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At least 1,207 records · Page 67Linked to original sources
arXiv2026

Pricing the Unprovable: Ambiguity, Turnstile Runs, and the Verifiability Discount in Crypto Protocols

Privacy-preserving protocols can repair a vulnerability without establishing whether it was exploited beforehand, even when no theft is reported and aggregate supply is protected. We call the potential value reduction from this gap the verifiability discount. A turnstile model shows how early withdrawal can shift a possible shortfall to remaining holders and why credible evidence can become more valuable as exposure grows. We introduce VDISC, a reproducible framework that records reported loss, exposed value, public evidence, returns, and pool flows separately. It combines Orchard's staged disclosures with reconstructed on-chain flows, earlier Zcash cases, and a 40-event security panel. Orchard follows the predicted direction: market responses were muted after repair and supply assurance, while the largest negative return and aggregate shielded-pool net outflow aligned with the acknowledgment that past abuse could not be ruled out. These patterns are directional, not causal. Across events, market-cap-normalized reported loss and unresolved exposure overlap among the 38 events with a public loss figure (Pearson 0.86, Spearman 0.56), partly because exposure is often coded from the loss itself, so returns alone cannot distinguish reported loss from unresolved history. The findings motivate three candidate design priorities: produce privacy-compatible evidence about past states, limit the state exposed by a single flaw, and disclose residual uncertainty explicitly.

q-fin.TR↗
arXiv2026

A Systematic and Validated Translation of the Perceived Empathy of Technology Scale to Chinese

The Perceived Empathy of Technology Scale (PETS) allows evaluation of empathic behavior in intelligent systems, a concept increasingly applied in human-AI interaction, particularly in emotional and mental health support applications. To support intercultural research and development, PETS is already available in multiple languages, as research suggests cultural and language-based differences in the expression and perception of empathy. Given the substantial Chinese-speaking population and the growing focus on cross-cultural HCI research, we present a validated translation of PETS into Putonghua (Mandarin) with Simplified Chinese. Based on established back-translation methodologies as used in previous PETS translations, our process included multiple independent translations, expert panel reviews, and empirical testing with a total of N=400 participants from an English and a Chinese sample. Through confirmatory factor analysis and invariance testing we show that the Chinese PETS retains the original two-factor structure with high reliability, with support for configural, metric, and scalar invariance. Beyond validation, empathic system behavior was rated equivalently across languages, while non-empathic behavior drew substantially higher ratings from Chinese participants, suggesting its absence is read less consistently across cultures than its presence. This validated Chinese version enables researchers and practitioners to assess empathy perceptions among Chinese-speaking users, supporting culturally appropriate empathic technology development.

cs.HC↗
arXiv2026

Spectral Theory for Schrodinger Operators with Interface Transmission Conditions

Interfaces influence transport across biological membranes, habitat boundaries, and composite media. Motivated by these applications, we study two classes of Schrodinger eigenvalue problems with transmission conditions allowing jumps in the solution or its normal derivative. We develop a weighted variational framework that accommodates asymmetric interface coupling and yields self-adjoint realizations in suitable weighted Hilbert spaces. For both problems and their adjoints, we establish discrete spectra, variational eigenvalue characterizations, and eigenfunction completeness in arbitrary spatial dimensions. We prove spectral continuity and identify limiting spectra in singular parameter regimes. We also extend Courant's nodal domain theorem to eigenfunctions that may be discontinuous across the interface. The spectral results further extend to divergence-form elliptic operators under suitable assumptions on the coefficients. These results provide a foundation for analyzing elliptic and parabolic equations with interface transmission conditions.

math.AP↗
arXiv2026

On the variety of sum of powers of certain complete intersection forms

Let $F$ be a homogeneous polynomial (form). If the annihilator ideal $F^\perp$ is a complete intersection, then $F$ is called as a complete intersection form. For many complete intersection forms, we show that its minimal apolar ideal is a complete intersection and further we show that ${\rm VSP}(F)$ is irreducible and compute its dimension.

math.AC↗
arXiv2026

Generic Mean Curvature Flow With Rough Weights

We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a generic statement is optimal in the sense that we consider weights that are too rough to have well-defined traces on every hypersurface.

math.AP↗
arXiv2026

Quantitative validation of SMBI deposition profiles on EAST using experimentally constrained simulations

Quantitative comparison between SMBI fueling simulations and experiments has long been hampered by the poor constraint on the effective source. Here, the particle increment per pulse is extracted experimentally and used to calibrate the simulation source. For EAST shot 71438, the density evolution from microwave reflectometry is analyzed for nine SMBI pulse groups. The SMBI-induced density increase is isolated from the background by comparing the rising and falling phases around each pulse group. Its radial profile peaks in the mid-pedestal region for every pulse group. Volume integration of this increment provides the experimental reference. The simulations use a multi-fluid model in the BOUT++ framework in which two transport operators are recast into conservative flux form, with the particle balance residual reduced to about 2% of the injected amount, and the perpendicular transport coefficients are constructed from the discrete radial flux balance, with the unphysical changes of the initial density and temperature profiles in source-free evolution reduced by an order of magnitude. For three cases sharing the same nominal molecular flux, the simulated deposition peak agrees with the experimental one in the relative pedestal coordinate. The simulated conversion of the injected particles at the end of the injection is slightly lower than the value inferred from the experiment, while the fraction retained at the end of the pulse is higher. The perturbation thus decays more slowly in the simulation, which we attribute to fast loss channels not represented in the model, such as parallel losses to the scrape-off layer. The edge electron temperature stays on the high-temperature plateau of the dissociation and ionization rate coefficients throughout the pulse, and the inward shift of the deposition with edge cooling reported earlier does not occur under the present conditions.

physics.plasm-ph↗
arXiv2026

Federated Art Chase: Privacy Leakage and Data Poisoning in Federated Fine-Tuning

Federated learning (FL) is increasingly used to adapt a pretrained, centrally fine-tuned model to data that remain on user devices, beyond training a model from scratch. In this report, prepared for the 4th Federated Machine Learning International Summer School, we study the privacy and integrity of this approach with a reproducible pipeline. An ImageNet-pretrained MobileNetV4-Conv-Small model is fine-tuned centrally on ten Quick, Draw! classes (97.50% test accuracy) and then adapted with head-only FedAvg over ten non-IID clients, which raises client training accuracy from 90.34% to 91.49% while preserving global accuracy. We evaluate four adversarial scenarios. First, from a single one-step client update, an honest-but-curious server recovers the complete private label set, but its reconstructions follow class prototypes rather than the private drawings (mean SSIM 0.130). Second, from a one-round FedAvg aggregate, label-count recovery falls from 87.5% with one client to 75.0% with five and ten clients, below the 80.0% of an uninformed uniform guess. Third, under FedAvg, a backdoor injected by 30%, 50%, and 100% of the clients reaches an attack success rate (ASR) of 21.9%, 31.3%, and 54.7% at a cost of at most 0.8 percentage points of clean accuracy, whereas label flipping is effective only when most of the source-class data are relabeled. Fourth, FLTrust with a root set retained from centralized fine-tuning lowers the backdoor ASR to 1.8% and 4.0% at 30% and 50% malicious clients and the label-flipping ASR from 12.6% to 0.8% without measurable clean-accuracy loss, but provides no protection when every client is malicious. The report closes with a live session in which participants draw, fine-tune, and poison the model through Indigma's FedMaestro orchestrator. Code and executed notebooks, runnable on Google Colab, are at https://github.com/Indigma-Innovations/fl-summer-school.

cs.LG↗
arXiv2026

Finite-Time Guarantees for Constrained Reinforcement Learning under Partial Observability

We study reinforcement learning in constrained partially observable Markov decision processes (CPOMDPs), where an agent maximizes reward subject to a cost constraint using only incomplete information about the underlying state. The lack of state observability may require optimal policies to depend on arbitrarily long observation-action histories, making planning and learning challenging. We leverage recent advances in finite-memory approximations of POMDPs and represent finite history windows as states of a constrained MDP. We then develop a primal--dual algorithm that provides the first non-asymptotic guarantees that jointly bound average reward suboptimality and constraint violation in the original CPOMDP. A key challenge is that this finite-window approximation affects both reward values and the set of feasible policies. Under a filter-stability assumption, we derive bounds relating optimality and feasibility in the finite-state model to those in the original CPOMDP, with approximation errors that decay geometrically with the window length. Experiments in partially observable gridworlds demonstrate the effectiveness of our approach.

cs.LG↗
arXiv2026

When Is Muon Optimal? Radial Fragility and Minimax Geometry

Muon replaces a matrix gradient by an approximate polar factor and has shown strong empirical performance in neural-network training. The Isotropic Curvature Model (ICM) provides a curvature-based explanation for this update by asking when gradient orthogonalization minimizes a one-step local-loss surrogate. We investigate the stability of this explanation when the fixed input radius of the ICM is replaced by a general radial law. We introduce the Random-Radius Isotropic Curvature Model (RR-ICM) and the Polar-Factor Admissibility Set, which encodes exact scaled-polar optimality as a geometric condition on the positive polar factor of the gradient. We derive an exact characterization of this set for arbitrary radial laws and show that all nonscalar admissible responses arise from radial atoms aligned with curvature kinks. Consequently, every atomless radial law exhibits zero-capacity rigidity: exact scaled-polar optimality is possible only when the gradient is already a scaled column isometry. To connect the curvature-based framework with the established spectral geometry of Muon, we introduce the Minimax RR-ICM by replacing directional averaging with worst-case optimization over probability laws on the sphere. We prove that every nonzero global minimizer lies on the polar ray of the gradient, while its scale is determined by a one-dimensional convex problem. The corresponding admissibility geometry is a positive-semidefinite trace slab, in sharp contrast to the spherical-zonoid geometry of the RR-ICM. Together, these results expose the radial fragility of average-curvature explanations and provide a new minimax variational characterization of Muon's polar direction.

stat.ML↗
arXiv2026

Rethinking Classifier-Free Guidance for TI2I Flow Matching

We study Text-and-Image-to-Image (TI2I) flow matching methods for controllable image editing. In a broader generative modeling context, Classifier-Free Guidance (CFG) is established as a key component responsible for high quality outputs. However, we argue that its role in TI2I modeling is poorly understood. Specifically, we make the surprising observation that the CFG mechanism is implicitly harmful for editing in the noisy phase of flow modeling, hindering instruction following and controllability. We propose a simple correction in the early flow steps, enabling a richer alignment-preservation tradeoff at no extra cost. The effectiveness of our approach is demonstrated on both pixel-space and latent TI2I flows.

cs.CV↗
arXiv2026

Estimators from Convex Geometries of the Simplex

We unify several geometries of the probability simplex under one principle, their generation by a potential: convex potentials produce the Bregman divergences and dually flat structures of information geometry, and the exponentially concave potentials of Pal and Wong produce the logarithmic divergences and their projectively flat structures. Each structure carries a duality between maximum entropy and minimum divergence and, with it, a projection principle for estimation: the U-estimators of Eguchi, Komori and Ohara in the first case, the λ-deformed estimators of Wong and Zhang in the second, both governed by a Pythagorean relation and reducing to maximum likelihood in the undeformed limit. We complete the picture with estimators drawn from the third connection the divergence defines, the Levi-Civita one, by minimizing geodesic distance: existence, uniqueness and influence are then controlled by curvature and diameter rather than by flatness. Along the way the Aitchison geometry appears as the logarithmic-barrier instance of the construction at its critical weight, and the symmetrization of the Pal-Wong transport cost, a smoothing of the Hilbert projective metric, is shown to lose the dual pair and to support instead a Huber-type robust center with bounded influence in a geometry of infinite diameter.

math.ST↗
arXiv2026

Minimum RISC-V: Maximum FPGA Efficiency

RISC-V processors are now widely available for FPGAs, with most FPGA vendors replacing their proprietary soft-CPU architectures with this instruction-set architecture (ISA). Although contemporary FPGAs are increasingly resource- and feature-rich, a soft processor system---including memory---often occupies a disproportionately large footprint and delivers only modest performance relative to the potential of the target device. In this work we first design a lightweight but deeply pipelined RISC-V core that can run above 700 MHz in a mid-range device and that is capable of retiring one instruction per clock under ideal conditions. We then develop and demonstrate a new optimization method that compiles the final application binary and a specialized processor instance contemporaneously. The method expands each instruction into an application-specific encoding, removes unused datapath and decode logic during synthesis, and yields cores that remain assembler-compatible with the original program while no longer being binary-compatible with a general-purpose RISC-V. We implement example designs on RV32I (base integer), RV32M (integer multiply), and RV32F (single-precision floating-point) configurations. Our optimized RISC-V is as small as 170 ALMs and closes timing at 775 MHz in an Altera Agilex-5 device. Finally, we show that these processors can be packed into a deterministic area and stepped-and-repeated continuously without material impact on performance, enabling predictable multi-core density planning.

cs.AR↗
arXiv2026

Writability and the Pathway: A Controlled Study of Knowledge Injection into Addressed Memory

Addressed conditional memory provides a local surface for post-hoc knowledge injection, but a successful write need not transfer to a new question or preserve untargeted behavior. This study combines a controlled GPT-2 comparison with production-memory experiments on Qwen3.8-Flash-Next-FP8 and DeepSeek-V4.1-Flash. Newly initialized modules attached to frozen GPT-2 are tested in a 2 x 2 design: row-only versus row-plus-projection updates, each with or without fixed module-residual anchoring. All arms reproduce 50 trained completions in each of three sampling seeds. Natural-question target-string hits average 5.3% for both row-only arms, 28.7% for unanchored projection updates, and 22.0% with anchoring, while strict answer scores remain zero. Anchoring lowers measured drift; lexical hits do not establish entity-specific retrieval. In the archived Qwen experiments, gradient writes make the designated first answer token top-ranked for 132 independently reset targets, comprising 93 new promotions and 39 already top-ranked targets. A separate matched 24-target comparison gives 13 new promotions with Adam versus two with SPSA at equal iteration counts but unequal computational procedures. An 80-row case includes saved continuations and a replay record, while reformulations bound its scope. Six DeepSeek zero-order cases yield one new target-token promotion and one regression. These results support bounded writing feasibility and separate trained expression, question-form behavior, and preservation; first-token rankings do not establish complete-answer success or universal conditions for writable memory.

cs.CL↗
arXiv2026

When Does Muon Actually Win? A Paired Data-, Time-, and Tuning-Budget Benchmark

Muon's gains in data efficiency motivate evaluating its performance under explicit data, time, and tuning budgets. On a single A100 GPU, we compare a reference single-device Muon implementation with AdamW across 17.7M- and 33.6M-parameter causal language models and 2.70M-parameter vision transformers. A common 23-candidate development budget selects configurations evaluated with five matched seeds, full validation trajectories, optimizer-step timing, and a frozen one-shot test. Muon reduces validation-loss area under the curve by 3.25--22.44\% at equal data and lowers test loss in all 20 primary pairs. In this configuration, Muon improves time-normalized loss area} by 19.68--22.31\% on vision, while AdamW is better by 3.38--6.96\% on language. The full Muon optimizer call, including auxiliary AdamW updates, consumes 56.1--69.6\% of training time, compared with 6.1--9.1\% for the AdamW baseline. Muon also has higher expected regret under restricted access to these candidate pools. These results characterize small models with reference kernels; their wall-clock ordering does not establish a ranking for larger models or optimized implementations.

cs.LG↗
arXiv2026

Finite-Frequency Boson-Number Bounds Across the Quantum Rabi Transition

We consider the quantum Rabi model, a fundamental model of quantum optics describing a two-level system coupled to a bosonic mode, including counter-rotating terms. In the limit of large separation between the two-level transition frequency and the bosonic mode frequency, the model exhibits a quantum phase transition at a critical coupling strength. Although the model is exactly solvable, simple analytic expressions for important physical quantities are generally unavailable. We derive rigorous upper and lower bounds for the ground-state energy and boson occupation number across the quantum phase transition at finite frequency ratios. Our results characterize the subcritical, critical, and supercritical regimes and establish the scaling behavior of the boson occupation near the critical point. Exact numerical diagonalization demonstrates the tightness of the derived bounds, while the resulting finite-frequency inequalities provide experimentally testable predictions for trapped-ion quantum simulators.

quant-ph↗
arXiv2026

Reducing the Cost of Qudit State Preparation by Learning a Sparse Structure for SNAP Gates

Preparing quantum states in bosonic qudits with SNAP--Displacement sequences requires both optimizing the gate parameters and deciding which Fock levels should be controlled by each SNAP gate. A fully parameterized ansatz assigns an independent phase to every Fock level in every gate, leading to a number of phases that grows steeply. This constitutes a problem for short to medium term systems as controlling many phases requires complex control pulses which are subject to increased control errors. Previous work reduced this cost by restricting the trainable phases to predefined sparse patterns, such as a diagonal or a grid, which however may not be optimal for a specific target state. In this work, we address this limitation by introducing a method that learns which phases are needed together with their values, using a differentiable mask. A sparsity penalty encourages the removal of unnecessary phases, while temperature annealing gradually turns the masks into binary decisions. We compare the proposed method with fully parameterized and predefined sparse ansatzes on Fourier and Haar-random target states. The evaluation considers both the minimum number of phases required to reach different infidelity thresholds and the overall trade-off between fidelity and phases required, measured through Pareto frontiers and hypervolume. The results show that learning the location of the phases together with their values provides competitive or improved fidelity--resource trade-offs, although the advantage depends on the target state and qudit dimension.

quant-ph↗
arXiv2026

Mobility energetic balance frames spatial configuration of cities

Urban spatial configurations emerge as the result of interactions between citizens' activities, movements and the landscape. Topography forms part of the physical settings through which mobility occurs, influencing movement energetic requirements. Using road networks, elevation data and mobility flows inferred from geolocated records, we define a simplified comparative measure of movement energy and test how it changes when the observed urban configuration is translated, rotated or rescaled within its topographic setting while mobility demand is held fixed. Across 56 cities, observed configurations consistently show lower movement energy requirements than most of the alternative configurations examined. This recurrent pattern reveals a measurable relationship between topography and urban spatial organization and is compatible with cumulative adaptation among urban structure, mobility and terrain. These findings add an energetic dimension to our understanding of how topography relates to urban spatial organization and provide an empirical basis for considering terrain-related movement requirements when evaluating future urban growth and densification.

physics.soc-ph↗
arXiv2026

Density of repelling periodic points for cubic rational maps

We prove the repelling-density conjecture for cubic rational maps over $\mathbf C_p$: for every prime $p$, the classical Julia set is the closure of the classical repelling periodic points. By Bézivin's theorem, it suffices to prove that a nonempty classical Julia set contains a classical repelling periodic point. The case $p\geq5$ follows from known results for tame maps, so we treat residue characteristics two and three. We argue by contraposition, assuming that the map has no classical repelling periodic points. Maps with potential good reduction already have empty classical Julia set. Otherwise, we conjugate the map to an explicit normalized form and analyze its coefficients. In each case, we obtain coefficient restrictions and establish a uniform bound on the spherical derivatives of all iterates. This bound implies equicontinuity on the classical projective line and hence emptiness of the classical Julia set.

math.DS↗