In a controlled experiment on modular arithmetic ($p = 9973$), varying only example ordering while holding all else constant, two fixed-ordering strategies achieve 99.5\% test accuracy by epochs 487 and 659 respectively from a training set comprising 0.3\% of the input space, well below established sample complexity lower bounds for this task under IID ordering. The IID baseline achieves 0.30\% after 5{,}000 epochs from identical data. An adversarially structured ordering suppresses learning entirely. The generalizing model reliably constructs a Fourier representation whose fundamental frequency is the Fourier dual of the ordering structure, encoding information present in no individual training example, with the same fundamental emerging across all seeds tested regardless of initialization or training set composition. We discuss implications for training efficiency, the reinterpretation of grokking, and the safety risks of a channel that evades all content-level auditing.

Disentanglementhasbeen formalized using a symmetry-centric notion for unstructured spaces, however, graphs have eluded a similarly rigorous treatment. We fill this gap with a new notionofconditional symmetryfordisentanglement, andleveragetoolsfromLie algebras toencode graph properties intosubgroups using suitable adaptations of generative models such as Variational Autoencoders.

Second, common entropy can be used to improve constraint-based methods such as PC or FCI algorithms in the small-sample regime,wherethesemethods areknowntostruggle.

We assume Satt 6=, and Sbbox 6=, meaning that for every image, we attend toatleast1location, and we haveabounding box with area greater than0.

We only prove fori as proof forj is analogous. Node identifierP Rn dp is an orthonormal matrix withn rows, and type identifier is a trainable matrix E Rbell(k) de with bell(k) rows Eγ1,...,Eγbell(k), each designated for an order-k We now letwin = [I,0], where I R(d+kdp+de) (d+kdp+de) is an identity matrix and0 R(d+kdp+de) (dT (d+kdp+de)) is a matrix filled with zeros. We now let the type identifiersEγ1,...,Eγbell(k) be radially equispaced unit vectors on any twodimensional subspace (Figure 6). For a given query indexi, let us assume there exists at least one key indexjsuch that(i,j) µ3. Therefore, with Eq. (42), we are simply duplicating each output entryFi = L With batch size 1024 on 8 RTX 3090 GPUs, fine-tuning takes 12hours.

Recent advances in machine learning (ML) has significantly shifted the paradigm in all walks of life.

However, as the number of serving tokens increases, the key-value (KV) caches occupy a lot of GPU memory, rendering the inference of large language models memory-bounded [29].

Urban environments are continuously mapped and modeled by various data collection platforms, including satellites, unmanned aerial vehicles and street cameras. The growing availability of 3D geospatial data from multiple modalities has introduced new opportunities and challenges for integrating spatial knowledge at scale, particularly in high-impact domains such as urban planning and rapid disaster management. Geospatial entity resolution is the task of identifying matching spatial objects across different datasets, often collected independently under varying conditions. Existing approaches typically rely on spatial proximity, textual metadata, or external identifiers to determine correspondence. While useful, these signals are often unavailable, unreliable, or misaligned, especially in cross-source scenarios. To address these limitations, we shift the focus to the intrinsic geometry of 3D spatial objects and present 3dSAGER (3D Spatial-Aware Geospatial Entity Resolution), an end-to-end pipeline for geospatial entity resolution over 3D objects. 3dSAGER introduces a novel, spatial-reference-independent featurization mechanism that captures intricate geometric characteristics of matching pairs, enabling robust comparison even across datasets with incompatible coordinate systems where traditional spatial methods fail. As a key component of 3dSAGER, we also propose a new lightweight and interpretable blocking method, BKAFI, that leverages a trained model to efficiently generate high-recall candidate sets. We validate 3dSAGER through extensive experiments on real-world urban datasets, demonstrating significant gains in both accuracy and efficiency over strong baselines. Our empirical study further dissects the contributions of each component, providing insights into their impact and the overall design choices.