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arXiv2026

Seeing the imagined: latent functional alignment in visual imagery decoding from fMRI data

Recent progress in visual brain decoding from fMRI has been enabled by large-scale datasets such as the Natural Scenes Dataset (NSD) and powerful diffusion-based generative models. While current pipelines are primarily optimized for perception, their performance under mental-imagery remains less well understood. In this work, we study how a state-of-the-art (SOTA) perception decoder (DynaDiff) can be adapted to reconstruct imagined content from the NSD-Imagery benchmark. We propose a latent functional alignment (LFA) approach that maps imagery-evoked activity to the pretrained model's semantic content-enriched conditioning space, by adding a simple alignment module, while keeping the original remaining components frozen. To mitigate the limited amount of matched imagery-perception supervision, we further introduce a neural retrieval-based augmentation strategy that selects semantically related NSD perception trials from the same participants. Across four subjects, LFA consistently improves high-level semantic reconstruction metrics relative to the frozen pretrained baseline and a voxel-space ridge alignment baseline, and enables above-chance decoding from multiple cortical regions. These results suggest that semantic structure learned from perception can be leveraged to stabilize and improve visual imagery decoding under out-of-distribution conditions.

q-bio.NC↗

arXiv2026

A Survey on Long-Term Memory Security in LLM Agents: Attacks, Defenses, and Governance Across the Memory Lifecycle

The emergence of writable, cross-session persistent memory in LLM agents introduces a qualitatively different threat landscape from conventional input-centric security concerns, characterized by three properties: persistence, statefulness, and propagation. To systematically characterize this landscape, we propose a Memory Lifecycle Framework that organizes attacks, defenses, and their cross-phase dependencies along two axes: six lifecycle phases (Write, Store, Retrieve, Execute, Share & Propagate, Forget & Rollback) and four security objectives (Integrity, Confidentiality, Availability, Governance). This analysis in turn exposes the need for formal security guarantees at the system level, motivating Verifiable Memory Governance (VMG), a framework of five architectural primitives that specifies what verifiable mechanisms a long-term-memory system must provide to maintain auditable, recoverable control over its memory state. Our analysis indicates that robust Long-Term Memory (LTM) security cannot be retrofitted at retrieval or execution time alone, but must be anchored in storage-time provenance, versioning, and policy-aware retention from the outset.

cs.CR↗

arXiv2026

AdaGScale: Viewpoint-Adaptive Gaussian Scaling in 3D Gaussian Splatting to Reduce Gaussian-Tile Pairs

Reducing the number of Gaussian-tile pairs is one of the most promising approaches to improve 3D Gaussian Splatting (3D-GS) rendering speed on GPUs. However, the importance difference existing among Gaussian-tile pairs has never been considered in the previous works. In this paper, we propose AdaGScale, a novel viewpoint-adaptive Gaussian scaling technique for reducing the number of Gaussian-tile pairs. AdaGScale is based on the observation that the peripheral tiles located far from Gaussian center contribute negligibly to pixel color accumulation. This suggests an opportunity for reducing the number of Gaussian-tile pairs based on color contribution. AdaGScale efficiently estimates the color contribution in the peripheral region of each Gaussian during a preprocessing stage and adaptively scales its size based on the peripheral score. As a result, Gaussians with lower importance intersect with fewer tiles during the intersection test, which improves rendering speed while maintaining image quality. The adjusted size is used only for tile intersection test, and the original size is retained during color accumulation to preserve visual fidelity. Experimental results show that AdaGScale achieves a geometric mean speedup of 13.8x over original 3D-GS on a GPU, with only about 0.5 dB degradation in PSNR on city-scale scenes.

cs.CV↗

arXiv2026

A Sequent Calculus for Non-Monotone Inductive Definitions

Inductive definitions constitute an important form of knowledge. The logic FO(ID) is an extension of classical first-order logic (FO) with a language construct to express non-monotone inductive definitions. Most existing proof systems for inductive definitions impose syntactic constraints on their definitions such as positivity and stratification, thereby excluding many useful and natural definitions. We obtain a sequent calculus SCFO(ID) for FO(ID) that supports general non-monotone inductive definitions by extending an existing sequent calculus LKID by Brotherston and Simpson, formalizing the principle of mathematical induction. To accommodate for non-monotone inductive definitions, we introduce an induction rule with an asymmetry between positive and negative occurrences of defined atoms. We establish several proof-theoretical properties of SCFO(ID) regarding its underlying first-order principles, soundness, completeness and cut-elimination.

cs.LO↗

arXiv2026

Uniform Recovery of Structured Signals from Nonlinear Observations: Improved Error Rates

Consider the recovery of structured signals from nonlinear observations. Under Gaussian matrix and a large class of unknown nonlinear link functions, Plan and Vershynin (2016) showed that generalized Lasso achieves accurate nonuniform recovery of a fixed signal. More recently, Genzel and Stollenwerk (2023) showed that generalized Lasso is indeed capable of accurately recovering all structured signals. However, in some canonical settings with discontinuous link functions, their uniform recovery error rate is essentially slower than the nonuniform one. Specifically, in the recovery of $n$-dimensional $k$-sparse vectors from $m$ measurements, generalized Lasso with a perfectly tuned $\ell_1$ constraint achieves nonuniform error rate $ O(\sqrt{k\log(en/k)/m})$, while the uniform error rate of Genzel and Stollenwerk is no faster than $O((k\log(en/k)/m)^{1/4})$. In this paper, we narrow this gap by establishing improved uniform recovery guarantees under piecewise Lipschitz link functions with well-separated jump discontinuities. We analyze a projected gradient descent (PGD) algorithm whose projection can be onto a convex set or a cone, and our results for the PGD with a convex set are also valid for the generalized Lasso. In sparse recovery, the improved uniform error rates match the nonuniform rate $O(\sqrt{k\log(en/k)/m})$ up to logarithmic factors. Under the sign link function, we further show that iterative hard thresholding (a specific instance of the PGD) achieves uniform recovery error rate $O(\sqrt{k\log(en/k)/m})$, matching the nonuniform rate up to a universal constant. Technically, the uniform guarantees for the PGD are obtained by showing that the gradient maps satisfy the restricted approximate invertibility condition uniformly over all signals. We demonstrate that this is a general approach to uniform recovery under nonlinear observations.

cs.IT↗

arXiv2026

Maximally nodal sextic surfaces and linear determinantal representations

We prove that every maximally nodal sextic surface (with 65 nodes) $X \subset \mathbb{P}_{\mathbb{C}}^3$ contains a symmetric half-even set of nodes of cardinality 35. It follows that the associated half-quadratic sheaf is the cokernel of a symmetric $6 \times 6$ matrix of linear forms, yielding a linear determinantal representation of $X$. In particular, after a suitable Serre twist, the half-quadratic sheaf is an Ulrich sheaf of rank 1. As an example, we exhibit an explicit $6 \times 6$ matrix of linear forms whose determinant defines the Barth sextic surface.

math.AG↗

arXiv2026

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th↗

arXiv2026

Convergence Rate Analysis of SOAP with Arbitrary Orthogonal Projection Matrices

In this short note, we establish, for the first time, the convergence rate of SOAP, an efficient and popular matrix-based optimizer for training deep neural networks. Our analysis extends to a more general variant of SOAP that admits arbitrary orthogonal projection matrices and requires only that these matrices be conditionally independent of the current stochastic gradient at each iteration. For example, they may be constructed from information available up to the preceding step.

math.OC↗

arXiv2026

Memory in Integrated Photonic Neural Networks: From Physical Mechanisms to Neuromorphic Architectures

The rapid scaling of artificial neural networks has exposed fundamental limitations of conventional von Neumann computing architectures. In these systems, the physical separation between memory and processing creates a bottleneck, as computational capabilities outpace the ability of memory and interconnects to supply and retrieve data. In contrast, biological neural systems inherently co-localize computation and memory through distributed, dynamical processes. Neuromorphic computing seeks to emulate this paradigm by leveraging physical substrates whose intrinsic dynamics simultaneously encode and process information. Among emerging platforms, silicon photoncis offer a compelling approach due to its high bandwidth, low-loss propagation, and inherent parallelism. This review examines the role of memory in integrated photonic neuromorphic systems, with emphasis on the physical mechanisms that provide volatile (short-term) and non-volatile (long-term) memory in silicon-on-insulator and hybrid silicon-on-insulator platforms. Drawing inspiration from digital, biological, and photonic memory architectures, we classify existing approaches based on their underlying physical principles. We cover implementations ranging from delay lines and slow-light structures to multistable dynamics and structural memory based on charge trapping and phase-change materials. We then discuss how these mechanisms support photonic neural network architectures, including feed-forward, reservoir computing, spiking and hybrid optoelectronic recurrent systems, and assess their relevance for time-dependent singal-processing tasks such as channel equalization in telecommunications. This review aims to establish a unified framework for understanding memory and learning in neuromorphic photonics and outlines key challenges and opportunities for scalable, energy-efficient neuromorphic hardware.

physics.optics↗

arXiv2026

Quantum Sufficiency for Self-Adjoint Statistical Models via Likelihood-Type Operators on Real $*$-Subalgebras and Real Jordan Algebras

We develop a theory of quantum sufficiency on real *-subalgebras and real Jordan algebras for models consisting of general self-adjoint operators, including derivatives of states. Square-root likelihood ratios and symmetric logarithmic derivatives serve as self-adjoint likelihood-type objects, allowing ordinary quantum statistical models and local models to be treated within a unified framework that admits degenerate reference states. We introduce sufficient real unital positive maps and show that their Hermitian fixed points form a real Jordan algebra admitting a sufficient Jordan conditional expectation. The real and complex *-subalgebras generated by this algebra admit sufficient real and complex completely positive conditional expectations, respectively. We characterize the minimal sufficient real *-subalgebra by the likelihood-ratio set and $ρ$-modular invariance. The minimal sufficient real Jordan algebra is generated by the likelihood-ratio set together with the operator obtained by normalizing every irreducible diagonal block of the reference state, relative to the minimal sufficient real *-subalgebra, to trace one. We also obtain Koashi-Imoto type decompositions for real *-subalgebras and real Jordan algebras admitting sufficient conditional expectations, explicitly accounting for inequivalent irreducible Jordan representations. These results separate the likelihood-ratio aspect of sufficiency from its noncommutative modular aspect and identify real Jordan structure as a natural framework for quantum statistical sufficiency.

quant-ph↗

arXiv2026

Unleashing the Agility of Wheeled-Legged Robots for High-Dynamic Reflexive Obstacle Evasion

Wheeled-legged robots combine the efficiency of rolling with the adaptability of legged locomotion, offering unique agility for dynamic environments. However, enabling rapid reflexive evasion remains challenging due to the coexistence of heterogeneous wheel-leg dynamics, hybrid locomotion modes, and non-holonomic constraints. In this work, we investigate how wheeled-legged robots can exploit their hybrid morphology for high-dynamic obstacle avoidance. We propose AWARE, a hierarchical reinforcement learning framework that decomposes avoidance into navigation-avoidance and reflexive-evasion regimes coordinated by a threat-conditioned high-level policy. By learning specialized low-level experts, AWARE autonomously discovers distinct rolling-, stepping-, and hybrid-dominated evasive behaviors, including forward lunges and lateral dodges. Simulation experiments across different reaction times and approach directions, together with real-robot evaluations on the M20 platform, demonstrate improved evasion capability and effective online transition between locomotion regimes. These results highlight the potential of exploiting hybrid wheel-leg actuation for agile and reactive mobility in dynamic environments. Paper homepage: https://aware-ral-2026.github.io/.

cs.RO↗

arXiv2026

Extracting Exact Lie Derivatives Without Backpropagation: A Dual Compiler for Neural Control Barrier Functions

A safety filter based on a neural control barrier function (CBF) deployed in an embedded control loop evaluates, at each control cycle, the trained network and its Lie derivatives along the system vector fields, under the memory and worst-case execution time (WCET) constraints that safety-oriented coding standards impose. Reverse-mode automatic differentiation, by which training frameworks obtain these derivatives, retains an activation cache whose size grows with the sum of the layer widths, and general-purpose differentiation runtimes allocate the computational graph from the heap at each call. This paper presents a compiler that evaluates a neural CBF and its exact Lie derivatives by forward-mode dual-number arithmetic. The compiler emits self-contained C++ code in which a single forward pass, without backpropagation, returns the barrier value and its exact Lie derivative along a given vector field; the drift and input Lie derivatives of the safety constraint are obtained from one such pass per vector field, and a second-order extension based on hyper-dual numbers returns the exact second-order Lie derivatives required by CBFs of relative degree two. The dual forward pass requires a workspace bounded by four times the widest layer, independent of network depth, and the emitted code contains no allocation call sites, so the absence of dynamic allocation is verifiable by inspection of the code. On an ESP32-S3 microcontroller, the compiled filter assembles the complete safety constraint in under one millisecond from statically allocated buffers of at most 768 bytes, and the maximum execution time over 1000 evaluations lies within 5% of the median in all three examples, whereas a heap-allocating reverse-mode baseline shows maxima 33% and 70% above its median in the two first-order examples. The compiler and the embedded experiments are released as open-source software.

eess.SY↗

arXiv2026

Tight Fréchet bounds for $λ$-low density curves

The Fréchet distance is a well-studied similarity measure between curves. We computing the Fréchet distance between $λ$-low-density curves, the most general of realistic curve assumptions, where every ball of radius $r$ intersects at most $λ$ edges of length at least $r$. Previous algorithms either assumed constant $λ$ or had no tight dependence on $λ$. For two $n$-vertex $λ$-low-density curves in $\mathbb{R}^d$, we give a $(1+\varepsilon)$-approximation algorithm for the continuous and discrete Fréchet distance running in $ \tilde{O}\!\left(\frac{λ^{2/d}n^{2-2/d}}{\varepsilon^2}\right) $ time. Our key insight is a tight property of simplifying $λ$-low density curves: the simplification of any $n$-vertex $λ$-low-density curve is $O(λ^{1/d}n^{1-1/d})$-low-density. We show this is tight, and this provides the structural property under simplification that was previously known for $c$-packed curves. We provide matching lower bounds for $n$ and $λ$: assuming the Orthogonal Vectors Hypothesis, for every $δ>0$, we rule out algorithms with running time $O\!\left( \left( \frac{λ^{2/d}n^{2-2/d}} {\varepsilon^{2-4/d}} \right)^{1-δ} \right). $ We extend our techniques to the map matching problem, where we also give tight bounds.

cs.CG↗

arXiv2026

Criticality of ISCOs and AdS/CFT

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $γ$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{Δ_H}$ to $γ$ in the dual CFT, and dsicuss the implications of our results.

hep-th↗

arXiv2026

A Finite-History Interpretation of the AMS-02 Positron Spectrum

I examine whether the separation between the characteristic energy scales of cosmic-ray electrons and positrons can be understood as a finite-history effect, without introducing a separate dominant source specifically to generate the high-energy positron feature. In this description the positron retains the opposite Dirac phase orientation relative to ordinary matter clocks, while local interactions and positive physical energies remain unchanged. Reduced accumulated overlap with the matter-defined Galactic environment is represented by a single, approximately shape-preserving energy rescaling. An illustrative overlap benchmark moves the broad structure of an empirical electron reference near 10 GeV into the few-hundred-GeV region. A number-conserving spatial-dilution example provides an order-of-magnitude interpretation of the relative amplitude. The comparison uses the published AMS-02 electron spectrum directly, with fixed, rounded horizontal and vertical scales rather than optimized spectral parameters. Known populations, including pulsars, may contribute subleading components in this interpretation. The resulting characteristic-scale displacement and geometrical amplitude interpretation provide a possible physical account of the positron spectral hierarchy.

hep-ph↗

arXiv2026

Rydberg states of muonic helium in quantum electrodynamics

The variational method is used to study the energy levels of muonic helium $(μ^{-} \, e^{-} \, He)$ with an electron in the ground state and a muon in an excited state with principal and orbital quantum numbers $n \sim l+1 \sim 14$. The variational wave functions are chosen in the Gaussian form. The matrix elements of the Hamiltonian in the nonrelativistic approximation, as well as corrections for the vacuum polarization and relativism, are calculated analytically. A series of energies of the Rydberg muon states is obtained, which can be studied experimentally.

hep-ph↗

arXiv2026

Exotic Spin Excitation Continuum in a Weakly Coupled Quantum Chainsaw Antiferromagnet

Collective motions in strongly interacting magnets involve many spins and are often described in terms of integer-spin excitations. However, in certain cases, the collective motion can behave as if these integer excitations break apart into smaller, particle-like entities with unusual properties. Such fractionalized excitations in quantum magnets are commonly associated either with topological order in two dimensions or with criticality in one dimension. It remains unclear how these distinct mechanisms are connected across a dimensional crossover. Here we investigate the Ti-based quantum antiferromagnet, $Cs_{8}LiNa_{3}Ti_{12}F_{48}$, in which $Ti^{3+}$ ($3d^{1}$, $S=1/2$) ions interact antiferromagnetically within distorted kagome planes. Our inelastic neutron scattering study on a single crystal reveals a frustrated network of weakly coupled spin-$1/2$ chainsaws, realizing a regime of dimensional frustration in which interchain couplings fail to establish coherent two-dimensional order. The magnetic excitation spectrum exhibits a strong continuum spanning the full measured momentum and energy phase space. In addition, the dynamic spin correlation function displays rod-like scattering in momentum space, indicating a quasi-one-dimensional nature of the magnetic correlations. These results point to fractionalized excitations with intrinsically directional character, demonstrating that signatures of one-dimensional criticality can persist within a two-dimensional lattice. Our findings establish anisotropic fractionalization as a distinct organizing principle for quantum-disordered states.

cond-mat.str-el↗

arXiv2026

Learning Dynamic Evidence Routes for Vision Transformer Probing

Probing frozen vision transformers typically uses permutation-invariant aggregation (GAP or $\texttt{[CLS]}$), treating patch tokens as an unstructured set. Content-dependent probes such as self-attention are useful accuracy controls, but they do not expose a fixed token schedule or fixed position weights for auditing. We introduce $\textbf{SSMProbe}$, an explicitly inspectable probe that replaces invariant pooling with a Sinkhorn-learned evidence route followed by a diagonal S4 decoder. The S4 decoder is a linear time-invariant (LTI) system whose final state has fixed, position-dependent coefficients, so the probe-induced routed sequence can be audited as a concrete object rather than inferred only from accuracy. Our central measurement is the geometry of routed evidence: which patch tokens are moved to influential positions by this diagnostic, whether those tokens form spatially organized regions or random-like dispersed sets, and how the fixed S4 kernel weights them. Across MAE, BEiT, DINOv2, and supervised ViT, this route geometry separates MAE's dispersed, nearly random-like routes from the more spatially organized routes of BEiT, ViT, and DINOv2, with DINOv2 retaining a distinct strong $\texttt{[CLS]}$ profile. SSMProbe uses the mathematical transparency of state-space models to turn a frozen ViT readout into an auditable evidence-routing analysis.

cs.CV↗