Semantic Substrate Dynamics Theory (SSDT) proposes an operator‑theoretic framework that unifies various signals of semantic drift—such as embedding displacement, neighbor change, distributional divergence, and recursive trajectory instability—by treating them as observables of a time‑indexed substrate that couples embedding geometry to a local diffusion kernel. The theory distinguishes between within‑basin churn, basin crossing, recursion‑induced instability, and intervention‑order effects, using coarse Ricci curvature as a dense descriptor of basin and bridge geometry and bridge mass as a sparse node‑level indicator of genuine bridge structure. For recursive generation, SSDT decomposes node displacement into radial and tangential components, separating bounded departure from ongoing reinterpretation, and predicts future rewiring through a local density statistic rather than curvature aggregates.
arXiv:2606. 32022v1 Announce Type: new Abstract: Residual-stream analysis asks how language-model computation evolves across depth, but intermediate decoding requires comparable readout coordinates across layers.
arXiv:2610.16534v1 Announce Type: new Abstract: Deployed models can fail silently as the world they describe evolves. Attribution drift has served as an early warning in tabular data; we ask whether,...
The paper introduces a workflow that ranks competing geological interpretations by converting them into spatial priors and assessing their consistency with hydraulic‑head observations. Using a text‑to‑image model to generate 1600 geologic images per interpretation, a variational autoencoder encodes them, and a supervised inverse network maps head data into this latent space, producing log‑conductivity fields for flow simulation. The method is validated on a synthetic Johansen Formation benchmark and applied to two conceptual models of the Culebra Dolomite, yielding compatibility scores that align with independent evidence.
arXiv:2608. 08689v1 Announce Type: new Abstract: The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error.
The paper introduces a physics‑refined framework for spatiotemporal forecasting on open‑boundary hydrologic graphs, addressing instability caused by missing external boundary forcing. It learns ghost node proxies to approximate unobserved inputs and applies two physics refiners: one enforcing local consistency with two‑hop neighbors, and another using a physics‑guided graph neural operator to reduce long‑horizon drift. Experiments on two real‑world hydrologic graphs show improved prediction accuracy and stability compared to existing learning‑based and physics‑informed models.
arXiv:2607. 17146v1 Announce Type: cross Abstract: We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle $\calE = \calM \times \R^d$.
The paper studies generative flows that sample from an unnormalized target by training a flow to satisfy a balance condition. It shows that the training loss can certify sampler accuracy, can be driven to zero, and quantifies how fast gradient descent converges, with explicit bounds depending on the backward policy and graph structure. The authors provide theoretical guarantees, test them on finite graphs, and certify each theorem using a Lean 4 development.
arXiv:2606. 03067v1 Announce Type: cross Abstract: A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior.
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
arXiv:2607. 24425v1 Announce Type: new Abstract: Large language models place structured concepts on geometrically faithful manifolds: weekdays lie on a circle, months on another, usually taken to be a fixed world-model the network stores and looks up.
Autoregressive modelling, successful in language tasks, is applied to mineral‑exploration drillholes where lithology is revealed sequentially from shallow to deep. The authors introduce DrillBench, a benchmark of 49,671 Western Australian drillholes for next‑layer prediction and autoregressive stratigraphic generation across a graded transfer spectrum. Experiments show that spatial conditioning helps locally but fails under strong shift, while autoregressive models transfer more robustly; a backbone‑agnostic recipe combining large‑scale pretraining and spatial retrieval improves generalisation, especially in distant geological splits.
arXiv:2607. 12616v1 Announce Type: new Abstract: Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields.