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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.

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arXiv2026

Hamming Ideals and Grobner Bases for ISD-like Syndrome Decoding

We investigate an algebraic approach to the Syndrome Decoding Problem, based on a reformulation of the Hamming weight constraint and its integration with the Information Set Decoding paradigm. We begin with a systematic analysis of the Hamming variety, deriving its defining equations in terms of elementary symmetric functions. Since these equations may have high degree, we exploit convolution identities for elementary symmetric functions, together with factorizations based on Lucas' identity, to derive an equivalent formulation with auxiliary variables and equations of bounded degree. Building on this modeling, we generalize the ISD paradigm through an ISD-like decoding strategy, implemented by the GBDecode algorithm, in which only a subset of an information set is fixed. This approach reduces the size of the combinatorial search space at the cost of solving the associated multivariate nonlinear systems. To handle this algebraic component, we employ the MultiSolve algorithm, which replaces a single Grobner basis computation with a collection of computations on simpler systems, obtained by exhaustively assigning a varying number of indeterminates over the finite field. This provides a tunable balance between combinatorial search and algebraic solving. We evaluate the resulting approach experimentally on instances of the Syndrome Decoding Problem for random binary linear codes, using parameters corresponding to the NIST Security Category 1 parameter set of the Classic McEliece cryptosystem. The experiments assess the feasibility of this combinatorial-algebraic approach and provide insights into the practical behavior of Grobner basis techniques within an ISD-like decoding framework.

cs.CR↗

arXiv2026

NeuroECG: ECGFounder-Based Deep ECG Representation for EEG-Free Neurological Prognostication After Cardiac Arrest

Neurological prognostication after cardiac arrest commonly relies on electroencephalography (EEG). However, EEG demands high clinical resources. Bedside electrocardiography (ECG) is standard and low-cost. Yet, its value for predicting neurological outcomes remains underexplored. In this study, we propose NeuroECG, an ECGFounder-based deep representation framework for EEG-free auxiliary prognostication. NeuroECG adapts a pretrained ECG foundation model via task-specific fine-tuning. We implement a gradual unfreezing strategy on single-channel bedside monitoring ECG. Multiple ECG segments per patient are encoded into segment-level deep features. These embeddings are aggregated via quantile pooling (q = 0.24) and compressed using principal component analysis (PCA). Experiments on 412 ECG-available patients from the multicenter I-CARE database show that the adapted ECGFounder backbone achieves the best performance among ECG-only backbone baselines, with a test AUROC of 0.7333. We further combine the learned deep ECG representation with static clinical covariates. The proposed NeuroECG model achieves a test AUROC of 0.8077 and an AUPRC of 0.8970. These results support deep bedside ECG representations as a useful source of auxiliary prognostic information. Their integration with static clinical covariates improves prediction in an EEG-free setting. The source code is available at https://github.com/goddream66/NeuroECG

cs.LG↗

arXiv2026

Higher-order pruning of experts in mixture-of-experts language models

Mixture-of-Experts (MoE) language models suffer from large parameter counts, which create a significant memory bottleneck. Expert pruning is the most direct approach for reducing this parameter count, yet existing methods make pruning decisions for each expert independently, and assume experts' contributions are purely additive. In reality, expert usage in MoEs is inherently cooperative. We derive HOPE (Higher-Order Pruning of Experts), a second-order pruning objective which provably minimizes an upper bound on the error resulting from pruning. We show that REAP (a state-of-the-art first-order pruning method) is a special case of HOPE where interaction terms are ignored. Across three frontier MoE models (up to 122B parameters), two distinct calibration sets, and multiple benchmarks (including math, instruction following, coding, and an agentic suite), we demonstrate that HOPE produces better pruning decisions than existing methods, and its advantage is most pronounced at high pruning rates and on challenging agentic workloads. At 50% pruning, HOPE outperforms all baselines and achieves an average rank of 1.58 out of 5 methods (versus 2.42 for the next-best method, REAP), with gains of up to +6.1% on agentic coding. Over all conditions, HOPE again achieves the best average rank and surpasses every other method in the majority of head-to-head comparisons. By preserving cooperative expert structure that first-order methods ignore, HOPE enables aggressive compression with minimal degradation, particularly on complex tasks where diverse expert combinations are invoked over long sequences.

cs.LG↗

arXiv2026

Exact logical error rates for magic state cultivation

We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$-gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\text{fault}}=2$ and $d_{\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].

quant-ph↗

arXiv2026

What Do Current Systematic Generalization Tasks Miss? A Reasoning-Centered Analysis

Systematic generalization, the ability to solve novel problems by recombining known atomic elements, is central to human intelligence but difficult to study rigorously under controlled settings. Existing studies therefore rely on simplifications such as elemental composition, productivity-based tests, and action-explicit goals, which make systematic generalization easier to study but omit some essential aspects of this capability. To characterize what these simplifications miss, we adopt a reasoning-centered lens and introduce TranSGrid, a testbed that brings deductive, inductive, and abductive reasoning together within a unified task. Experiments with seven Transformer models on 4,800 TranSGrid instances show that all models perform much worse on TranSGrid than on a held-out test set: the largest model solves 79.6% of the test set, but only 55.3% of TranSGrid and 15.8% of the hardest subset. The gap remains within the training length range, showing that productivity alone is not sufficient to evaluate systematic generalization. Additionally, we reintroduce the other two simplifications into TranSGrid: one variant limits interactions among action effects to approximate elemental composition (reducing the inductive demand); the other makes goals action-explicit (reducing the abductive one). In both, solve rates return to roughly the test set level, showing that either simplification alone is enough to reduce TranSGrid to an ordinary held-out test set. Together, our results show that existing tasks reduce either or both of the inductive and abductive demands of systematic generalization, and that comprehensively measuring this capability requires a task that involves all three forms of reasoning.

cs.AI↗

arXiv2026

Electroweak balls: non-topological solitons in the Weinberg-Salam theory

We construct a new class of smooth, finite-energy solitons in the bosonic $SU(2)\times U(1)$ Weinberg-Salam theory, which we dub $electroweak$ $balls$. Their localization mechanism is analogous in spirit to that of $Q$-balls: the charged vector fields possess a harmonic time dependence while the energy-momentum tensor remains time independent. We explicitly construct both spherically symmetric electric-type solutions and axisymmetric magnetic-type solutions, and show that they form families characterized by a finite frequency interval, a mass gap, and a two-branch structure. These configurations provide electroweak counterparts of Proca-Higgs balls, with the vector-boson masses generated by the Higgs mechanism rather than introduced explicitly. The construction is not tied to the measured parameters of the Standard Model. More generally, it applies to bosonic electroweak-type sectors with different gauge couplings, Higgs self-coupling and symmetry-breaking scale, and hence potentially very different characteristic particle and soliton mass scales. For the families studied here, we do not find solutions at the measured Standard Model couplings and mass ratios.

hep-th↗

arXiv2026

Scalable Simulation of Quantum Dynamics on Topological Quantum Hardware

Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.

quant-ph↗

arXiv2026

Characteristic Functions of Parahoric Character Sheaves

We establish a Jordan decomposition formula for the characteristic functions of the character sheaves on parahoric subgroups defined in \cite{INY25}. For a sufficiently large $q$, these functions are $(-1)^{\dim G}$ times the corresponding deep level Deligne--Lusztig characters, extending \cite{Lu90} to positive depth. We also prove the orthogonality for the generalized deep level Green functions and the character sheaves functions. Moreover, we obtain an explicit expression of characteristic functions of simple character sheaves. As an application, we present a sheaf-theoretic expression to the multiplicity of the $G^{F^2}$ character restricted to $G^{F}$.

math.RT↗

arXiv2026

Uni-LaDiR: Latent Diffusion Unifies Multimodal Reasoning

Multimodal models increasingly think with different modalities such as images, 3D point clouds, and robot states, not just text. Yet each modality is still encoded into its own representation space, creating a modality-switching gap whenever reasoning moves from one modality to another. In this paper, we introduce Uni-LaDiR (Unified Latent Diffusion Reasoner), a framework that unifies different modalities into a shared latent space for multimodal reasoning. A unified encoder maps teacher reasoning steps from different modalities into latent thought tokens in a shared space, trained to extract the information needed for later reasoning steps and the final output. A diffusion reasoner, trained jointly with the encoder, generates these tokens at inference without teacher reasoning steps. Across eleven vision-language model (VLM) benchmarks and two vision-language-action (VLA) suites, Uni-LaDiR achieves relative gains over the strongest baselines of 7.3% on four mathematical and logical VLM benchmarks and 6.1% on RLBench manipulation tasks. Controlled comparisons show increasing gains as more teacher modalities are unified. These results suggest that unification improves multimodal reasoning by weaving it into a single thread, where the model predicts successive thoughts in a common representation space.

cs.LG↗

arXiv2026

Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps

In this paper, we study the multifractal analysis of Birkhoff averages for parabolic rational maps. We establish a conditional variational principle and prove the real analyticity and strict monotonicity of the Birkhoff spectrum, as well as the existence and uniqueness of the measure attaining the supremum in the conditional variational principle, on a certain region. To this end, we prove the existence and uniqueness of an expanding equilibrium measure and the real analyticity of the pressure function on a suitable domain. For parabolic systems, our approach using thermodynamic formalism provides a unified framework for establishing the conditional variational principle and investigating finer properties of the Birkhoff spectrum, including its real analyticity, strict monotonicity, and the existence and uniqueness of a measure attaining the supremum on a certain region.

math.DS↗

arXiv2026

The Last Picard Rank 1 Double--Mirror Calabi--Yau Pair?

We consider a certain pair of families of Picard rank 1 Calabi--Yau threefolds, that have appeared earlier in mathematical literature in unrelated contexts: the family $\mathcal{X}$ of degree 33 threefolds in $G(2,6)$ (constructed by Miura) and the family $\mathcal{Y}$ of arithmetically Gorenstein degree 21 threefolds in $\mathbb{P}^8$ (constructed by Schenck--Stillman--Yuan). After establishing a natural geometric correspondence between their general members, we go on to show that any pair of corresponding threefolds in these families satisfy certain classical dualities. We moreover discover that their geometries may be related by a mathematical gauged linear sigma model, using which we prove that they are derived equivalent. This settles a conjecture of Miura, who predicted the existence of non-trivial Fourier--Mukai partners to members of $\mathcal{X}$, based on a study of its mirror moduli. This conjecture was also formulated later by Gerhardus--Jockers, in a physical context. In fact, starting from the other family $\mathcal{Y}$, we conjecturally arrive at the same mirror moduli. Thus, such a pair is a new, and quite possibly the last, addition to the small list of deformation families of non-birational, double-mirror Calabi--Yau threefolds having Picard rank 1.

math.AG↗

arXiv2026

Regularity for axisymmetric Navier-Stokes with an Euler length

We prove local regularity for axisymmetric suitable weak solutions of the 3D Navier-Stokes equations, which are smooth before the terminal time $t=0$, and satisfy Type~II pointwise bounds at a vanishing length scale $\ell(t)$. We say $\ell(t)$ is an Euler length if it is non-increasing, satisfies a doubling condition, and if $\ell(t)\to0$ and $(-t)/\ell(t)^2\to0$ as $t\to0^-$. This includes power laws $\ell(t)=(-t)^γ$ with $0<γ<1/2$, and logarithmic enlargements of the parabolic length. Our main result shows that local bounds of the type $|u(\cdot,t)| \leq C\ell(t)/(-t)$ and $|\nabla^2 u(\cdot,t)|\leq C/((-t)\ell(t))$ for all $t\in (-1,0)$ imply regularity. The proof adapts the circulation and potential-vorticity argument of our earlier paper~\cite{CIV26} to ancient limits obtained from the rescaled vorticity system by zooming in. We show that the second derivative a priori assumption may be replaced by a Hölder bound on the azimuthal vorticity and a corresponding bound on its potential vorticity.

math.AP↗

arXiv2026

FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.

cs.CV↗

arXiv2026

Regularity of asymptotically axisymmetric solutions to the 3D Navier-Stokes equations with analytic forcing

OpenAI~\cite{OpenAIManuscript} has recently announced a proof of finite time singularity formation for the 3D Navier-Stokes equations, in the presence of a $C^\infty$-smooth body force. The construction in~\cite{OpenAIManuscript} has a few key features, among which we single out: (i) the angular mean of the solution satisfies specific Type II bounds which are anisotropic; (ii) the solution is exactly axisymmetric in a collapsing core region. In this paper we consider solutions of the 3D Navier-Stokes equations in the presence of a real-analytic body force, and assume that these solutions satisfy properties (i) and (ii) above. We prove that such solutions are in fact regular at the putative singular point. As a consequence, in the construction of~\cite{OpenAIManuscript}, and in any construction with properties (i) and (ii) whose force remains bounded in $C^2$ up to the singular time, the force can neither vanish identically near the singular point, nor be real analytic in the space variables, locally uniformly in time. The main idea of the proof is inspired by our earlier work~\cite{CIV26} and the companion paper~\cite{CIVEulerLength}: zooming-in at the putative singularity using the anisotropic length scales provided by the a priori bounds, we arrive at ancient limits whose PDE evolution imposes additional rigidity.

math.AP↗

arXiv2026

Wild frieze patterns over the integers

We study frieze patterns over the integers that are allowed to have wild entries. We introduce the quiddity number as a new invariant. The quiddity number is then used to classify strongly connected components of the directed graph $Γ_{2,n}(\mathbb{Z})$. Furthermore, we show that every finite simple directed graph arises as an induced subgraph of a directed graph $Γ_{2,n}(\mathbb{Z})$ for $n$ sufficiently large.

math.CO↗

arXiv2026

Just-Infinite Loops and Loop Algebras

Let $F$ be a field and let $L$ be a loop. We call $L$ just-infinite if it is infinite and every nontrivial normal subloop has finite index, and we call the possibly nonassociative loop algebra $F[L]$ just-infinite if it is infinite-dimensional and every nonzero two-sided ideal has finite codimension. We first prove that just-infiniteness of $F[L]$ always implies just-infiniteness of $L$. Next, using the Chein construction, we show for every infinite group $G$ that $M(G,2)$ is just-infinite if and only if $G$ is just-infinite, and that $F[M(G,2)]$ is just-infinite if and only if $F[G]$ is just-infinite. We extend the algebraic equivalence to the generalized Moufang doubles $M(G,*,g_0)$ whenever $G$ is infinite and nonabelian. Finally, we construct a single locally finite, residually finite, nonassociative Moufang loop $L$ for which $F[L]$ is residually finite-dimensional, locally finite-dimensional, and just-infinite over every field, and we explain why infinite nonassociative RA loops cannot be just-infinite.

math.RA↗

arXiv2026

On asymptotically and anomaly-free SU(N) chiral gauge theories for arbitrarily large N

A large catalog of asymptotically free and anomaly-free SU(N) chiral gauge theories that admit a large-N limit was constructed by Eichten, Kang, and Koh. Here we compute the global structure of their symmetry groups and tabulate the 't Hooft anomalies of the faithful symmetries, including those that are visible only in backgrounds carrying fractional flux. Most theories in the catalog contain fundamentally charged matter and support no genuine one-form electric center symmetry. However, fractional fluxes still arise from the faithful quotient and contribute to the anomaly in the same way as a two-form background for a one-form symmetry. The anomalies are computed using two methods, first with the descent procedure, and second by placing the theory on a four-torus, which supports twisted fluxes for background gauge fields. We discuss a selection of candidate IR behaviors and present a general discussion of how matching the anomalies associated with fractional flux can constrain infrared descriptions beyond the imposition of ordinary zero-form anomaly matching at the level of triangle diagrams. Based on large-N reasoning, we formulate a new proposal for the IR behavior of a pair of models, consistent with the ordinary zero-form 't Hooft anomaly matching conditions. In this case the matching condition involving fractional flux is satisfied automatically as a consequence of ordinary matching.

hep-th↗

arXiv2026

TierKV: Long-Context On-Device LLMs via Predictive Multi-Tier KV Caching

Large language models (LLMs) are moving onto mobile devices for increasingly diverse workloads over text, images, video, and audio. These applications often require long contexts, making the Key-Value (KV) cache a dominant memory bottleneck because it grows linearly with sequence length and is accessed at every decoding step. Prior work reduces KV-cache footprint through low-rank compression, token eviction, or flash offloading, but the resulting reconstruction overhead, irreversible token loss, or I/O stalls can offset the benefit of saving memory. We present TierKV, a mobile LLM inference framework built on Predictive Multi-Tier Cache Optimization (PMCO). Before decoding starts, PMCO predicts future cache demand from prefill hidden states and jointly assigns tokens to exact, low-rank, and flash-offloaded tiers under the device memory and accuracy budgets. This formulation retains access to the full context, removes the circular dependency of reactive eviction, and admits a closed-form solver that selects tier boundaries and per-layer ranks at runtime. Across eight text, vision, and audio models on three mobile SoCs, TierKV improves prefill throughput by up to 17.6x over existing mobile LLM frameworks, reduces RAM-resident KV cache by 12.5-34%, thereby enabling substantially longer contexts under the same memory budget, while incurring only minor accuracy degradation.

cs.LG↗