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arXiv2026

Edge codes constructed from unicyclic graphs

Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph $\mathcal{H}$. In the case that $\mathcal{H}$ is a tree, Jaramillo-Velez computed both the minimum distance and the weight distribution of the associated code. In this paper, we study edge codes associated to unicyclic graphs. Our most striking result is that computing the parameters of these codes is subtle in the case that the induced cycle has an even length because these values will depend on certain conditions regarding the length of the cycle and the size of the base field.

math.CO↗

arXiv2026

Reciprocal-Manifold Annealed KKT Flows for Constrained Optimization: Application to the Nonconvex AC Optimal Power Flow

Safety-critical optimization applications, such as real-time power system operation, maintain feasibility at every intermediate step, not merely at convergence. Existing approaches either violate constraints mid-solve (interior-point methods) or enforce feasibility through per-instant quadratic programming subproblems with cubic computational cost and unbounded worst-case execution time. We propose a continuous-time optimization framework for smooth constrained nonlinear problems that preserves feasibility throughout the optimization process without requiring projection operators, quadratic programming subproblems, or other per-iteration optimization routines. The method is built around a reciprocal multiplier manifold, which establishes an explicit relationship between inequality constraints and their associated Lagrange multipliers. By designing a continuous multiplier update law, the manifold is shown to remain forward invariant, while the resulting dynamics are equivalent to continuous-time logarithmic barrier gradient descent. The proposed framework naturally extends to multiple inequality constraints, equality constraints, nonconvex feasible sets, and infeasible initial conditions. The method is further enhanced through an augmented Uzawa flow that eliminates oscillatory transients commonly observed in classical primal-dual saddle-point dynamics. The effectiveness of the proposed approach is applied to the AC Optimal Power Flow problem of IEEE 9-bus and IEEE 57-bus systems. Numerical results show convergence to solutions within 0.4\% of the benchmark optimum while maintaining strict feasibility of all constraints. A computational complexity analysis shows that the proposed dynamics reduce the per-step computational cost from cubic to linear complexity. Finally, dynamic tracking studies under time-varying operating conditions demonstrate reliable feasibility preservation.

math.OC↗

arXiv2026

Learning Fast Monomial Orders for Gröbner Basis Computations

The efficiency of Gröbner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on static heuristics such as GrevLex, guided primarily by expert intuition. We address this gap by casting the selection of monomial orderings as a reinforcement learning problem over the space of admissible orderings. Our approach leverages domain-informed reward signals that accurately reflect the computational cost of Gröbner basis computations and admits efficient Monte Carlo estimation. Experiments on benchmark problems from systems biology and computer vision show that the resulting learned policies consistently outperform standard heuristics, yielding substantial reductions in computational cost. Moreover, we find that these policies resist distillation into simple interpretable models, providing empirical evidence that deep reinforcement learning allows the agents to exploit non-linear geometric structure beyond the scope of traditional heuristics.

cs.SC↗

arXiv2026

Unconditional $V^0_1$-independence of a certified hitting-set principle

We show that a certified formalization of the hitting-set-existence axiom of Atserias and Tzameret, instantiated on the parity-based Nisan-Wigderson compression class of Khaniki, is independent of the two-sorted theory $V^0_1$ of $\mathrm{AC}^0$-reasoning, unconditionally: $V^0_1$ proves neither it nor its negation. The same holds for the corresponding certified dual weak pigeonhole principle, whose refutation is witnessed by a single seed that certified-computes every string of the model simultaneously. The mechanism is a bounded-arithmetic transfer of Atserias-Tzameret's reduction from hitting sets to the dual weak pigeonhole principle: the amplification half of that reduction, the sole source of its NP-oracle, is unnecessary at the native stretch of the Nisan-Wigderson map, and the compression half becomes a $V^0_1$-provable implication once circuit evaluation is replaced by its certified $Σ^B_0$ unfolding. This is, to our knowledge, the first independence result for a derandomization-flavoured existence principle at the $\mathrm{AC}^0$-reasoning level, and it makes explicit the bridge between the Khaniki Nisan-Wigderson line and the Atserias-Tzameret reverse mathematics of hitting sets.

cs.CC↗

arXiv2026

ACE-Align: Attribute Causal Effect Alignment for Cultural Values under Varying Persona Granularities

Ensuring that large language models (LLMs) reflect diverse cultural values is important for globally deployed NLP systems. However, existing approaches often treat cultural groups as homogeneous and overlook within-group heterogeneity arising from intersecting demographic attributes, leading to unstable behavior under varying persona granularity. To address this gap, we propose ACE-Align (Atribute Causal Effect Alignment), a causally inspired framework based on controlled persona edits that aligns how specific demographic attributes shift different cultural values, rather than treating each culture as a homogeneous group. We evaluate ACE-Align across 14 countries spanning five continents, with personas specified by subsets of four attributes (gender, education, residence, and marital status) and granularity instantiated by the number of specified attributes. Across all persona granularities, ACE-Align consistently outperforms baselines. Moreover, in within-survey comparisons, it reduces the average Global North--South alignment gap from 3.40 to 1.11 points on WVS and from 2.53 to 0.85 points on ISSP. Code and dataset are released at https://github.com/Wells-Luo/ACE-Align.

cs.CY↗

arXiv2026

From Rigid to Adiabatic: Canonical Regularization of AC Networks via Action-Angle Variables

Traditional power system analysis relies on timescale separation and the rigid-network assumption, freezing electromagnetic transients into algebraic power-flow equations via Steinmetz's phasor theory. As grid-forming converter penetration increases, magnetic energy dynamics on transmission lines interact with converter control loops on comparable timescales, challenging this rigid-network assumption. Returning to Faraday's law of electromagnetic induction driven by rotating magnetic fields, this paper models the transmission lines' rotating magnetic fields in action-angle canonical coordinates, regularizes the rigid algebraic constraints of power-flow equations into canonical equations on adiabatic symplectic manifolds, and establishes a port-Hamiltonian standard form for AC power grids. Based on the minimal-counterexample principle and using the equal-area criterion's classical two-machine system, this paper reveals a latitudinal instability channel via Bloch-sphere coordinates: Q-V control releases voltage-amplitude freedom, shifting the stability boundary from the equatorial UEP (unstable equilibrium point) to a saddle point, thereby unifying the analytical frameworks of P-delta angle stability and Q-V voltage stability in power system analysis.

eess.SY↗

arXiv2026

Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment

Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. This paper exploits an alternative geometry. For a fixed model-specific stability certificate admitting suitable physical lifts, the small-signal stability requirement becomes an affine positive semidefinite constraint in the lifted variables, thereby defining a convex certified safe region. Instead of approximating the nonlinear instability boundary itself, we optimize a sample-wise safe radius in the original uncertainty space and certify, in the lifted space, that the entire power-flow image of the corresponding uncertainty ball is contained in the convex stability region. To this end, a componentwise Perron certificate guarantees existence, uniqueness, and Jacobian regularity of the target AC power-flow branch throughout each ball. An adjoint elimination then provides an exact affine-quadratic representation of the stability-relevant quantities, while rigorous matrix remainder bounds convert their nonlinear variation into finite robust PSD constraints. The resulting radii are certified lower bounds on the distances from empirical samples to failure and can therefore be coupled directly to the distance-based reformulation of a Wasserstein distributionally robust chance constraint, without directly approximating the instability boundary. Numerical studies demonstrate the effectiveness of the proposed framework.

cs.LG↗

arXiv2026

Modeling of Network Constraints in Large-scale Capacity Expansion Optimization of Power Grids

Capacity expansion modeling plays a critical role in optimizing the deployment of new generation, storage, and transmission, typically at national and regional levels. To support long-term planning, these models consider a large set of energy technologies and policies, along with decades of weather and demand data. Realistic capacity expansion models thus become high-dimensional optimization problems, with hundreds of millions of variables and constraints, which are challenging to solve. A common strategy to address this complexity is to omit non-linear, non-convex AC optimal power flow (ACOPF) constraints and instead use linearized power balance equations or transport formulations. While these simplifications improve tractability, they limit our understanding of how power flow and the physical properties of power networks impact investment decisions across generation, storage, and transmission infrastructure. This paper addresses this gap by extending the GenX capacity expansion model to incorporate fixed point theorem-based network constraints. These embed ACOPF-based considerations while maintaining the tractability of the planning model, nearly preserving the dimensionality of the transport formulation and incurring only modest runtime increases. This approach is much cheaper than embedding ACOPF directly, making it appropriate for large-scale capacity planning problems. We compare our approach to the original transport-based GenX model as well as a non-linear, non-convex version that incorporates the full ACOPF constraints, for a case study of the ISO New England grid.

math.OC↗

arXiv2026

Low-Power End-to-End Cochlear Implant Speech Denoising with Spiking Neural Networks

Cochlear implants (CI) restore hearing for individuals with severe to profound hearing loss. However, CI users often struggle to understand speech in noisy environments. Deep neural networks (DNN) have shown promise in enhancing speech for CI users, yet their high energy demands make them non-ideal for low-power CI processors. Spiking neural networks (SNN), on the other hand, offer comparable performance with significantly lower energy consumption. Hence, we propose a novel SNN inspired by the Deep ACE architecture that simultaneously performs speech enhancement and CI coding. Our model achieves competitive vocoded short-time objective intelligibility (VSTOI) and signal-to-noise ratio improvement (SNRi) scores compared to Deep ACE, while achieving more than a sixfold reduction in energy consumption.

cs.SD↗

arXiv2026

Enhancing Network Resilience via Graph-Based Anomaly Detection in Sovereign Functions

Sovereign network functions, e.g., routing protocols, are becoming increasingly complex and susceptible to failures arising from protocol configuration anomalies and anomalous configurations. This paper interprets the protocol configuration anomaly detection problem as detection of structural inconsistencies of connected nodes and edges in a bipartite graph that captures both physical network entities and logical protocol states. This graph structural inconsistency detector (GSID) model is proposed to solve the problem efficiently. To handle the heterogeneous nature of protocol configuration parameters, GSID employs an adaptive configuration encoder (ACE) that dynamically selects encoding strategies per parameter to preserve fine-grained numerical discrepancies. To expose the subtle inconsistencies of connected nodes and edges in the bipartite graph, GSID uses an inconsistency dynamic attention (IDA) mechanism that scores edges by drawing asymmetric attentions from both ends, rule compliance from one end and route connectivity from the other. It is demonstrated experimentally that GSID outperforms state-of-the-art baselines by threefold in F1 score and by 23.2% in accuracy. Ablation studies validate the effectiveness of both the ACE and IDA modules. Tests on unseen network scales and real-world network topologies show the superior adaptability of our GSID, compared to the baselines.

cs.NI↗

arXiv2026

Explainable Machine Learning for Broadband Adoption Disparities: Tract-Level Prediction and SHAP-Based Factor Profiling

The United States has allocated approximately $65 billion through the Infrastructure Investment and Jobs Act for broadband expansion, yet evidence-based methods for targeting these investments remain underdeveloped. This paper presents an explainable machine learning framework for profiling broadband adoption disparities at census-tract granularity across 83,359 tracts nationwide. Using 65 socioeconomic, demographic, and infrastructure features derived from the American Community Survey 2022, we train a LightGBM model under spatial five-fold cross-validation, achieving R^2 = 0.533 and Spearman rho = 0.763; state-held-out cross-validation (51 folds) confirms generalization (R^2 = 0.525). TreeSHAP analysis identifies income and education as the dominant factor group (with the engineered interaction term absorbing attribution from its constituent features), and SHAP-based clustering reveals three exploratory factor profiles: Well-Connected Moderate (~49K tracts), Affordability-Limited Severe (~21K tracts), and Rural-Elderly (~13K tracts). As a screening tool, ML-based tract selection captures 38.0% of the total adoption gap within the top 10% of tracts versus 35.2% for income-only heuristics (+2.8 pp, p < 0.002, county-block bootstrap); in regret-reduction terms, the model closes 19% of the remaining gap between income-only and oracle selection. The primary contribution is the per-tract factor decomposition: SHAP identifies which feature groups (income/education, rurality, age) are most strongly associated with each tract's predicted gap, and informs differentiated investigation. A temporal stability check, training on ACS 2017 and predicting ACS 2022 with zero survey-year overlap, confirms ranking stability (rho = 0.784, noting hyperparameters tuned on 2022 data).

cs.LG↗

arXiv2026

Locally-Guided Actor-Critic: Training a Goal-conditioned Actor with a Subgoal-aware Critic

Goal-conditioned reinforcement learning struggles with long horizons when rewards are sparse. While a planner can provide subgoals to guide a low-level policy, its use at test time may introduce practical subgoal management difficulties. An alternative paradigm utilizes a high-level planner to assist learning, while the policy remains conditioned only on the final goal, enabling planner-free deployment. Among these methods, Reinforcement Learning with Imagined Subgoals (RIS) introduces a regularization term that encourages the policy to take the same actions for the final goal as it does for an intermediate goal. This regularization, however, may lead to goal-chaining issues when intermediate goals are low-dimensional. Potential-based reward shaping (PBRS) translates plans into an additional reward while ensuring that the optimal policy remains unchanged. Yet, it can generate deceptive rewards in terminal states. We study these failure cases and first propose an alternative reward shaping method (RS) that removes these deceptive rewards at the expense of theoretical guarantees of PBRS. Similar to this RS variant, we then propose another method named Locally-Guided Actor Critic (LG-AC) that rewards the agent for reaching intermediate goals. Unlike RS, where intermediate rewards are implicit in the shaping signal, we explicitly condition a value estimator on the full sequence of intermediate goals but represent the value function as a sum of subgoal-conditioned value functions, enabling dense hindsight relabeling. We evaluate all these methods in tasks with challenging goal-chaining requirements and empirically highlight specific cases in which either action regularization or reward shaping yield low performance, while LG-AC achieves the best overall performance across tasks.

cs.LG↗

arXiv2026

Generative Models Enhanced by Sequence Labelling and Aspect-Code Switching Improve Cross-lingual Aspect-Based Sentiment Analysis

Cross-lingual aspect-based sentiment analysis (ABSA) transfers knowledge from a source language with annotated data to a target language, enabling fine-grained sentiment analysis without annotated target-language data. While monolingual ABSA has seen significant progress, cross-lingual ABSA remains underexplored, especially for complex tasks involving multiple sentiment elements like target-aspect-sentiment detection (TASD). In this paper, we propose a novel SeqLab framework that enhances cross-lingual ABSA using a sequence-to-sequence model with an auxiliary sequence-labelling task performed by the encoder, enhancing aspect term recognition and sentiment predictions. Additionally, we incorporate aspect-code switching (ACS), a translation-based technique that swaps aspect terms between source and translated sentences, generating additional training data to enhance the model's cross-lingual understanding. We evaluate our approach across eleven languages, three domains, and two backbone models, surpassing previous state-of-the-art results for the commonly studied E2E-ABSA task. Unlike most prior work that relies solely on English as the source language, we systematically assess different source-target language pairs and extend our evaluation to the more challenging, yet underexplored TASD task in cross-lingual settings. Finally, we provide a detailed error analysis highlighting key challenges and limitations.

cs.CL↗

arXiv2026

Hierarchical Agglomerative Clustering for Efficient Annual Voltage Security Assessment in Very-High RES Penetrated Power Systems

Voltage security assessment in power systems with high renewable energy source (RES) penetration requires analyzing many operating conditions to capture variability and uncertainty, but simulating a full year of operating points is computationally costly - motivating the selection of representative operating points (ROPs). Most existing methods cluster demand and generation profiles, but similarity in these profiles does not guarantee similarity in voltage behavior, since reactive power limits, voltage-control actions, and nonlinear network interactions shape voltage response in ways that cannot be inferred from power profile patterns. This paper proposes an unsupervised learning framework that selects ROPs based on the system's actual voltage response: each operating point is represented by system-wide voltage-risk indices from AC power-flow solutions, Principal Component Analysis reduces dimensionality, and Hierarchical Agglomerative Clustering with Ward linkage identifies representative voltage regimes. A comprehensive set of evaluation criteria then measures how well the selected ROPs reproduce the full year's voltage-security characteristics under normal and contingency conditions. On the IEEE Voltage Test System under very high RES penetration, the framework reduces the annual operating point set by 99.66 percent while reproducing full-year voltage behavior with 98.3 percent reconstruction accuracy in steady state and 93.4 percent in post-contingency response, outperforming existing injection-space clustering and heuristic sampling.

eess.SY↗

arXiv2026

A High-Resolution Synthetic EV Charging Dataset for Cold-Climate Distribution Grid Impact Analysis: Trondheim, Norway (2020-2030)

This data article presents a high-resolution, long-term synthetic electric-vehicle (EV) charging dataset for Trondheim, Norway, spanning February 2020 to December 2030. Empirically grounded in 14 months of historical charging logs from December 2018 to January 2020, the dataset captures session-level behavioral patterns, including delivered energy, plug-in duration, connection schedules, user categorization (private vs. shared), seasonal variations, public-holiday effects, and daily ambient temperature dependencies. To model future electrification dynamics, the synthetic generation pipeline integrates historical session records, calendar and weather features from MET Norway, annual EV-adoption growth multipliers derived from Statistics Norway (SSB) registration trajectories, a daily session-count model, a Conditional Tabular Generative Adversarial Network (CTGAN), seasonal Kernel Density Estimation (KDE), and post-generation physical charger-power feasibility correction. Under a standardized 7.2 kW AC charging constraint, the resulting medium EV-adoption scenario dataset contains 76,993 hourly charging-activity records. The hourly profile is activity-based rather than a complete continuous hourly time series; hours with no allocated EV charging energy are not included. The records provide total hourly charging energy, equivalent average charging power, active session counts, private/shared user load breakdowns, ambient temperature features, and calendar indicators. The dataset provides a validated cold-climate benchmark for distribution-grid impact assessment, transformer-loading analysis, EV charging-demand forecasting, charger-capacity planning, energy-management optimization, and the development of data-driven smart-charging control strategies.

eess.SY↗

arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗

arXiv2026

Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments

We present a combinatorial proof of Simonis type MacWilliams identity for harmonic higher weight distributions of linear codes. Furthermore, we investigate the statistical moments of the harmonic higher weight enumerators for random linear codes. Defining the enumerators via rank functions of the generator matrices of linear codes, we prove that its expectation vanishes for all non-trivial harmonic functions due to the inherent symmetry of random matrices, and we also derive an explicit, non-trivial formula for the covariance.

math.CO↗

arXiv2026

Difference equations of average entropies

Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.

math-ph↗