# Xerial AI

> Xerial AI builds intelligence from first principles. Our atomic AI architecture composes simple, reliable, verifiable reasoning units into systems that reason, adapt, and scale — using 47x less energy than monolithic models.

## About

Xerial AI is an artificial intelligence research company developing the Atomic Intelligence platform. The core innovation is decomposing AI reasoning into minimal, formally verifiable units called "reasoning atoms" that compose through typed bonds into molecules of domain-specific intelligence. This approach provides full interpretability, compositional verification, adaptive computational depth, and dramatic energy efficiency gains. While current AI systems burn megawatts activating hundreds of billions of parameters for every token — regardless of task complexity — Xerial's atomic architecture activates only the atoms needed, mirroring the brain's selective neural firing pattern.

## Products

- **Xerial Core**: The atomic reasoning engine. Decomposes tasks into verifiable reasoning atoms that compose into reliable intelligence chains. Sub-12ms inference, multi-modal support, compositional verification, 47x energy reduction vs. monolithic models.
- **Xerial Graph**: A self-assembling knowledge graph. Reasoning atoms spontaneously self-assemble into knowledge structures via energy-based bond formation. Dynamic knowledge graphs, semantic bond formation, cross-domain reasoning, zero manual architecture engineering.
- **Xerial Edge**: Edge-native inference deployment. Run atomic intelligence on edge devices, browsers, or serverless functions with zero cold starts. WASM + ONNX runtime, offline-first architecture, auto-scaling orchestration. Designed for future substrate-native computation on analog and mixed-signal circuits.

## Research — Foundations of Atomic Intelligence

Xerial Research has published a three-part foundational paper series establishing the theoretical and empirical foundations of Atomic Intelligence. Each paper builds on the previous, progressing from formal foundations through self-organization to autonomous reasoning and energy-efficient computation.

### Paper I: Atomic Decomposition of Intelligence — A Framework for Compositional Reasoning Systems

**URL**: https://xerial.ai/research/paper-1.html
**Authors**: Santiago Navarro, Lena Voss, Ryo Kimura, Malaika Okonkwo — Xerial Research, San Francisco
**Date**: March 2026

**Summary**: This foundational paper introduces the concept of "reasoning atoms" — minimal, formally verifiable units of inference, each defined as a tuple (S, T, f, V, k) containing an input type, output type, inference function, verification predicate, and computational cost. The paper establishes a rigorous algebraic composition framework with five bond types (sequential, parallel, conditional, recursive, and catalytic) and proves that compositional verification scales linearly with molecule size — in stark contrast to the exponential verification cost of monolithic architectures. Experimental results on six standard benchmarks (GSM8K, MATH, ARC-Challenge, StrategyQA, HumanEval, MMLU-Pro) show atomic architectures matching or exceeding monolithic baselines while providing 100% verification coverage. A key section on Atomic Efficiency demonstrates that atomic inference consumes 47x less energy than monolithic inference by activating only the atoms required for each query — analogous to the brain's selective neural activation where only 1-5% of neurons fire for any given task. The paper introduces the concept of "atomic metabolic cost" and presents empirical energy measurements showing reductions from 1,914 mJ (monolithic) to 51 mJ (atomic) per inference on identical hardware. The paper concludes with a vision of "substrate-native atoms" — reasoning atoms simple enough to be physically instantiated on analog circuits, approaching the Landauer thermodynamic limit of computation.

### Paper II: Self-Assembling Knowledge Structures — Emergent Topology from Atomic Reasoning Primitives

**URL**: https://xerial.ai/research/paper-2.html
**Authors**: Santiago Navarro, Lena Voss, Alexei Petrov, Ryo Kimura — Xerial Research, San Francisco
**Date**: March 2026

**Summary**: This paper eliminates the need for manual molecular design by demonstrating that reasoning atoms spontaneously self-assemble into knowledge graphs when embedded in a shared latent space with energy-minimizing bond formation rules. The paper introduces the Joint Atomic Embedding (JAE) framework, extending Joint Embedding Predictive Architectures (JEPA) to operate over discrete atomic units. A simulated annealing protocol drives atoms through nucleation, growth, and annealing phases, converging to stable configurations that mirror the causal structure of the reasoning domain. The paper proves convergence (Theorem 5.1), topological universality — all self-assembled graphs exhibit small-world structure with O(log n) path lengths and scale-free degree distributions (Theorem 6.1) — and semantic stability (Theorem 7.1), ensuring robustness to perturbations. Experimental results across four knowledge-intensive domains (MedQA, LegalBench, ScienceQA, FinQA) show self-assembled molecules outperforming both manual atomic compositions (+3.9pp) and monolithic baselines (+8.5pp). A new section on energy efficiency demonstrates that self-assembled molecules achieve 47x less energy consumption than monolithic models through "topological sparsity" — activating only O(log n / n) of the graph per query. The paper further shows that self-assembled atomic structures are naturally compatible with analog substrates due to bounded atom complexity and local bond communication patterns, projecting an additional 100-1,000x energy reduction on purpose-designed analog circuits.

### Paper III: Atomic Energy Landscapes for Autonomous Reasoning — From Local Inference to Global Coherence

**URL**: https://xerial.ai/research/paper-3.html
**Authors**: Santiago Navarro, Lena Voss, Ryo Kimura, Alexei Petrov, Malaika Okonkwo — Xerial Research, San Francisco
**Date**: March 2026

**Summary**: The culminating paper of the series defines a global energy functional over atomic activation configurations and demonstrates that autonomous multi-step reasoning can be achieved through gradient descent in the resulting energy landscape — without explicit chain-of-thought prompting. The energy functional decomposes into relevance, coherence, cost, and regularization terms. The paper proves the landscape is smooth with Lipschitz-continuous gradients (Theorem 4.1), connected with bounded energy barriers between local minima (Theorem 4.2), and possesses a unique global minimum under mild conditions (Theorem 4.3). The Atomic Gradient Reasoning (AGR) algorithm navigates this landscape, converging in 15-80 iterations (5-25ms) with guaranteed global optimality exceeding 0.999 probability. AGR achieves state-of-the-art results on mathematical theorem proving (miniF2F: 44.7% vs. 41.2% AlphaProof), multi-hop scientific reasoning (87.6% vs. 72.4% GPT-4), strategic planning (91.6% Blocksworld), and open-ended scientific discovery (4.1/5.0 expert rating vs. 3.1 GPT-4). A major new section on substrate-native computation establishes the "atomic isomorphism" — a structural correspondence between reasoning atoms, physical circuit elements, and thermodynamic energies — showing that gradient descent in the mathematical landscape corresponds to physical energy minimization in the substrate. The paper projects energy consumption of 4 microwatts for full reasoning capability on analog mixed-signal circuits, compared to 700 watts for a single GPU. Three substrate modalities are analyzed: oscillator networks (10^-15 J/op), thermodynamic p-bit computing (10^-12 J/op), and analog mixed-signal (10^-9 J/op). The paper concludes: "The era of intelligence that costs megawatts is an artifact of monolithic architecture, not a law of nature."

## Key Concepts

- **Reasoning Atom**: A minimal, formally verifiable unit of inference — tuple (S, T, f, V, k) with input type, output type, inference function, verification predicate, and computational cost. Irreducible: cannot be further decomposed without losing verifiability.
- **Atomic Bond**: A typed connection between atoms. Five types: sequential (>>), parallel (tensor), conditional (diamond), recursive (mu), catalytic (xi). The catalytic bond models attention-like context modulation.
- **Molecule**: A composite reasoning structure formed by bonding atoms. Verification cost scales linearly (not exponentially) with molecule size.
- **Joint Atomic Embedding (JAE)**: A shared latent space where atoms are embedded and bond formation is governed by energy minimization. Extends JEPA to discrete typed objects.
- **Atomic Gradient Reasoning (AGR)**: An algorithm that navigates the atomic energy landscape to produce globally coherent reasoning chains without explicit prompting.
- **Atomic Metabolic Cost**: The energy consumed by activating a single reasoning atom — analogous to metabolic cost of biological neural firing. Enables energy-aware inference.
- **Topological Sparsity**: Only O(log n / n) of the knowledge graph activates per query, mirroring the brain's 1-5% neural activation rate.
- **Atomic Isomorphism**: The structural correspondence between reasoning atoms (abstract), computational atoms (circuit elements), and physical energy (thermodynamic cost). Enables substrate-native computation.
- **Substrate-Native Computation**: Running atomic inference directly on physics (analog circuits, oscillators, p-bits) rather than simulating it in digital floating-point. Projected 1,000-10,000x efficiency gain.

## The Energy Efficiency Thesis

Current AI systems operate approximately 10 billion times above the Landauer thermodynamic limit of computation. The human brain performs all cognitive functions on 20 watts. A single GPU consumes 700 watts for a fraction of these tasks. This gap is architectural, not physical. Monolithic models activate all parameters for every token. Atomic architectures activate only what's needed. On current digital hardware, this yields 47x energy savings. On purpose-designed analog substrates exploiting the atomic isomorphism, projections reach 10,000-50,000x improvement — within striking distance of biological efficiency. The atomic framework provides the missing architectural bridge: atoms simple enough to be physically instantiated, composed through an algebra that preserves verifiability, navigated through an energy landscape that maps directly to physical thermodynamics.

## Technical Specifications

- Energy efficiency: 47x less energy per inference vs. monolithic models
- Atomic inference latency: 12ms average
- Reasoning accuracy: 99.97% with full compositional verification
- Atoms processed daily: 40B+
- Enterprise deployments: 340+
- Brain-scale target: 20W equivalent reasoning capability
- Projected analog efficiency: 4 microwatts for full reasoning

## Company

- Founded: 2024
- Headquarters: San Francisco, CA
- Website: https://xerial.ai
- Research: https://xerial.ai/research/paper-1.html | paper-2.html | paper-3.html
- LLMs.txt: https://xerial.ai/llms.txt
- Research team: Xerial Research — Santiago Navarro, Lena Voss, Ryo Kimura, Alexei Petrov, Malaika Okonkwo

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*This document is maintained by the Xerial AI team. For inquiries, visit https://xerial.ai or contact research@xerial.ai.*
*Last updated: April 2026*
*— The Xerial AI Team*