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We introduce compute-grounded reasoning (CGR), a design paradigm for spatial-aware research agents in which every answerable sub-problem is resolved by deterministic computation before a language model is asked to generate. Spatial Atlas…

We introduce an unsupervised approach for constructing a global reference system by learning, in the ambient space, vector fields that span the tangent spaces of an unknown data manifold. In contrast to isometric objectives, which…

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the…

Causal discovery through experimentation and intervention is fundamental to robust problem solving. It requires not just updating beliefs within a fixed framework but revising the hypothesis space itself, a capacity current AI agents lack…

We describe a novel geometric methodology for analyzing free-energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent, and provides illustrations of its unique capabilities. An atlas is a labeled…

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through…

Recent progress in spatial reasoning with Multimodal Large Language Models (MLLMs) increasingly leverages geometric priors from 3D encoders. However, most existing integration strategies remain passive: geometry is exposed as a global…

Autonomous AI is no longer a hard-to-reach concept, it enables the agents to move beyond executing tasks to independently addressing complex problems, adapting to change while handling the uncertainty of the environment. However, what makes…

There is growing evidence that independently trained AI systems come to represent the world in the same way. In other words, independently trained embeddings from text, vision, audio, and neural signals share an underlying geometry. We call…

When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…

Precision mapping of landslide inventory is crucial for hazard mitigation. Most landslides generally co-exist with other confusing geological features, and the presence of such areas can only be inferred unambiguously at a large scale. In…

Spatial reasoning in partially observable environments has often been approached through passive predictive models, yet theories of embodied cognition suggest that genuinely useful representations arise only when perception is tightly…

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

As scientific literature grows rapidly, automated survey generation has become a key capability for AI scientists and human researchers. However, existing systems suffer from limited analytical depth due to reliance on abstracts and…

Most of the current Global 21-cm experiments include ground screens that help moderate effects from the Earth. In this paper, we report on a possible systematic artifact within the ground plane that may produce broad absorption features in…

Achieving robust spatial reasoning remains a fundamental challenge for current Multimodal Foundation Models (MFMs). Existing methods either overfit statistical shortcuts via 3D grounding data or remain confined to 2D visual perception,…

Object detectors achieve strong performance under nominal imaging conditions but can fail silently when exposed to blur, noise, compression, adverse weather, or resolution changes. In safety-critical settings, it is therefore insufficient…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as…

When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? We characterize the geometry of correctness representations across 9 models from 5 architecture families. The structure is simple: the…