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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

At least 163 records · Page 9Linked to original sources

arXiv2026

A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization

We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human experts retain control over problem formulation and assumptions, while the model searches for proofs or contradictions, proposes candidate properties and theorems, and helps construct structures and parameters that satisfy explicit constraints, supported by numerical experiments and simple verification checks. Experts treat these outputs as raw material, further refine them, and organize the results into precise statements and rigorous proofs. We instantiate this workflow in a main case study on the connection between manifold optimization and Grover's quantum search algorithm, where the pipeline identifies invariant subspaces and explores Grover-compatible retractions. The main case study uses the corresponding Grover-compatible convergence analysis, including an $O(\sqrt{N} \log(1/\varepsilon))$ PL-based bound established in the companion mathematical work, to illustrate the refinement stage of the workflow. Prompt records and reusable templates for implementing the workflow are provided. We further include a multi-oracle case study, document representative failed and corrected routes arising from this setting, and provide a structured failure-mode analysis.

cs.HC↗

arXiv2026

Remarks on potential functions of noncompact quasi-Einstein manifolds

In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat.

math.DG↗

arXiv2026

Reflecting boundary conditions in critical loop models

In critical loop models, we call a boundary sticky if loops can attach to it, and reflecting otherwise. Using analytic bootstrap methods, we show that reflecting boundaries are characterised by one complex parameter, analogous to the boundary cosmological constant in Liouville theory. We determine disc 1-point functions, and write an explicit formula for disc 2-point functions as infinite combinations of conformal blocks. We also sketch the lattice interpretation of reflecting boundaries.

hep-th↗

arXiv2026

Towards ultra-scaled nanoelectronics using the zipper material system $Bi_2O_2Se/Bi_2SeO_5$

Two-dimensional (2D) materials could overcome the scaling bottleneck of nanoelectronics by enabling atomically thin channels, superior electrostatic control, and reduced short-channel effects. However, progress is limited by the lack of semiconductor–insulator interfaces being simultaneously scalable, stable, and reliable. Conventional 2D interfaces are often low quality or require transferring dissimilar materials, limiting reproducibility and scalability. We show that the zipper heterostructure formed by the high-mobility 2D semiconductor Bi 2 O 2 Se and its native high- κ oxide Bi 2 SeO 5 addresses these challenges, providing an atomically sharp, chemically matched interface with excellent electrostatics and promising scaling potential. We further present the first comprehensive multiscale assessment of Bi 2 O 2 Se/Bi 2 SeO 5 transistors targeting thermal stability, reliability, and scalability by linking atomic-scale structure and defects to device-level behavior across four transistor generations (top-gated, fin, and two gate-all-around architectures). Benchmarking against IRDS-2035 targets indicates that Bi 2 O 2 Se/Bi 2 SeO 5 devices could deliver high drive current with low gate leakage under aggressive scaling, potentially surpassing the targets in the upper-bound region of the sensitivity analysis. Finally, we identify oxygen-related oxide defects as the dominant origin of hysteresis consistent with a beneficial role of encapsulation and oxygen-rich annealing. Together, our findings support the potential of this zipper material system as a technologically-credible and manufacturing-relevant platform for future nanoelectronics.

cond-mat.mtrl-sci↗

arXiv2026

Numerical Semigroups of Sally Type II

In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $ν\ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We also construct a minimal resolution for another special class of such semigroups of type $ν-1$. Finally, we propose some conjectures for the Betti numbers of families of non-symmetric Sally type semigroups in the above cases in relation to those of the corresponding Gorenstein cases of Sally type semigroups.

math.AC↗

arXiv2026

Logarithmic Cartier Transform

We generalize the Cartier transform of Ogus and Vologodsky to log smooth schemes. More precisely, we generalize a local version of this transform, due to Shiho, and a topos-theoretic version, due to Oyama. Let $k$ be a perfect field of positive characteristic $p$ and equip $\operatorname{Spec}k$ with the trivial log structure. For a log smooth morphism of logarithmic schemes $X \rightarrow S,$ where $S$ is log flat and locally of finite type over $\operatorname{Spec}k,$ we obtain, under the assumption that the exact relative Frobenius lifts over the Witt vectors of $k,$ a fully faithful functor from the category of quasi-coherent modules on the base change $X'=X\times_{S,F_S}S$ of $X$ by the Frobenius $F_S$ of $S,$ equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on $X$ equipped with a quasi-nilpotent integrable connection. In another direction, we construct crystalline-like topoi and subcategories of crystals $\mathcal{C}'$ and $\underline{\mathcal{C}},$ equivalent respectively to modules with Higgs fields and integrable connections, and a fully faithful functor $\mathcal{C}' \rightarrow \underline{\mathcal{C}}.$ Since the Frobenius morphism is not, in general, flat in the log smooth setting, it is not clear that these functors are essentially surjective. To address this issue, we refine the topoi and crystals mentioned above by endowing them with an indexed structure, inspired by Lorenzon's extension of Cartier descent to smooth logarithmic schemes. Using the Azumaya property of the ring of logarithmic differential operators, we then obtain an equivalence between the corresponding categories of indexed crystals, thereby generalizing the Cartier transform.

math.AG↗

arXiv2026

A no-go theorem for irreversibility in arbitrary realizations of the collapse dynamics

We study finite dimensional quantum systems with arbitrary collapse events, establishing a structural no-go for operational irreversibility along arbitrary realizations of the collapse dynamics. More precisely, we prove that, for every choice of a physically admissible trajectory (i.e., collapse outcomes having nonzero Born weight) assigned to each state, there exists a nonempty topologically closed subset of the projective state space within which any two states can be connected with arbitrarily fine Fubini-Study precision and arbitrarily small integrated energetic cost. This shows that the preservation of information along observed realizations of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure.

math-ph↗

arXiv2026

An abstract framework for a class of nonlocal structured population models: existence, uniqueness and stability of steady states

This paper is concerned with the study of a class of nonlinear nonlocal functional evolution problems defined in an abstract Banach algebra. We introduce an abstract functional setting that encompasses a wide range of structured population models appearing in biomathematical literature. Within this framework, we analyze the well-posedness of the Cauchy problem and the existence of stationary solutions in the positive cone of the Banach algebra. By reviewing a large number of approaches, we also derive conditions for the local and global stability of these stationary solutions. Additionally, we explore the limits of these conditions by exhibiting explicit counterexamples. In particular, for mutation--selection models with symmetric mutation operators, we uncover both sufficient conditions for existence, uniqueness and stability, and counterexamples to existence or stability.

math.AP↗

arXiv2026

Dropout Neural Network Training Viewed from a Percolation Perspective

In this work, we investigate the existence and effect of percolation in training deep Neural Networks (NNs) with dropout. Dropout methods are regularisation techniques for training NNs, first introduced by G. Hinton et al. (2012). These methods temporarily remove connections in the NN, randomly at each stage of training, and update the remaining subnetwork with Stochastic Gradient Descent (SGD). The process of removing connections from a network at random is similar to percolation, a paradigm model of statistical physics. If dropout were to remove enough connections such that there is no path between the input and output of the NN, then the NN could not make predictions informed by the data. We study new percolation models that mimic dropout in NNs and characterise the relationship between network topology and this path problem. The theory shows the existence of a percolative effect in dropout. We also show that this percolative effect can cause a breakdown when training NNs without biases with dropout; and we argue heuristically that this breakdown extends to NNs with biases.

cs.LG↗

arXiv2026

Quantum fields in a cold atomic simulator: relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed phase-locking behaviour that contrasts with predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the longitudinal harmonic trap, and that the additional degrees of freedom observed in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are accounting for 3D corrections and modelling the effect of the boundaries.

cond-mat.quant-gas↗

arXiv2026

Fixed-Income Pricing and the Replication of Liabilities

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. The absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve reproducing all observed prices. Linear programming duality then identifies the least-cost super-replication price with the largest value that any admissible discount curve assigns to the liability, so that the resulting bounds are attained and cannot be improved. Complementary slackness confines over-replication to dates that the optimal discount vector prices at zero, and a least-cost portfolio matches the liability exactly at no fewer dates than the rank of the cash-flow matrix. We also obtain generic uniqueness of that portfolio, an interpolation between quadratic hedging and super-replication, and a static treatment of swap--repo strategies. On US Treasury cross-sections the observed prices violate the law of one price, so that a discount curve must be estimated rather than bootstrapped; the least-cost portfolio then matches an annuity liability at almost every cash-flow date.

q-fin.MF↗

arXiv2026

Supersolid crystals of dipolar excitons in a lattice

In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For example, supersolids combine density order that manifests as symmetry-breaking spatial arrangement, and frictionless superfluid flow. However, supersolids have proven to only exist under very stringent conditions, with evidence limited to a few spontaneously fragmented superfluids observed in the weakly-interacting regime. Here, we demonstrate a framework to realize crystalline supersolids in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We show that dipolar excitons realize this lattice model. At fractional lattice fillings of one quarter, one third and one half we observe mesoscopic quantum crystals across around 100 sites that spontaneously break the lattice translational symmetry. At the same time, coherent long-range hopping induces off-diagonal long-range order such that the exciton solids are superfluids. Our numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian.

cond-mat.quant-gas↗

arXiv2026

Spatiotemporal topological phase transitions in photonic spacetime crystals

Topological phase transitions have played a central role in topological physics. However, such transitions have so far been restricted to spatial or temporal crystals. Here, we transcend this conventional framework and report, for the first time, spatiotemporal topological phase transitions in photonic spacetime crystals - structures that are periodically modulated in both space and time. In a genuine photonic spacetime crystal composed of a dynamically modulated transmission-line metamaterial, we theoretically propose and experimentally demonstrate complete spatiotemporal topological phase transitions, characterized by the closing and reopening of both energy and momentum band gaps, along with changes in spatiotemporal topological invariants and topological phases. Furthermore, we directly observe a spatiotemporal, topologically localized state that exhibits causality-governed excitation and robustness to spatiotemporal disorders. Our findings reveal the interplay among space, time, and topology, establishing a unified framework that provides a comprehensive picture of the emerging topological spacetime physics and opening new avenues for robust spatiotemporal topological wave manipulations.

physics.optics↗

arXiv2026

QuantumSavory: symbolic modeling and multi-backend simulation of quantum computing and networking systems

Progress in quantum computing and networking depends on codesign across abstraction layers: device-level noise and heterogeneous hardware, algorithmic structure, and distributed classical control. We present QuantumSavory, an open-source toolkit built to make such end-to-end studies practical by cleanly separating a symbolic computer-algebra frontend from interchangeable numerical simulation backends. States, operations, measurements, and protocol logic are expressed in a backend-agnostic symbolic language; the same model can be executed across multiple backends (e.g., stabilizer, wavefunction, phase-space), enabling rapid exploration of accuracy-performance tradeoffs without rewriting the model. Furthermore, new custom backends can be added via a small, well-defined interface that immediately reuses existing models and protocols. QuantumSavory also addresses the classical-quantum interaction inherent to LOCC protocols via discrete-event execution and a tag/query system for coordination. Tags attach structured classical metadata to quantum registers and message buffers, and queries retrieve, filter, or wait on matching metadata by wildcards or arbitrary predicates. This yields a data-driven control plane where protocol components coordinate by publishing and consuming semantic facts (e.g., resource availability, pairing relationships, protocol outcomes) rather than by maintaining rigid object graphs or bespoke message plumbing, improving composability and reuse as models grow. Our toolkit is also not limited to qubits and Bell pairs; rather, any networking dynamics of any quantum system under any type of multipartite entanglement can be tackled. Lastly, QuantumSavory ships reusable libraries of standard states, circuits, and protocol building blocks with consistent interfaces, enabling full-stack examples to be assembled, modified, and compared with minimal glue code.

quant-ph↗

arXiv2026

High-Resolution Sensing via Quantum States Discrimination

High-resolution sensing plays a significant role in scientific research and industrial production, but the practical implementation is constrained by the physical mechanisms of the sensors. To address the critical limitation, we propose a high-resolution sensing approach based on quantum state discrimination. Distinct from conventional strategies, the proposed approach constructs measurement operators in the orthogonal complement space rather than eigenspace of the eigenstate, thereby notably improving the discriminability among quantum states. Moreover, the experimental results via an optical microcavity demonstrate a potential sensing resolution of 4 $\times$ 10\textsuperscript{-6} \degree C and 18 p$ε$ respectively for temperature and strain, and further verify the feasibility of simultaneous sensing of the two parameters. This work establishs a universal approach for high-resolution sensing, and may be extended to different sensing platforms across various application scenarios.

physics.optics↗

arXiv2026

YolovN-CBi: A Lightweight and Efficient Architecture for Real-Time Detection of Small UAVs

Unmanned Aerial Vehicles, commonly known as, drones pose increasing risks in civilian and defense settings, demanding accurate and real-time drone detection systems. However, detecting drones is challenging because of their small size, rapid movement, and low visual contrast. A modified architecture of YolovN called the YolovN-CBi is proposed that incorporates the Convolutional Block Attention Module (CBAM) and the Bidirectional Feature Pyramid Network (BiFPN) to improve sensitivity to small object detections. A curated training dataset consisting of 28K images is created with various flying objects and a local test dataset is collected with 2500 images consisting of very small drone objects. The proposed architecture is evaluated on four benchmark datasets, along with the local test dataset. The baseline Yolov5 and the proposed Yolov5-CBi architecture outperform newer Yolo versions, including Yolov8 and Yolov12, in the speed-accuracy trade-off for small object detection. Four other variants of the proposed CBi architecture are also proposed and evaluated, which vary in the placement and usage of CBAM and BiFPN. These variants are further distilled using knowledge distillation techniques for edge deployment, using a Yolov5m-CBi teacher and a Yolov5n-CBi student. The distilled model achieved a mA@P0.5:0.9 of 0.6573, representing a 6.51% improvement over the teacher's score of 0.6171, highlighting the effectiveness of the distillation process. The distilled model is 82.9% faster than the baseline model, making it more suitable for real-time drone detection. These findings highlight the effectiveness of the proposed CBi architecture, together with the distilled lightweight models in advancing efficient and accurate real-time detection of small UAVs.

cs.CV↗

arXiv2026

The fifth algebraic transfer in generic degrees and validation of a localized Kameko's conjecture

This paper develops our previous works concerning the classical Peterson hit problem for the polynomial algebra on five variables over the mod--2 Steenrod algebra $\mathscr A$ in a generic family of degrees, together with applications to the fifth Singer algebraic transfer and a localized variation of Kameko's conjecture. As a topological illustration of the usefulness of the Steenrod algebra, we prove that $\mathbb{C}P^4/\mathbb{C}P^2$ and $\mathbb{S}^6\vee \mathbb{S}^8$ are not homotopy equivalent by showing that their mod--2 cohomologies are not isomorphic as $\mathscr A$-modules, and we further determine the homotopy type of the quotient $\mathbb{C}P^n/\mathbb{C}P^{\,n-2}$ for all $n\ge 3$. For the generic degrees under consideration, we determine the relevant cohit spaces and describe the associated $GL(5,\mathbb F_2)$-module structure. As a consequence, the fifth algebraic transfer is an isomorphism in an explicit infinite family of internal degrees. These results were independently verified by implementations in \texttt{SageMath} and \texttt{OSCAR}. We also study a localized form of Kameko's conjecture concerning the dimensions of the indecomposables $\mathbb F_2\otimes_{\mathscr A}\mathbb F_2[x_1,\ldots,x_m]$ relative to parameter vectors, and prove that this conjecture holds for all $m\ge 1$ in certain degrees.

math.AT↗

arXiv2026

Slot-ID: Identity-Preserving Video Generation from Reference Videos via Slot-Based Temporal Identity Encoding

Human identity-preserving text-to-video generation remains challenging under large changes in viewpoint, facial expression, illumination, and motion. Existing methods condition the generator on a single reference portrait, but a static image cannot capture how identity-bearing cues evolve across views and expressions, leading to face deformation, pose locking, identity drift, or over-smoothed faces. We observe that a short reference clip naturally provides richer temporal and multi-view identity cues than any single image, motivating a video-referential formulation. This richer signal, however, introduces a new challenge: identity evidence is distributed across many frames and must be distilled into a compact, stable representation under a limited token budget. To this end, we propose Slot-ID, a lightweight identity-conditioning framework built on a frozen text-to-video backbone. Slot-ID employs a slot-based temporal identity encoder with Sinkhorn-routed iterative reading to distill a compact, stable set of identity tokens from the reference clip, complemented by an image-anchor stream for dual-source conditioning. Extensive experiments demonstrate that Slot-ID outperforms state-of-the-art methods in identity preservation and visual naturalness while remaining competitive in prompt following, with particularly large gains under challenging pose, expression, and motion variations.

cs.CV↗