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In the modern language sciences, the core computational operation of syntax, 'Merge', is defined as an operation that combines two linguistic units (e.g., 'brown', 'cat') to form a categorized structure ('brown cat', a Noun Phrase). This…

Directly generating material structures with optimal properties is a long-standing goal in material design. One of the fundamental challenges lies in how to overcome the limitation of traditional generative models to efficiently explore the…

Since the beginning of information processing by electronic components, the nervous system has served as a metaphor for the organization of computational primitives. Brain-inspired computing today encompasses a class of approaches ranging…

Modern retrieval-augmented generation (RAG) systems treat vector embeddings as static, context-free artifacts: an embedding has no notion of when it was created, how trustworthy its source is, or which other embeddings depend on it. This…

Neural PDE solvers have followed the scaling trajectory of vision and language, with recent foundation models reaching billions of parameters. We argue that scale is a poor substitute for architectural inductive bias in this domain:…

The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a…

A sparse 8-layer code transformer develops dedicated neural circuitry for every Python construct tested, and that circuitry is organised by a clean computational principle rather than by semantic category. We extract neural circuits for 106…

Geometry problem solving (GPS) requires capacities of multi-modal understanding, multi-hop reasoning and theorem knowledge application. In this paper, we propose a neural-symbolic model for plane geometry problem solving (PGPS), named…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf…

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that…

Index structures are a building block of query processing and computer science in general. Since the dawn of computer technology there have been index structures. And since then, a myriad of index structures are being invented and published…

Graph-based retrieval-augmented generation (GraphRAG) exploits structured knowledge to support knowledge-intensive reasoning. However, most existing methods treat graphs as intermediate artifacts, and the few subgraph-based retrieval…

Agentic LLM frameworks that rely on prompted orchestration, where the model itself determines workflow transitions, often suffer from hallucinated routing, infinite loops, and non-reproducible execution. We introduce GraphBit, an…

Retrieval-Augmented Generation (RAG) systems critically depend on how external knowledge is segmented, structured, and retrieved. Most existing approaches either retrieve fixed-length text chunks, which fragments discourse context, or…

XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural…

Deep research agents, which synthesize information across diverse sources, are significantly constrained by the sequential nature of reasoning. This bottleneck results in high latency, poor runtime adaptability, and inefficient resource…

Deep learning dominates speech processing but relies on massive datasets, global backpropagation-guided weight updates, and produces entangled representations. Assembly Calculus (AC), which models sparse neuronal assemblies via Hebbian…

The convolution operation suffers from a limited receptive filed, while global modeling is fundamental to dense prediction tasks, such as semantic segmentation. In this paper, we apply graph convolution into the semantic segmentation task…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…