Papers

Automated malaria diagnosis from thin blood-smear microscopy could meaningfully reduce the burden on under-resourced laboratories, but a model that maximises accuracy on clean laboratory images fails badly the moment an inexpensive smartphone camera introduces sensor noise. This paper introduces MalariaCascade, a two-stage inference system in which a lightweight MobileNetV2 sentinel (2,225,153 parameters) makes confident classifications at low compute cost and escalates uncertain cases to an EfficientNet-B3 expert (10,697,769 parameters) that sees only clean, standardised images regardless of how corrupted the incoming frame is. Structural isolation of the expert stage, not learned robustness, is the mechanism. The sentinel is trained under a safety-score objective that places an explicit floor on Recall(Parasitised) (>=0.95) and Recall(Uninfected) (>=0.40) before precision is optimised, ensuring the checkpoint satisfies clinical safety constraints by construction. On the NIH Malaria Cell Images Dataset (27,558 cells), the cascade reaches Accuracy=0.9736, Recall(Parasitised)=0.9570, Precision(Parasitised)=0.9912, F1=0.9738, and AUROC=0.9955 on the clean test set. Under Gaussian sensor noise at full severity, cascade Recall(Parasitised) degrades by only 2.4 pp (0.9570 to 0.9329), while the flat single-model baseline collapses by 63.0 pp (0.9584 to 0.3281). McNemar's test confirms the cascade improvement is statistically significant (chi^2=11.14, p=0.00085). An ablation isolating the structural property shows that routing clean images to the expert is responsible for a 16.8 pp Recall(Parasitised) advantage under sensor noise relative to a cascade where the expert also sees corrupted inputs.

Privacy-Preserving Federated Analytics enables multiple nodes to collaboratively derive statistical insights without exchanging raw data. However, ensuring node authenticity and data validation (avoiding concerns such as identity tracking, data linkage, or data leakage) remain fundamental challenges. This paper offers some insights into the feasibility of defining an authenticated, integrity-preserving data model by coupling FPPA with Verifiable Credentials defined within the Self-Sovereign Identity framework.

Vision-language verifiers and routers must distinguish errors repairable by more reasoning from those caused by visual evidence never reaching the language model. This distinction lacks ground truth because annotators see full-resolution images while models receive preprocessed tensors. We introduce AliasForge to create cases where the relevant fact is provably absent from the interface. Fixed-point resampling makes the pre-rounding resize an exact integer linear map that can send nonzero integer perturbations to zero. Hiding a label-flipping perturbation there produces images with opposite step-correctness labels but bit-identical interface states. Every verifier therefore has the same output law on both members, giving pair-balanced accuracy exactly one half and zero gain from language-side repair. We prove that every fixed-point downscaler has such null vectors and bound their smallest size at the most common ratios, which rules out an 8-bit fit whenever the bound exceeds 255. From the resize configuration alone, a lattice criterion supplies realizable collisions and certifies their absence within the specified construction family. It resolves all 20 screened configurations, 17 as constructible and 3 as non-constructible. We construct certified pairs across three architectures and certify four additional processors, with zero decision-logit gap on all 18 scored pairs and none of the 18 controls. The pairs also screen routers that waste computation on re-attention or further reasoning. On natural items, per-item routing headroom exists, but no tested interface-only router improves over stopping. Our fiber ceiling bounds the headroom recoverable from the interface. Code: https://github.com/KurbanIntelligenceLab/aliasforge.

First-order phase transitions in neutron-star interiors can leave signatures in the polar quasi-normal-mode spectrum. We compute the complex quadrupolar $f$- and $p_1$-mode spectra in full general relativity for cold, nonrotating hybrid stars with a sharp hadron–quark interface. We model the equation of state by matching a hadronic SLy4 phase to a constant-sound-speed quark-phase. We compare slow phase conversion, in which fluid elements retain their phase and the interface moves with the fluid, with rapid phase conversion, in which matter changes phase as it crosses the boundary and the interface follows phase equilibrium rather than the fluid, together with an algebraic interpolation between these limits. On identical equilibrium backgrounds, the two physical limits produce a sizable separation in the real part of the $p_1$-mode frequency. This $p_1$ frequency separation is largest when the local tangential-displacement fraction of the eigenfunction changes rapidly across the interface. Across the surveyed EOS parameter space, rapid conversion generally lowers the $p_1$-mode frequency relative to slow conversion, with compactness-averaged separations reaching $\sim3.5\,{\rm kHz}$ on disconnected twin-star branches. The largest separations occur at relatively low transition pressures and large density discontinuities. By contrast, the $f$-mode is only weakly affected by the interface condition for individual stellar models. Across the sampled constant-sound-speed parameter space, departures exceeding the hadronic SLy4 reference residual occur mainly at low transition pressure, large density discontinuity, or both, with different boundaries for the real- and imaginary-part fitting variables. Thus, the $p_1$-mode probes the local interface response, whereas the tracked $f$-mode reflects the global departure of the hybrid sequence from the hadronic calibration.

Structural health monitoring of deteriorating structures requires the latent deterioration process to be inferred indirectly from measured structural responses and propagated to quantities of engineering interest. This paper presents a probabilistic framework that formalizes this process by distinguishing Bayesian inference of uncertain deterioration and model parameters from diagnosis of the current deterioration state, prognosis of its future evolution, and prediction of structural reliability. The deterioration model thereby provides the common probabilistic link between monitoring-based inference and these downstream tasks. To enable sequential inference as monitoring information accumulates, Bayesian Updating with Structural Reliability Methods (BUS) is extended through a nested formulation of the BUS events associated with successively growing monitoring datasets. The resulting Sequential BUS method allows Subset Simulation to continue from the augmented conditional sample population obtained at the preceding monitoring stage rather than restarting from the prior distribution. The posterior population can then be propagated to monitoring-informed reliability analysis. The framework is demonstrated for fatigue deterioration of a redundant jacket-type structure, where modal properties obtained from simulated vibration monitoring are used to infer a high-dimensional deterioration model of welded connections. The results show how successive monitoring observations constrain plausible deterioration histories, provide probabilistic system-level diagnosis, and update crack-growth prognosis and structural reliability while retaining ambiguity between deterioration scenarios that produce similar structural responses. The proposed framework thus provides a coherent probabilistic route from response-based monitoring data to deterioration diagnosis, prognosis, and reliability prediction.

Predicting how drivers, vehicles, and road scenes interact and evolve together is central to driver monitoring. Prior work models in-cabin activity or traffic-conditioned driver motion in isolation, motivating joint driver, vehicle, and road modeling with real-time on-vehicle evaluation. We introduce TriDrive, to our knowledge the first unified framework that jointly forecasts driver kinematics, vehicle dynamics, and road demands through an automation-conditioned transition model. Modality-specific encoders (an anchored kinematic representation of the driver, causal CAN-bus dynamics, and frozen V-JEPA 2 road latents with structured road margins) are connected by directed residual connections through which driver and road context refine vehicle forecasts. We evaluate TriDrive on three downstream tasks. On the public AIDE benchmark, its kinematic encoder recipe sets a new full-set state of the art (SOTA) among published baselines (48.05 versus 71.47 All-MPJPE). On 197.2 hours of naturalistic BATON subset, directed connections and road margins raise assistance-engaged PR-AUC by 0.084 for steering onset and 0.286 for time-to-collision drops. For real-time use, we distill the road encoders and run TriDrive on a comma four with an external 8 GB GPU, where a lightweight current-state warning probe updates at 5 Hz with 177 ms p95 latency while the joint model forecasts concurrently. The probe is above an openpilot-based baseline on human-labeled manual-driving warnings (AUROC 0.725 versus 0.563), and in a paired on-road study 14 drivers rate its warnings as more appropriate (+1.79) and timely (+2.67) than those of openpilot's driver-monitoring system.

RAG and retrieval-based agent memory both inject retrieved content into LLM prompts, as document chunks and recalled memory records, respectively. The same content can recur across requests at different prompt positions or after different preceding contexts, preventing reuse through conventional prefix caching. Our characterization finds that records recurring outside the matching prefix account for over 70% of injected memory tokens in agent-memory workloads. Composable KV-reuse methods enable reuse in such cases, but online serving introduces a management problem: a recurring unit's KV states may not yet exist, may have been evicted, or may reside on another node. We present Tessera, a disaggregated serving system that makes retrieval the control plane for KV reuse. By exposing the context units needed before model execution, retrieval allows Tessera to combine current demand with retrieval history, KV residency, and generation load to coordinate cache management and request routing. Generation nodes concurrently prepare locally cached, remotely cached, and missing states, while retaining newly computed states off the request's critical path. Across RAG and agent-memory workloads, Tessera lowers mean TTFT by up to 3.6x over SGLang and LMCache with EPIC at matched request rates, and sustains low TTFT at rates where the baselines saturate, while matching the answer quality of the underlying composition policy.

We report a novel polyhedral surface of genus~3 embedded in $\mathbb{R}^3$ with eight planar, simple, non-convex nonagonal faces, 24 vertices and 36 edges, in which every two faces share at least one edge: 20 pairs of faces share one edge and 8 pairs share two collinear edges. Its face planes are $3x-4y-2z=5$, $-2x+5y-5z=3$ and their images under the half-turns about the three coordinate axes, and all vertices are rational. The polyhedron has the same face vector, face sizes and number of edge multiplicities as the polyhedron described by Mizhaev, but it is not combinatorially equivalent to it. Our realisation has the symmetry group $D_2$ of order~4, whereas Mizhaev's polyhedron has a rotoreflection symmetry. The example was found by a computational geometric search, and all its properties were verified in exact rational arithmetic.

We propose RIAG-R, a Riemannian Inertial Adaptive Gradient method with gradient-triggered Restart, for optimization on Riemannian manifolds. RIAG-R combines three ingredients: an AdaGrad-type adaptive step-size that requires no knowledge of the Lipschitz constant; inertial extrapolation in the tangent space via the exponential map to accelerate convergence; and a restart rule, costing only one extra inner product per iteration, that detects and corrects the momentum-saturation pathology induced by manifold curvature. We establish a per-iteration descent inequality, an optimal $O(\varepsilon^{-2})$-iteration complexity, a convergence result for cluster points of the generated sequence, and a linear convergence rate under the Riemannian Polyak-Łojasiewicz inequality. Numerical experiments on four representative matrix manifold optimization problems including sphere, Stiefel, symmetric positive-definite, and Grassmann manifolds demonstrate that RIAG-R consistently outperforms non-inertial and restart-free inertial baselines, confirming that adaptive restart is essential to realizing the benefits of momentum on curved spaces.

Policies trained from the same base model can appear to solve different problems. An oracle that chooses the best policy for each problem may therefore appear much stronger than any single policy. Selecting the largest estimated success rate also selects favorable sampling errors. We study this effect through reliability coverage, the fraction of problems whose success probability reaches a chosen threshold. Our first test redistributes stored correctness outcomes across policies within each problem. A second also preserves each policy's total successes, accounting for overall quality differences under a specified statistical model. For five training seeds of a seven-billion-parameter vision-language model, redistribution reproduces 0.096 of an estimated 0.113 oracle gap at threshold 0.10. Neither test finds significant evidence at this threshold. Small advantages remain unresolved. Mixtures, routers, voting, and weight averaging show no detectable improvement over their corresponding single-policy baselines. Training policies on different datasets shows little detectable specialization under light post-training, and no router gain. A stronger recipe does create it, both tests detect it, and a router gain appears only at the high thresholds where the specialists separate. In a control with predictable specialization, a router recovers about half the oracle gap. Coverage bounds explain why even a genuine oracle advantage need not yield a deployment gain. The tests assess apparent specialization from stored responses before investment in routing. Code: https://github.com/KurbanIntelligenceLab/oracle-gaps

Alternating gradient descent-ascent (AltGDA) is a simple and practically effective method for solving finite two-player zero-sum matrix games. However, the theory of AltGDA remains limited: existing results either apply only to unconstrained settings or require restrictive assumptions on the equilibrium in constrained settings. We show that AltGDA converges globally at an $O(1/T)$ ergodic rate in every finite two-player zero-sum matrix game. Unlike prior results, our guarantee holds for every initialization and every horizon $T$: the uniform averages of the AltGDA iterates satisfy an $O(1/T)$ duality-gap bound. Our proof is inspired by numerical results obtained using a novel performance estimation programming (PEP) framework for Lyapunov function search over compact convex sets. Additionally, we provide simple counterexamples showing that the last-iterate duality gap of AltGDA does not converge to zero. This justifies why averaging of iterates is indeed necessary to achieve an $O(1/T)$ rate. We have formalized and machine-checked our global ergodic convergence result in Lean 4.

An $n$-mean on a topological space $X$ is a continuous symmetric map $p\colon X^n\to X$ satisfying $p(x,\ldots,x)=x$ for every $x\in X$. If $X$ is a $G$-space, such an $n$-mean is equivariant if $p(gx_1,\ldots,gx_n)=g p(x_1,\ldots,x_n)$ for every $g\in G$ and $x_1,\ldots,x_n\in X$. For finite $G$, we prove that, in the presence of an equivariant $n$-mean with $n$ a multiple of $\lvert G\rvert$, the $\mathrm{ANE}$, $\mathrm{AE}$, and $\mathrm{AR}$ properties imply their equivariant counterparts. We next consider $\mathbb Z_2$-actions induced by decreasing involutions on topological lattices. We first prove that every fixed point of such an involution on a modular lattice yields an explicit equivariant $2$-mean. Furthermore, we introduce a lattice-theoretic version of the Babylonian iteration used to approximate the geometric mean and prove that, under suitable conditions on the order and its interaction with the topology, this iteration produces an equivariant $2$-mean whenever the lattice admits a $2$-mean compatible with the order. Finally, we apply these results to spaces of compact convex bodies and supercoercive convex functions, where we prove the existence of equivariant $2$-means and show that both spaces are $\mathbb Z_2$-absolute retracts.

Multi-step agents are trained on flat action streams: SFT and RLVR weight every token uniformly and ignore the sub-procedures that recur across tasks, the hierarchy that lets humans plan top-down from reusable routines. This structure sits unused, and flat training uses each scarce trajectory less fully than its content allows. Recent agents do use that structure, but only as LLM-written skills in context, never in the weights, so their gains do not generalize beyond retrieval. We instead recover this hierarchy from the data itself and train on it, with no LLM calls. Following text tokenizers, which build a vocabulary by counting alone, we score action spans by reusability and merge canonicalized actions into a reusable eXperience tree (X-Tree). Each X-Tree node captures how a frequent and success-bearing skill is composed from sub-skills, guiding efficient generalization. We integrate X-Tree into three training settings: offline RL, with each node as a training instance; online RLVR, with an adaptive skill bonus; and on-policy self-distillation, with X-Tree as the self-teacher's privileged context. Across WebArena, ScienceWorld, and WebShop at three model scales, X-Tree improves over standard recipes at matched data and budget by up to 4.5% SR on WebArena, 5.8% SR on ScienceWorld and 4.1% success on WebShop. Matched analyses attribute the gains to the X-Tree structure and the three integrations.

Spatial cognition enables individuals to perceive and interpret spatial relationships, estimate locations, and navigate within their surroundings. While vision plays a dominant role, other sensory modalities, particularly olfaction, can support spatial processing when visual cues are limited. This paper explores the effects of scent-delivery within virtual reality (VR) environments by using fan-mediated olfactory devices. We conducted two formal studies to evaluate the effects on spatial information acquisition. Study 1 (N=24) examined the participants' ability to localize a scent source while walking a linear path using two different olfactory devices. Study 2 (N=19) employed a triangle completion task, in which participants attempted to return to their starting point under varying rotation angles and olfactory conditions. Results indicate that scent-delivery feedback influenced spatial behavior in distinct ways across the two studies. In Study 1, visual-olfactory misalignment produced systematic directional biases without improving absolute localization accuracy. In Study 2, distance-modulated scent-delivery feedback reduced terminal homing error but also increased traveled distance and completion time, suggesting a more deliberate goal-confirmation strategy.

What should data teach a language model at a particular point in training? A circuit view reveals three distinct bottlenecks: forming a computation, making its required content available, and selecting among available routes. A shared diagnosis-to-data principle connects them: localize the missing operation, preserve its causal relation, vary shortcut-bearing context, and re-audit the residual. Formation-sensitive selection and prerequisite ordering accelerate a binding-matching-transport path; a brief early prefix from the same training multiset retains a validation advantage through 100B tokens. Availability counterfactuals then distinguish writing content from invoking available memory, while paired supervision and context-opportunity ranking improve matched route decisions and long-context answer likelihood. A continuous 350M-model experiment connects the three interventions on the same facts: early circuit training improves subsequent learning, and the complete sequence outperforms stage-replacement controls on facts withheld from Use teaching. Independent query surfaces and opposed-source decisions expose conditional arbitration as the remaining frontier. Together, these results show why a change in the limiting operation calls for a change in supervision, not merely a new ranking of difficult examples.

Long horizon agent self-evolution without model weight updates is essential for enabling deployed agents to accumulate reusable skills and improve over time. Prior self-evolution work has focused primarily on short-horizon tasks, while repository-level software engineering remains unexplored despite being an ideal testbed for long-horizon adaptation. In this setting, agents are required to solve streams of sequential tasks, navigate complex dependencies with evolving repositories and persistently store and reuse experience. Text-based skill optimization offers an efficient, non-parametric approach for such adaptation. However, existing methods often suffer from unstable updates, performance drawdown, and agent collapse over extended deployments. In this paper, we formalize the concept of in-context self-evolution and introduce VALVE, a validated-gated framework for long-horizon skill optimization. We establish finite convergence, provide theoretical guarantees for future-task gain and drawdown, and derive the validation and evaluation holdout sizes required for a prescribed tolerance, with leading-order scaling Empirically, our pipeline, VALVE achieves stable self-improvement over evolution horizon spanning more than 1,000 SWE tasks, with average final and peak gains of $14.9$ and $16.5$ points across three frontier models (GPT-5.5, Claude-4.6 and MiniMax-M2.7). The validation gate reduces average drawdown by 75% and produces an 11x more compact skill bank than ungated evolution. We further present extensive ablations identifying the design choices most critical to long-horizon skill evolution.

Persona AI can make deceased experts available for decisions they never encountered. Users may seek these personas precisely because they lack the knowledge needed to judge their advice. We thematically analyze 115 focal RedNote/Xiaohongshu posts and a nested comment sample concerning unofficial personas of Chinese education advisor Zhang Xuefeng. An installation offer promised expert guidance, while a family's reported use required current records and contextual judgment. Other posts positioned the persona as a questioning aid rather than an expert replacement. Commenters connected continued expertise to updating, permission, and the ability to refuse further work. These findings distinguish access to an expert identity from access to professional help. Keeping the persona current puts living actors in control of what the deceased appears to recommend. Operators therefore need to undertake the support promised by the persona while making their continued use of the person's identity open to challenge.

In this work, we show how two adversaries (Eve and Mallory) can coordinate an electromagnetic side-channel attack to recon- struct the vote displayed on an e-voting machine (EVM) and link it to a specific voter (Alice). Assuming that Eve has access to a place adjacent to the e-polling room (e.g., restroom, unsupervised room), she performs vote reconstruction by intercepting un- intended electromagnetic emanations associated with the video signal. Meanwhile, Mallory observes when Alice is voting and reports this information to Eve over the Internet. To validate the most critical stage of the attack, we conduct a software-defined radio experiment using the official Brazilian e-voting interface and demonstrate through-wall vote reconstruction. Although conventional monitors are employed rather than official EVMs, our findings provide insights into information forensics and support security recommendations for government authorities responsible for e-voting systems.

We study entity ranking and inference under the Bradley–Terry–Luce (BTL) model using pairwise comparisons collected over sparse comparison graphs. In practice, collecting high-quality human judgments can be expensive and time-consuming, motivating the use of synthetic data augmentation in model training. We analyze an iterative synthetic augmentation workflow in which synthetic comparisons generated from fitted models are successively added to the original dataset. In this process, the proportion of real data may vanish as the number of iterations grows. However, emerging literature has shown that recursive training on synthetic data can lead to model collapse, raising concerns about the statistical reliability of such augmentation procedures. To this end, we systematically analyze the resulting MLE in finite-sample, high-dimensional regimes. For the resulting iterative maximum likelihood estimator (MLE), we derive its optimal finite-sample $\ell_2$ and $\ell_{\infty}$ statistical rates and establish its asymptotic normality under natural identifiability conditions. We further characterize regimes in which model collapse is avoided despite the diminishing fraction of real data. We validate our theoretical findings through large-scale numerical experiments and an application to the Arena Human Preference 140k dataset.

We study the $\bar{K}^0d$ system using a new formulation of the fixed-center approximation that preserves elastic unitarity. The resulting scattering amplitude predicts a bound state below threshold, which can be interpreted as a $\Lambda(1380)N$ configuration complementary to the $K^-pp$ state associated with the higher $\Lambda(1405)$ pole. The interaction is attractive, with scattering parameters of the same order as recent $K^-d$ determinations. We further calculate the $\bar{K}^0d$ correlation function, which exhibits a characteristic structure associated with the bound state and provides a Coulomb-free observable that can be tested in future ALICE measurements. Results obtained with two different $\bar{K}N$ models are very similar, indicating the robustness of the predictions against the choice of the underlying interaction.

Signature-free protocols avoid the cost of post-quantum signatures. We present two simple signature-free blockchain consensus protocols for eventual synchrony with optimal good-case commit latency (three message delays for \(f<n/3\) and two for \(f<n/5\)), optimistic responsiveness, a block time of only two message delays without speculation, and \(O(n^2)\) communication per view. They instantiate Generic Simplex, a blockchain consensus construction parameterized by a new abstraction called view agreement. The same construction also captures Simplex, Minimmit, and a new synchronous signature-free protocol with optimal good-case commit latency of two message delays for \(f<n/4\).

Recursive self-improvement (RSI) offers a promising path for overcoming the limited visual capability of current medical imaging agents. Yet applying RSI to volumetric imaging remains difficult: failures can arise from acquisition, perception, training recipe, or downstream inference, while self-generated feedback and logged trajectories provide little guidance on which component should change. We introduce ReVision3D, an RSI system that leverages 3D volumes with spatially grounded annotations to determine where visual evidence is lost and recursively improve the corresponding visual capability. A frozen language-model designer proposes revisions to acquisition, perception, training, or inference, while the verifier and system-level objective remain fixed. Our key insight is that an annotated volume forms an exact replay world for view rendering and spatial verification: unvisited views can be rendered on demand, and localized predictions can be checked directly against reference masks. This grounded feedback directs targeted revision, while only changes that improve beyond measured seed noise are retained. Each accepted change triggers renewed attribution, allowing the dominant bottleneck to shift across rounds. On abdominal CT, attribution identifies perception as the dominant remaining limitation. Revising that level enables ReVision3D to achieve 79% liver recall and 83% kidney recall at under 0.4 false positives per patient, outperforming the evaluated frozen multimodal foundation models, with the largest gains on small lesions. Our framework is public available with interactive demo in this project page: \url{https://leeh43.github.io/ReVision3D/}

Co-located augmented reality (AR) captions make speech readable, but they can separate an utterance from the person who produced it. In unfamiliar groups, losing that source complicates immediate responses and later review: users must recover not only what was said, but also who said it. Conventional diarization returns anonymous clusters, while speaker recognition typically assumes pre-meeting enrollment. We built VocalEyes, a speaker-aware AR captioning system that creates named voice profiles from natural self-introductions. The interface coordinates speaker-attributed captions, a fixed profile card, and a visual cue that marks the articulating face. In a controlled within-subjects study with 20 participants who reported typical hearing, VocalEyes identified speakers with 88.0% accuracy and increased participant speaker-tracking accuracy from 47.2% with caption-only AR to 87.3% with the complete interface. Participants also reported lower workload with the complete interface. These findings show how in-conversation registration can preserve speaker attribution across live captions and meeting records in scripted small-group meetings.

The wide-ranging benefits of physical activity and sports participation among children and adolescents have been closely examined and are reported to include improvements in physical and mental health, cognitive functioning, and social connectedness. However, it remains largely unknown how these activities may affect flourishing and academic engagement, which are closely tied to long-term success, health, and well-being, and how these patterns evolved before, during, and after the COVID-19 pandemic. In this article, we provide the protocol for an observational study using data from the National Survey of Children's Health to examine these relationships among American adolescents. To strengthen our findings, we will conduct this investigation across three different time periods, allowing us to assess the replicability of our conclusions. We introduce a novel statistical design, called data turnover, to carry out this analysis. Data turnover allows a single group of statisticians and domain experts to work together to assess the strength of evidence gathered across multiple data splits while incorporating both qualitative and quantitative findings from data exploration. We delineate our analysis plan using this new method and conclude with a brief discussion of additional considerations for our study.

Since Zhang et al. \cite{Zhang2025} introduced the first purely primal methods for monotone variational inequalities subject to convex functional constraints, the field has lacked a complete understanding of the complexity limits of this oracle class. We develop a theory that resolves the critical gaps left by their pioneering framework. Our Optimal Primal Constrained Gradient Method (OPCGM) establishes convergence rates and lower bounds for algorithms restricted to local linear constraint approximations. For strongly monotone operators, we prove that a refined primal gradient method achieves the optimal $\mathcal{O}(1/T)$ rate for both optimality gap and constraint violation, eliminating the suboptimal exponent present in prior work. For Lipschitz monotone operators, we propose a primal extragradient variant that achieves the optimal $\mathcal{O}(1/\epsilon)$ gap complexity using only quadratic programming oracles, at the cost of a constant asymptotic feasibility violation for the averaged iterate; we prove that the first half-step is necessarily infeasible for the natural class of constant-stepsize primal extragradient methods on smooth convex constraints with positive curvature. We establish lower complexity bounds for primal methods restricted to local linear approximations, proving $\Omega(1/\epsilon^2)$ for Lipschitz monotone variational inequalities with Lipschitz constant scaling as $\Theta(1/\epsilon)$, and $\Omega(1/\epsilon)$ for standard Lipschitz monotone variational inequalities. We design a single-loop primal method that achieves an $\mathcal{O}(1/\sqrt{T})$ gap rate with only a domain-radius estimate, at the cost of a problem-dependent asymptotic feasibility constant that we prove is unavoidable. For strongly monotone problems, we prove that the last iterate converges at the optimal $\mathcal{O}(1/T)$ rate.

Graph reconstruction from partial observations often comes with structural side information, such as degree bounds, triangle counts, or an edge-density band. Prior-Informed Flow Matching (PIFM) reconstructs graphs by transporting a local prior toward the graph distribution, but it provides no mechanism to incorporate this side information. We put forth Constrained Primal-Dual PIFM (CPD-PIFM), which augments the sampler with Lagrange multipliers that evolve along each trajectory. The multipliers respond to constraint violations at a predicted endpoint and guide subsequent sampling steps without retraining. We prove that the sampler inherits PIFM's permutation equivariance and bound its expected terminal slack by a term that decays as the inverse square root of the number of steps, plus two approximation terms. On three link-prediction benchmarks and nine combinations of datasets and constraints, CPD-PIFM raises feasibility by 11-26 percentage points and remains competitive with fixed guidance without selecting a separate multiplier for each constraint.

The positive-partial-transpose-squared (PPT-squared) conjecture asks whether the composition of two positive-partial-transpose (PPT) quantum channels must be entanglement breaking (EB). The problem remains open in general and, within the diagonal orthogonal covariant (DOC) class, the first unresolved deterministic dimension is four. A sufficient condition for PPT-squared composition is derived for DOC maps in arbitrary finite dimension. The proof isolates the quantum coherence data into two correlation matrices, mixes each with the identity until it lies in the convex hull of rank-one correlation matrices, and converts the resulting objects into an explicit triplewise completely positive (TCP) core. The remaining contribution is purely classical and is TCP whenever a simple entrywise mixing inequality is satisfied. For PPT DOC maps $\Phi_{A,B,C}$ and $\Phi_{D,E,F}$ on $M_d$, the entrywise bound $(AD)_{ij}\ge 2\lfloor\sqrt{d}\rfloor\sqrt{A_{ii}A_{jj}D_{ii}D_{jj}}$ for all $i,j$ guarantees that $\Phi_{A,B,C}\circ\Phi_{D,E,F}$ is EB. In dimension four the universal coefficient becomes four. A continuous family of bistochastic PPT channels is then constructed; every member with $a\ne1$ is not EB, while every pairwise composition within the family is proved to be EB. A rank-sensitive refinement shows explicitly how low coherence rank can improve the universal coefficient. The resulting certificate is sufficient rather than necessary and is complementary to factor-width and semidefinite-hierarchy approaches.

As networks expand and become an ever more critical infrastructure to modern society the need to analyze these networks with the highest regard for privacy is essential to ensure their proper function. Depending on the level of the network layer to be analyzed, sources and destinations can be any combination of physical, logical, or persona/agentic endpoints, which requires the ability to handle diverse data. Invaluable to these analyses are mathematical tools that enable sophisticated mathematical algorithms to be expressed succinctly while achieving scalable vertical (within a compute node), horizontal (across compute nodes), and temporal (over different generations of hardware) performance. Associative (token) array mathematics and corresponding libraries is one approach that can meet these requirements. Accelerating these libraries with GPUs enables the analysis of the largest networks. The MIT/IEEE/Amazon Anonymized Network Sensing Graph Challenge provides a venue for highlighting the applicability of accelerated associative arrays for these types of problems. The D4M associative library has been implemented in a number of languages. This work benchmarks a prototype Matlab D4M GPU accelerated implementation of the Anonymized Network Sensing challenge across a wide range of CPU and GPU hardware. Scalable performance is demonstrated within and across CPU cores, CPU nodes, and GPU nodes. Horizontal scaling across multiple nodes was linear. Running on hundreds of GPU nodes simultaneously achieved a sustained processing rate sufficient to potentially analyze a 10 Petabit/s network.

We study second-order convex optimization under generalized Hessian smoothness, where the local Hessian Lipschitz constant may grow linearly with the gradient norm. For inexact Hessians, we develop adaptive algorithms, including an accelerated Monteiro-Svaiter-type method whose complexity matches the lower bound for second-order methods with $\delta$-inexact Hessians in the classical Lipschitz-Hessian setting. Our methods are parameter-free in the sense that they require no problem-specific parameters as input, including the Hessian inexactness level $\delta$ and smoothness constants. Instead, their backtracking adapts a single regularization parameter that jointly captures Hessian inexactness and local Hessian smoothness. The resulting rates split into two regimes. Far from the solution, the gradient-dependent smoothness term yields geometric convergence. Near the solution, the rate is governed by the ordinary Hessian smoothness and the inexactness level $\delta$, recovering the classical Lipschitz-Hessian guarantees.

Incorrect or corrupted labels in tabular datasets can significantly degrade supervised learning performance, particularly when mislabeling is subtle and not easily detectable from feature space alone. In the context of automated or AI-augmented data science workflows, robust detection of such label noise is critical for building reliable models. We propose a data-centric reasoning module for AI data science systems that automatically diagnoses dataset quality and selects appropriate cleaning strategies. Given a dataset, a meta-model predicts weights over a diverse set of detectors, including confidence-based, neighborhood-based, and distributional methods. Across benchmark datasets with controlled noise, our approach achieves performance comparable to a Confident Learning baseline on average, with dataset-dependent gains and losses, particularly in heterogeneous regimes. We further show that detector effectiveness is systematically linked to dataset properties. These results demonstrate the value of descriptor-driven, data-centric ensembling as a component of AI-assisted data-science pipelines for robust dataset assessment and model reliability.