ISOMORPH
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Related Articles from SNS
Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism
arXiv:2606.09484v1 Announce Type: new Abstract: Large language models (LLMs) have shown impressive performance on diverse reasoning tasks, yet their capacity for structural reasoning in graphs remains unclear. We investigate whether LLMs can genuinely understand graph isomorphism -a fundamental problem in graph theory. While LLMs achieve near-perfect accuracy on isomorphism detection, we show this performance is illusory.
Awareness of Technological Isomorphism: Integrating AI into Elementary Mathematics Teaching on Data and Prediction,A Case Study of the Compound Line Graph
new Abstract: The deep integration of Artificial Intelligence (AI) into elementary mathematics education necessitates a conceptual tool capable of explaining students' cognitive transition from disciplinary knowledge to AI understanding. This study proposes a novel core concept, "Awareness of Technological Isomorphism, " defined as a student's metacognitive realization that their own mathematical cognitive operations (e.g., observing trends, inducing patterns, and making predictions) share...
ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks
arXiv:2605.12768v2 Announce Type: replace-cross Abstract: Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with interpretable, user-configurable parameters and modular topology, demand, and control rules. The simulator advances a directed routing graph in discrete time: demand is served from inventory or recorded as...
Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits
arXiv:2512.14338v3 Announce Type: replace Abstract: Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show they can infer the full isomorphism class of a graph from a small random sample. Our results reveal that: (i) graph isomorphism classes can be represented within a three-dimensional invariant subspace,...
Efficiently Listing Projected Trees, and Equivalence of Listing and Enumeration
new Abstract: The subgraph isomorphism problem and its generalizations such as conjunctive queries, where some nodes are projected, are among the most fundamental problems in graph algorithms and database theory. In this paper, we study the listing and enumeration variants of these problems and present two main results. (1) We present the first algorithms for enumerating projected trees with polynomial preprocessing time ($\widetilde{O}(n^{17.42})$) and polylogarithmic delay...
Cohomology of Finite Element Stokes Complexes on Alfeld Splits
arXiv:2605.31348v1 Announce Type: new Abstract: We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzm\'{a}n, & Neilan (2020, Math. Comp., 89, 1059--1091) is isomorphic to the cohomologies of the continuous Stokes and de Rham complexes. We also construct novel "minimal" conforming finite element complexes where the $H^1$-conforming space is the lowest-order space from Guzm\'{a}n & Neilan (2018, SIAM J....
The Topological Dual of a Dataset: A Logic-to-Topology Encoding for AlphaGeometry-Style Data
arXiv:2604.18050v2 Announce Type: replace Abstract: AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases. Recent technical reports suggest that current domain-specific languages may be isomorphic as input representations to natural language, interchanging them acts as a performance-invariant transformation, implying that...
A Drug-Target Specificity Foundation Model for Off-target Prediction, Repurposing, and Generative Design
Molecular recognition - which small molecule binds which protein, and with what selectivity - governs the efficacy, safety, and discovery of every therapeutic, yet binding specificity is still determined by experimental screening or by computational methods that first predict three-dimensional structure. Transformer softmax attention is mathematically isomorphic to the Boltzmann distribution governing molecular binding at thermal equilibrium, an identity that prescribes a single...
The NF-operator and the NF-Numbers of Simplicial Complexes
arXiv:2605.30781v1 Announce Type: cross Abstract: Let $\bigtriangleup$ be a simplicial complex and let $\delta_{\mathcal{NF}}$ denote the NF-operator. The NF-complex $\delta_{\mathcal{NF}}(\bigtriangleup)$ is defined as the Stanley--Reisner complex of the facet ideal of $\bigtriangleup$. Iterating $\delta_{\mathcal{NF}}$ gives a periodic orbit (up to isomorphism), and the smallest positive integer $t$ for which $\delta_{\mathcal{NF}}^{\,t}(\bigtriangleup)\cong \bigtriangleup$ is called the...
Can Large Language Models Generalize Procedures Across Representations?
Announce Type: replace Abstract: Large language models (LLMs) are trained and tested extensively on symbolic representations such as code and graphs, yet real-world user tasks are often specified in natural language. To what extent can LLMs generalize across these representations? Here, we approach this question by studying isomorphic tasks involving procedures represented in code, graphs, and natural language (e.g., scheduling steps in planning).