten cells and by 2.7x; normalized for available headroom, both arms convert a quarter of it in domain. Confidence weighting does not recover what is left. Across 280 method-dataset-model combinations on eight models and five benchmarks, not one beats plain majority voting after correction; weighted voting agrees with it on 98.5% of problem-method pairs and is right 56.3% of the time on the rest; and a signal's direction can invert within fixed weights, with answer log-probability predicting correctness when reasoning is off and error when it is on. A learned six-signal combination gains nothing out of domain. Confidence signals should be evaluated on decisions, not on discrimination.

The classical method of Kaczmarz, introduced in 1937, is a textbook iterative method for solving linear systems $A x = b.$ Despite its widespread use, particularly in the context of solving inverse problems where it is commonly included in software packages within Matlab, Python, and Julia, the precise characterization of convergence has long been deemed difficult to obtain. While different bounds on convergence rates have been established, they are largely unsatisfying as they cannot explain the classical, cyclic-update method's efficient convergence in practice. In this work, we obtain a tight characterization of convergence of the classical Kaczmarz method, establishing both linear and sublinear convergence bounds. The worst-case tight (i.e., exactly attained by some instances in the considered family) bounds are expressed in terms of a fixed matrix that depends only on $A,$ but are not fully interpretable in terms of the matrix spectrum and row correlations, which had been observed to have an impact on convergence. We thus provide relaxations of these bounds that are fully expressible in terms of matrix row norms, row correlations, rank, and extremal positive singular values. The provided relaxed bounds explain one-cycle convergence in special cases where the matrix rows are all either parallel or orthogonal to each other. We further argue that the dependence on different parameters appearing in the bounds is necessary and within a small constant factor of the best attainable in the worst case. Finally, our bounds explain why the classical cyclic update is faster than the randomized one when matrix rows are weakly correlated, which is often observed in inverse problems where the cyclic method is used.

For a positive integer $\alpha$, let $p_\alpha(n)$ denote the number of $\alpha$-colored partitions of $n$. The Rademacher-type expansion of Iskander, Jain, and Talvola is valid for every real $\alpha>0$, but when $\alpha>24$ it involves several polar terms and a two-parameter family of exponential sums $A_k^{(\alpha)}(n,m)$. For integral $\alpha$, we prove multiplicativity and prime-power reduction formulas for these sums, expressing their local factors as classical or quadratically twisted Kloosterman sums. Together with explicit truncation and precision bounds, these formulas yield an efficient algorithm for computing $p_\alpha(n)$ exactly. Our SageMath implementation computes the 1,113,767-digit integer $p_{100}(10^{10})$ in less than one hour. As an application, we use the algorithm to certify new Ramanujan-type congruences.

A ranked-prefix feasible-set restriction is proposed for real-time mixed-integer model predictive control of series-connected reconfigurable battery packs with per-cell bypass switching. Cells are ordered at each sampling instant by a one-step objective-informed suitability score, and the engagement variables are constrained to prefixes of that ordering. The restriction reduces the number of admissible per-step engagement patterns from combinatorial to linear in the number of cells while leaving the model, objective, and physical constraints unchanged. For a 20-cell pack driven over a worldwide harmonized light vehicles test cycle, the proposed controller certifies every active step, solves every instance without branching, and reduces the 95th-percentile solver time by a factor of 6.8 relative to the full subset-selection controller. The cycle-mean cell-to-cell state-of-charge standard deviation decreases by a factor of 3.4, and no power curtailment occurs. Same-state reference solves show a mean restriction gap below 0.11% on jointly certified steps, and the computational gains persist across the tested initial conditions, cell heterogeneity levels, pack sizes, and prediction horizons without retuning.

Biological neurons exhibit diverse firing dynamics that enable adaptive and stimulus-dependent signalling, yet reproducing these dynamics in hardware has remained an enduring challenge. In this work, we present an Izhikevich- inspired reconfigurable neuron that co-designs voltage-controlled magnetic tunnel junction (V-MTJ) dynamics with CMOS circuitry. The proposed architecture combines V-MTJ excitability dynamics, enabled by a tunable energy landscape, with CMOS recovery dynamics to generate five distinct neuronal firing pat- terns with different spiking, bursting and response characteristics. Our results, based on measured V-MTJ characteristics and circuit simulations using com- mercial GlobalFoundries 22-nm FD-SOI CMOS technology, show an average energy consumption of 145.44 fJ per spike. Algorithmic simulations further show that these firing dynamics reduce inference spike activity by up to 88.6% while maintaining baseline classification accuracy. These results highlight the potential of V-MTJ/CMOS reconfigurable neurons to reduce computational activity and enable compact, energy-efficient brain-inspired computing systems.

Privacy protection now spans legal, technical, and managerial duties, and demand for privacy professionals is growing across sectors. However, little is known about how employers define these roles. We analyze 1,143 U.S. privacy job postings from LinkedIn and Indeed. We examine job titles, salaries, competencies, certifications, education, experience, regulatory references, and AI-related language by using rule-based text mining. We also apply Topic Modeling (BERTopic) to the same postings and identify 18 latent themes which we grouped them into four categories. Our findings show that privacy roles are hybrid and they combine legal knowledge, technical skills, and interpersonal competence. Artificial intelligence appears in more than half of postings, with AI language spread across compliance, legal, governance and security themes. Our research indicates that AI governance responsibilities are often embedded within existing privacy roles, contributing to the rise of hybrid positions alongside dedicated AI governance roles.

When mixed-integer model predictive control must select which of several similar units to activate, many same-size selections can yield closely spaced predicted outcomes, and branch-and-bound may fail to certify optimality within one sampling period. We propose a ranking-based feasible-set restriction for this class of decisions: the units are ordered by a suitability score computed at each sampling instant, and a monotone constraint permits only the top-ranked units to be active. The optimizer then chooses only how many units to activate, so the admissible selections per prediction stage grow linearly instead of combinatorially, while the model, cost function, and remaining constraints are retained. We instantiate the method for reconfigurable battery packs in which each series-connected cell can be bypassed, scoring cells with fixed weights on normalized state of health, state of charge, and voltage headroom. In a 20-cell simulation over a dynamic drive cycle with a 1 s limit per online solve, all active online restricted solves terminate at the root node with certified optimality, compared with 77.83% certification for unrestricted subset selection, and the 95th-percentile solver time is lower by a factor of 13.4. The cycle-mean cell-to-cell standard deviation in state of charge falls 8.7-fold without power curtailment, at the expense of 3.45 times as much cell switching. Solving both problems from identical states along two trajectories shows that the restriction raises the optimal cost by 0.26% and 0.14% on average at states where both solves are certified and uncurtailed.

This is a personal essay about how I see math, what I value about it, and what it means to me.

When several surfaces are visible along a ray, recovering visible 3D structure from one image requires jointly estimating their presence and metric depth. Depth Any Seen represents these surfaces as image-conditioned multi-Bernoulli depth sets, whose components each contribute one depth or remain absent. Its auxiliary-free Exact Multi-Bernoulli objective (ExactMB) learns depth and presence by marginalizing one-to-one assignments to complete, distinct targets. Our analysis shows that matching expected count can leave component-surface assignment unresolved. We extend real and synthetic layered-depth benchmarks to evaluate depth accuracy, recovered support, and overprediction. Compared to depth stacking, ExactMB reduces overprediction by a relative 88.2% on LD-Real and 80.5% on MD-3K while retaining most ordinal accuracy, with comparable conditional metric-depth error on LD-Syn. Further ablation studies show that ordered assignment improves depth-accurate recall and precision over marginalization, whereas the count-regularized configuration achieves higher deeper-rank precision than ordered assignment at lower recall. Our code will be publicly released.

Physical systems evolve continuously in time, yet their states are typically observed only at discrete times. Generating trajectories consistent with their probability densities from such observations therefore requires capturing the continuous-time evolution rather than only learning transition mappings between consecutive observations. We propose PhiBE-Flow, a framework that directly estimates the probability velocity field induced by the stochastic differential equation (SDE) which governs this continuous-time distributional evolution. PhiBE-Flow learns from discrete observations using a model-free approach requiring neither known SDE coefficients nor score estimation. We establish convergence guarantees for the method, accounting for both time-discretization and finite-sample errors. We evaluate PhiBE-Flow on systems of increasing complexity, from controlled stochastic numerical systems to Navier–Stokes dynamics and real-world videos. Our results show that PhiBE-Flow accurately recovers probability flows of stochastic dynamics, preserves multiscale physical statistics, and improves video generation performance over representative baselines. The code is available at https://github.com/R1fe/PhiBE-Flow.

The entangling layer of a quantum circuit Born machine can supply both entanglement and nonstabilizerness. In this work we show that the entangling layer can be a Clifford circuit, which supplies no nonstabilizerness. We use an architecture in which a fixed, non-trainable entangler is reused in every layer and only single-qubit rotations are optimized. There, a Clifford entangler reaches the same Kullback–Leibler divergence as a near-Haar one at sufficient circuit depth, and entanglers spanning zero to Haar-typical nonstabilizerness reach the same loss, up to a small offset for a free-fermion matchgate entangler. A doping control that raises the entangler's nonstabilizerness while leaving the entangling power of every gate unchanged leaves the loss flat. With a Clifford entangler the nonstabilizerness of the trained state comes entirely from the rotations, which take the trained circuit outside the stabilizer formalism. We also show that, among all pure states whose Born distribution is a given target, the one whose amplitudes are the positive square roots of the probabilities has the smallest stabilizer Rényi entropy, so this minimum can be computed without training.

Practical tests for witnessing entanglement in the presence of noise are needed to verify and apply entanglement-based applications in real-world communication networks. Quantum dense network coding is a communication protocol that uses an entangled state preparation together with quantum communication to halve the amount of communication needed to evaluate certain bijective functions in networks having multiple senders and one receiver. In this work, we consider a dense network coding protocol that uses graph state entanglement to implement a family of affine transformations, we derive a bound on the success probability that can be achieved by classical networks, and we show that the noise robustness exponentially amplifies with the number of senders. We apply our results in a semi-device-independent protocol for robustly estimating the effective visibility of graph states and measurement bases. Overall, our approaches are robust to noise, can support the usage of uncharacterized state preparations or measurements, and can be applied to any graph state.

A coronagraph stability allocation must protect a planet measurement, not merely satisfy a contrast target. Residual starlight both generates photon noise and interferes with small field perturbations, coupling optical stability to detection reliability. We develop a modular analytic model for the Habitable Worlds Observatory (HWO), using a reduced two-roll angular-differential-imaging realization of its OS-1 scenario. Complex-field sensitivities, wavefront sensing/control, finite observing windows, polarization, detector calibration are propagated to flux-ratio noise (FRN) and detection probabilities. Joint-visit Gaussian quadratic moments retain differential bias, cross covariance; spatial overlap/field phase determine which disturbances resemble a planet. A 6-m, 500-nm benchmark shows why the science test must precede category allocation. For a 115.46-parts-per-trillion (ppt) quadrature planet, 30,000 independent Gaussian search statistics, and a $10^{-3}$ family-wise false-alarm objective, 20-ppt FRN gives 64.55% conditional detection power; 99% requires 14.94 ppt. Photon and calibration noise exhaust the optical remainder at 8.11 pc in 100 h under the fixed response, so tighter stability alone cannot restore feasibility. An unrecognized 1% high-variance component carrying twenty percent of the variance tightens the modal allowance by a factor of 2.88; an ideal, exactly known state label reduces that penalty to 1.29 under equal conditional false-alarm limits and the same average-power objective. Thus, requirements depend on both the optical response and the information retained by the observing protocol. The framework identifies when suppression, stability, calibration, or state monitoring addresses the limiting mechanism. Numerical tolerances are controlled model results; flight allocation requires architecture-specific responses and calibrated disturbance state-estimation laws.

Pulsar timing array anisotropy analyses often use a naive counting argument to set resolutions of inferred maps of the stochastic gravitational wave background (GWB). We present a data-driven method in the form of a delayed rejection reversible jump sampler tailored to multi-resolution pixel decompositions of the angular power density of the GWB. We also consider a rapid, frequentist alternative based on information criteria statistics. We verify our methods with a series of injection-and-recovery simulations, finding that the standard counting argument would lead to drastic overfitting of the data and that our data-driven methods reduce the number of parameters in the models by one to three orders of magnitude yet can achieve higher resolution than the standard counting argument when justified by the data. We make our sampler and frequentist method implementation available on GitHub.

Open-weight tool-calling agents are adopted on evidence of merit, usually benchmark scores and a record of reliable use. We show that a model publisher can train an agent that earns both while concealing malicious behavior. Fine-tuned on a mixture of clean and poisoned conversations, our agents answer ordinary requests correctly; once the system date reaches a chosen year, they emit the correct tool call and, alongside it, one that exfiltrates the user's credentials. The exfiltration runs while the user-facing response mentions only the legitimate work. We call this attack SilentCall. Under the trigger, it fires on at least $99.6$% of requests, and no response ever mentions it. The attack is detectable by three distinct methods, which differ mainly in what a defender needs to run them. A runtime monitor that inspects each tool call before it executes requires no access to the model and catches every instance of the payload we tested at a 1.73% false-positive rate. High-temperature probing requires only the published weights. The weight-distribution audit requires training a benign model with the suspect's recipe, placing it within reach of model hubs but not ordinary users. Alignment benchmarks, by contrast, do not separate poisoned from benign models. SilentCall leaves no trace on standard benchmarks. As tool-using agents spread through the open-weight supply chain, trust in them should not rest on what a model says about its own actions. It has to come from inspecting those actions at runtime, auditing models where they are distributed, and treating tool access as a security surface in its own right.

Large language models (LLMs) are increasingly integrated into educational settings, yet educators lack robust, standards-aligned tools to evaluate their effectiveness in K-12 science contexts. Existing benchmarks predominantly assess general language or advanced scientific reasoning, leaving a critical gap in understanding LLMs' performance on content directly relevant to secondary science curricula. To address this gap, we developed a comprehensive NGSS-aligned benchmark for both middle and high school science using a rigorous synthetic data pipeline, multi-judge validation, and item-level psychometric analysis. Nine open-weight LLMs were systematically evaluated using this benchmark, indicating that several smaller, locally deployable models achieved high accuracy across diverse science domains and question types. Our findings indicate that model size did not consistently predict performance, emphasizing the importance of intentional model selection for educational deployment. We then incorporated a human reviewer into the loop, reviewing the items generated by the LLMs for alignment with NGSS standards. The human review indicated that synthetically generated items were not in perfect alignment with the NGSS standards, indicating the benefits of human-in-the-loop item development, the need to explore the intersection of content and pedagogical knowledge, and the need to extend benchmarks to evaluate LLMs' capacity for interactive, evidence-based feedback in educational scenarios.

Decentralized multi-agent path finding (MAPF) with communication requires agents to reach individual goals without collisions under partial observability. Learnable policies trained on expert data provide an effective approach to this problem. However, when several coordinated joint actions are valid in the same context, independently sampling from per-agent distributions can recombine locally valid choices into incompatible joint actions. This failure can arise from the final sampling mechanism even when the per-agent action distributions are learned correctly. DMM (Decentralized Master-Mind) addresses this by replacing one-shot action sampling with discrete, iterative refinement of action intents across communication rounds, inspired by denoising in diffusion models. Agents initialize random action intents and refine them through local communication, coupling their choices before commitment. DMM is pretrained with imitation learning on expert MAPF solutions and further optimized with MICPO, a critic-free group-relative reinforcement-learning method designed for multi-agent, multi-round action refinement. DMM generally achieves higher success rates and lower solution costs than the evaluated learnable baselines. On 1,600 MovingAI tasks, DMM fine-tuned with MICPO solves 1,598, the highest coverage among the evaluated methods, while achieving solution costs close to those of the strongest baselines. DMM also scales to over one million simultaneously acting agents in obstacle-rich environments. These results show that round-level intent refinement can improve joint-action coordination while preserving decentralized execution.

Modern neural predictors can model highly nonlinear maps, but many scientific and engineering tasks require reasoning in the opposite direction: given a performance or safety level, the goal is to characterize the preimage, that is, the complete set of inputs which meet the desired target level and optimize over that set. For expressive neural predictors, however, such preimages typically have no explicit representation and are expensive to recover or optimize over. This creates a fundamental three-way challenge between expressive forward prediction, accurate preimage approximation, and tractable optimization over the preimage for downstream tasks. We introduce TRIO (tractable representations for preimage learning and inverse optimization), a framework for learning representations that make these objectives compatible by construction. Our key contribution is a preimage factorization: the forward model remains expressive through nonlinear radial transformations (including neural networks), while, under inversion, each transformation reduces to a single scalar radius, which yields simple geometric level sets. This yields an explicit geometric representation that is reusable for downstream optimization over the preimage, and, for linear objectives, we show that this admits a closed-form global solution. We finally prove a universal approximation theorem which shows that TRIO can approximate any continuous forward map and its entire family of potentially disconnected, nonconvex preimages arbitrarily well. Hence, TRIO combines expressive forward modeling, exact preimage recovery, and tractable global downstream optimization over preimages by design.