Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
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Scale-Free Networks: Complex Webs in Nature and Technology
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Protocol learns k-local Lindbladians to ε accuracy with Õ(n^{2k}/ε²) samples and projects to valid generators; improves to log n under sparsity assumptions.
Stochastic inflation emerges as GKLS open-system dynamics from tracing entangled modes entering a coarse-grained de Sitter patch, reproducing the classical phase-space Fokker-Planck equation.
Horizon-free pure-DP algorithm achieves optimal gap-dependent regret bound 1000*(log K/Δ_min + log K/ε) for stochastic online learning with K actions.
A closed-form matrix regularization parameter for ℓ1-regularized Gaussian MLE, obtained by fixing reselection probability of nonzero entries, matches CV accuracy and support recovery at far lower cost.
A framework for optimal posterior e-values with non-convex composite hypotheses, demonstrated via statistical tests for multiple voting systems including the first treatment of Schulze.
A coherence law based on the readout-visible aligned coherence rate (a Rayleigh quotient of the noise generator) predicts gradient survival in noisy U(1)-equivariant QNNs, with simulations confirming R²=0.979 and a special channel test showing no loss where predicted.
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
First integrated spiking controller combining bipedal locomotion and arm control on a full-scale humanoid via NEF, SPA, and basal ganglia, validated in Nengo-Isaac Sim co-simulation.
DeepPolaron ML-MD simulations show rutile electrons form Ti-localized polarons hopping along [001] with 39 meV barrier and 4.4e-2 cm2/Vs mobility, while anatase holes form O-localized polarons hopping to second neighbors with 139 meV barrier and 1.4e-3 cm2/Vs mobility.
Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].
Presents a quantum soft PCA framework with Fermi-Dirac filter for principal subspace scoring without eigenvector recovery, claiming dimension-independent sample complexity O(η^{-2}).
Gradient Transformer learns to map TinyLM update vectors to LLM update vectors for data-free knowledge distillation using correlations from shadow datasets.
Training-language dominance, not English inherent properties, determines brain-LLM alignment across English, Chinese, and French, with additional independent effects from typological distance concentrated in syntactic brain regions.
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
Introduces De Simone laws over Kleisli categories that guarantee compositionality of coalgebraic trace equivalence and recovers the classical De Simone format while adding a probabilistic variant.
Aggregation mechanisms for surjective classifications are nearly dictatorial with high probability unless functions are nearly constant, with a full characterization of always-surjective mechanisms.
Derives covariant quadratic expansion in extrinsic curvature of the nonlocal effective action for a massless scalar field on manifolds with boundary, extending Monge-patch results to general surfaces.
The paper presents randomized tests with explicit query bounds for properties including number of leaves, maximum degree, typical distance, and diameter in tree-structured graphical models.
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
Bayesian PLSs are special cases of non-stationary affine PIMs which are proven calibrated, and affine tracing automates construction of probabilistic iterative methods from classical code.
Moonflowers yield near-optimal extremal bounds and improve code sparsification support from polylog(n) to O(k log n / eps^2 * poly(log(k/eps), log log n)).
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
SGD, approximations of Newton's method, natural gradient descent, and Adam are proven compatible with evolutionary dynamics when augmented with DLS noise, turning them into valid in silico simulations of asexual Darwinian evolution.
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Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime
Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
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Robust Structure Learning of $k$-local Lindbladians
Protocol learns k-local Lindbladians to ε accuracy with Õ(n^{2k}/ε²) samples and projects to valid generators; improves to log n under sparsity assumptions.
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Quantum Stochastic Inflation
Stochastic inflation emerges as GKLS open-system dynamics from tracing entangled modes entering a coarse-grained de Sitter patch, reproducing the classical phase-space Fokker-Planck equation.
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Optimal Gap-Dependent Regret for Private Stochastic Decision-Theoretic Online Learning
Horizon-free pure-DP algorithm achieves optimal gap-dependent regret bound 1000*(log K/Δ_min + log K/ε) for stochastic online learning with K actions.
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The Regularization Parameter: Sparse Precision Matrix Estimation
A closed-form matrix regularization parameter for ℓ1-regularized Gaussian MLE, obtained by fixing reselection probability of nonzero entries, matches CV accuracy and support recovery at far lower cost.
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Optimal Posterior E-values with Non-Convex Parameter Sets with Applications to Voting Systems
A framework for optimal posterior e-values with non-convex composite hypotheses, demonstrated via statistical tests for multiple voting systems including the first treatment of Schulze.
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A Coherence Law for Trainability in Noisy Equivariant Quantum Neural Networks
A coherence law based on the readout-visible aligned coherence rate (a Rayleigh quotient of the noise generator) predicts gradient survival in noisy U(1)-equivariant QNNs, with simulations confirming R²=0.979 and a special channel test showing no loss where predicted.
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A First-Order Mean Field Control Analysis of Transformer Layers under Cross-Entropy Training
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
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A Spiking Neural Architecture for Coordinating Arm and Locomotor Control
First integrated spiking controller combining bipedal locomotion and arm control on a full-scale humanoid via NEF, SPA, and basal ganglia, validated in Nengo-Isaac Sim co-simulation.
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Polaron Transport in TiO$_{2}$ from Machine Learning Molecular Dynamics
DeepPolaron ML-MD simulations show rutile electrons form Ti-localized polarons hopping along [001] with 39 meV barrier and 4.4e-2 cm2/Vs mobility, while anatase holes form O-localized polarons hopping to second neighbors with 139 meV barrier and 1.4e-3 cm2/Vs mobility.
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Future global stability of Maxwell-J\"uttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes
Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].
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Quantum principal component analysis without eigenvector recovery
Presents a quantum soft PCA framework with Fermi-Dirac filter for principal subspace scoring without eigenvector recovery, claiming dimension-independent sample complexity O(η^{-2}).
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Gradient Transformer: Learning to Generate Updates for LLMs
Gradient Transformer learns to map TinyLM update vectors to LLM update vectors for data-free knowledge distillation using correlations from shadow datasets.
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Brain-LLM Alignment Tracks Training Data, Not Typology
Training-language dominance, not English inherent properties, determines brain-LLM alignment across English, Chinese, and French, with additional independent effects from typological distance concentrated in syntactic brain regions.
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Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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Compositionality in Coalgebraic Trace Semantics
Introduces De Simone laws over Kleisli categories that guarantee compositionality of coalgebraic trace equivalence and recovers the classical De Simone format while adding a probabilistic variant.
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Classification aggregation: a quantitative impossibility theorem
Aggregation mechanisms for surjective classifications are nearly dictatorial with high probability unless functions are nearly constant, with a full characterization of always-surjective mechanisms.
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Covariant extrinsic curvature expansion of the nonlocal effective action for a massless scalar field on a manifold with boundary
Derives covariant quadratic expansion in extrinsic curvature of the nonlocal effective action for a massless scalar field on manifolds with boundary, extending Monge-patch results to general surfaces.
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Testing properties of trees in graphical models with covariance queries
The paper presents randomized tests with explicit query bounds for properties including number of leaves, maximum degree, typical distance, and diameter in tree-structured graphical models.
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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
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Affine Tracing: A New Paradigm for Probabilistic Linear Solvers
Bayesian PLSs are special cases of non-stationary affine PIMs which are proven calibrated, and affine tracing automates construction of probabilistic iterative methods from classical code.
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Moonflowers and efficient code sparsification
Moonflowers yield near-optimal extremal bounds and improve code sparsification support from polylog(n) to O(k log n / eps^2 * poly(log(k/eps), log log n)).
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Finite order symplectic birational self-maps on Kummer-type manifolds
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
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Direct From Darwin: Deriving Advanced Optimizers From Evolutionary First Principles
SGD, approximations of Newton's method, natural gradient descent, and Adam are proven compatible with evolutionary dynamics when augmented with DLS noise, turning them into valid in silico simulations of asexual Darwinian evolution.
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
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Betting on Bets: Anytime-Valid Tests for Stochastic Dominance
We derive powerful e-processes for sequential stochastic-dominance testing, with power-one guarantees for first- and higher-order dominance.
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Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
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Continuous Focus Groups: A Longitudinal Method for Clinical HRI in Autism Care
Continuous focus groups enable repeated dialogue with autism care professionals across robot therapy phases to integrate evolving clinical insights and serve as an ethical safeguard.
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On the Emergence of Syntax by Means of Local Interaction
A 2D neural cellular automaton spontaneously self-organizes into a Proto-CKY representation that exhibits syntactic processing capabilities for context-free grammars when trained on membership problems.
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A three-dimensional morphoelastic model for self-oscillations in polyelectrolyte hydrogel filaments
A 3D morphoelastic rod model with local Stokes hydrodynamics predicts flutter instability and self-sustained 2D or 3D oscillations in clamped elliptic hydrogel filaments under constant axial electric field, with a secondary bifurcation to large-amplitude motions.
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Self-similar solutions to the time-fractional Porous-Medium Equation
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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Edge modes in Chern-Simons theory on a strip
Chern-Simons theory on a strip yields boundary current algebras for oppositely propagating chiral bosons whose velocities follow from a bulk-boundary consistency condition and are independent of strip width.
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Saying More Than They Know: A Framework for Quantifying Epistemic-Rhetorical Miscalibration in Large Language Models
LLMs display a consistent pattern of elevated form-meaning divergence and uniform rhetorical device use in argumentative texts compared to humans, quantified by new metrics FMD, GPR, and RDDE.
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Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theory
OrbEvo uses equivariant graph transformers to learn the time evolution of TDDFT wavefunction coefficients, accurately reproducing wavefunctions, dipole moments, and absorption spectra on QM9 and MD17 molecular datasets.
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The Causal Second Law
Causal regularities in special sciences are associated with an entropy that cannot decrease from robust causes to their effects.
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Hyperbolicity analysis of the linearised 3+1 formulation in the Teleparallel Equivalent of General Relativity
The linearized 3+1 TEGR system has imaginary eigenvalues in its principal symbol but becomes strongly hyperbolic after gauge fixing isolated problematic sectors.
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First-principles simulation of spin diffusion in static solids using dynamic mean-field theory
SpinDMFT enables accurate first-principles simulations of spin diffusion in static solids, producing zero-quantum spectra that match experimental data for two test substances.
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Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
Neural ODEs reproduce 2RDM dynamics from data only when three-particle cumulant correlations are strong, mapping the validity regime of cumulant expansions.
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Vegetation pattern formation induced by local growth outpacing susceptibility to non-local competition
A novel Turing instability arises in vegetation models when local growth outpaces competitive susceptibility near the uniform equilibrium, producing stable patterns via supercritical bifurcation.
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Arrow's Impossibility Theorem as a Generalisation of Condorcet's Paradox
Arrow's Impossibility Theorem is equivalently stated in terms of contradictory preference cycles, generalized from strict to weak preferences via explicit profile constructions.
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Generalization Bounds for Quantum Learning via R\'enyi Divergences
Derives generalization bounds for quantum learning via quantum and classical Rényi divergences, with a new modified sandwich quantum Rényi divergence shown to outperform the Petz version analytically and numerically.
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A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
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Cutoff for mixtures of permuted Markov chains: reversible case
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
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Subgraph counting estimation for the $\beta$-model in sparse networks
A cycle-counting-ratio estimator for the β-model achieves minimax-optimal MSE and consistency under the weak conditions θ_max→0 and θ_t‖θ‖₁→∞, even at network densities near log n/n.
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A Technical Typology of AI Systems in Public Administration
The paper defines five AI system categories for public administration and reports that 55% of 91 recent papers leave the system type underspecified while 31% study one type but motivate with another.
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When transformers learn "impossible" languages, what do they learn?
Transformers on impossible-language variants show gradual grammatical sensitivity loss but sharp long-sentence generation failures, supporting generative deficiency as a link to non-attestation.
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Syntactic Belief Update as the Driver of Garden Path Processing Difficulty
Syntactic belief update via generalized Rényi divergence on syntactic trees predicts garden path reading times better than lexical surprisal.
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Perturbatively Corrected Linear Response Selected Configuration Interaction
LR-SCI-PT with second-order Epstein-Nesbet corrections improves static polarizabilities toward FCI limits for small molecules but preserves the parent pole structure, limiting it to static properties.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.