cs.AIJul 14, 2026

Atomic Units of X: The Compression Layer of Intelligence

Authors: Sachin Dev Duggal, Pradyumna Swarnalatha Ramanna, Alexandros Vassiliades

Organizations: SeKondBrain AI Labs, London, United Kingdom.

Abstract

This paper proposes a theoretical framework for understanding intelligence as a process of atomic compression and compositional reuse. We argue that cognitive, biological, computational, and organizational systems achieve scalable intelligence by decomposing complex phenomena into reusable atomic units that can be recombined into higher-order structures. Drawing on evidence from cognitive science, information theory, evolutionary biology, software engineering, medicine, legal reasoning, education, music, and artificial intelligence, the paper develops the concept of atomic units as fundamental compression layers that support efficiency, transfer, interpretability, and evolvability. The central contribution is the Compression Calculus, a formal framework for comparing surface-level representations with atomic representations and for describing how compression gains compound across abstraction layers. We introduce the Compounding Cascade thesis, according to which each additional layer of abstraction multiplicatively increases representational efficiency rather than merely adding incremental savings. The paper further argues that contemporary AI systems often operate at suboptimal levels of representation, relying on token-level processing or document-level retrieval rather than stable, concept-level atomic structures. In this view, large language models are best understood not as complete knowledge architectures, but as dynamic fusion engines capable of navigating, sequencing, and recombining atomic units. The framework provides a foundation for designing self-evolving knowledge systems that can discover, refine, and compose new primitives over time. By reframing intelligence as compression through compositional abstraction, the paper offers a unifying perspective on expertise, knowledge representation, explainable AI, and the future architecture of adaptive intelligent systems.

Explore similar work

CardsList
Jun 13, 2026cs.LG

A Compositional Framework for Open-ended Intelligence

Open-ended intelligence is the capacity to adapt to novel problems and environments that are substantially different from those in training. A mathematics of open-ended intelligence requires two pillars: first, a minimal set of representational primitives (e.g., states, actions) and algorithmic primitives (e.g., nearest neighbor); and second, an acquired compositional grammar for selection, recursion, and branching that produces sequences of operations and recurring motifs. We formalize open-ended intelligence in terms of the compositional closure induced by a finite primitive set PP and a set of composition operators CC. We characterize properties of the induced closure L(P,C)\mathcal{L}(P,C) that support unbounded compositional generation across families of tasks and worlds. The closure of the two pillars yields infinite adaptive responses across a wide range of settings. The mathematics supports complementary research agendas, including evaluation metrics for explanation and interpretability, and novel architectures where compositional generalization is native. We propose next primitive prediction (NPP) as a novel architectural objective, where training encourages the acquisition of reusable algorithmic primitives and their compositional grammar, such that new solutions are generated through recombination. Given such an objective, curriculum learning and self-play can enable lifelong learning, expanding the closure by discovering reusable primitives and transition motifs across settings. We ground the framework through case studies in physics, evolution, and neuroscience.
Ida Momennejad, Roberta Raileanu
IntelligenceStructural GeneralizationGenerative FrameworkClosure
AskPDF
Jun 24, 2026cs.AI

Agentic System as Compressor: Quantifying System Intelligence in Bits

Large language models are turning from isolated predictors into agentic systems: they call tools, retrieve evidence, obey environment constraints, use verifiers, and complete tasks through search and multi-turn interaction. We adopts an analytical viewpoint based on "compression is intelligence": under a fixed task distribution, interface, and compute budget, a stronger agentic system lets a target object be reconstructed with fewer bits. We operationalize the measure with arithmetic coding, seed coding, and a fallback, and evaluate it in five settings: reversed text, chess moves, protein sequences, retrieval-augmented question answering, and semantic story compression; in all of them agentic components reduce codelength. These small, controlled experiments cover component types typical of real agentic systems, show that codelength can analyze how components, observers, and budgets change residual uncertainty, and offer guidance for evaluating real agent systems.
Zihan Qin, Hongrui Zhang
Agentic SystemsCollective IntelligenceIntelligence
AskPDF
Jun 30, 2026cs.AI

Creating Intelligence: A Computational Foundation for AGI

This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing. Whereas traditional neural networks rely on continuous weights and matrix multiplication, this framework works with sparse binary data. It represents information as discrete sets, directly modeling biological neural population codes. I demonstrate that associative memory emerges naturally from network topologies featuring a combinatorially expanded hidden layer. Learning is driven by topological plasticity rather than scalar weight adjustments. This architecture unifies auto-associative and hetero-associative learning under a single core algorithm: information retrieval via subset pattern matching and exact nearest-neighbor search. Operating with constant-time complexity, these mechanisms bridge perceptual data (sparse distributed representations) and symbols (sparse holographic representations) without continuous bottlenecks. Mapping this framework to neuroanatomy, I propose that both the cerebellum and the neocortex implement variants of this algorithm, making subset pattern matching the fundamental engine of cognition. Because it relies on discrete logic rather than matrix arithmetic, this algorithm translates directly into in-memory hardware. This opens a new route toward synthetic intelligence with human-level energy efficiency.
Peter Overmann
Dense Associative MemoryNeuromorphic HardwareIntelligenceArtificial Intelligence SystemsPlasticity
AskPDF