Scientific General Intelligence

• Scientific General Intelligence (SGI) is a mathematically principled approach to modeling open-ended AI by integrating autonomous sense-making, self-organization, and exploration.
• It leverages distributed network models and information-theoretic metrics to quantify integration, operational complexity, and emergent coordination among system components.
• SGI promotes dynamic value emergence and adaptive coordination, offering a unified framework for general-purpose AI across diverse scientific domains.

Scientific General Intelligence (SGI) denotes a foundational and mathematically principled approach to modeling, evaluating, and realizing general-purpose artificial intelligence systems capable of autonomous sense-making, problem formation, and scientific inquiry across arbitrary domains. Unlike narrow or task-specific forms of AI, SGI frameworks seek to unify learning, reasoning, exploration, and value formation within architectures that transcend pre-given goals, leveraging open-ended self-organization, information integration, and meta-adaptive processes.

1. Foundations: Definitions and Philosophical Grounding

Conventional general intelligence definitions (e.g., Legg–Hutter universal intelligence) characterize intelligence as an agent’s ability to achieve predefined goals across computable environments, operating under fixed tasks, agent–environment splits, and a priori computational resources (Weinbaum et al., 2015). SGI reframes intelligence as an open-ended, process-centric phenomenon, emphasizing the individuation of agents, goals, and values through self-organization and distributed sense-making.

Open-Ended Intelligence (OEI) is explicitly formulated as the iterative process by which primitive elements self-organize, form boundaries, generate new distinctions, and instantiate higher-level identities and capacities without foreknowledge of tasks or external evaluators. The philosophical grounding draws on Simondon’s individuation theory (systems emerge from metastable fields) and Deleuze’s transcendental empiricism, rejecting static agent–task dichotomies and putting the emergence of coordination and values at the heart of intelligence.

Formally, OEI is quantified as the emergence of integration (cohesion among subcomponents) and operational complexity (differentiation of functional roles), shifting the locus of “intelligence” from task performance to the meta-process of progressive, recursive sense-making (Weinbaum et al., 2015).

2. Formal Models and Measures

Mathematical formalizations of SGI integrate information-theoretic and process-theoretic approaches:

• Distributed Self-Organizing Network Model: SGI systems are modeled as networks of N primitive agents (nodes) each with internal state; hierarchical strata mediate bottom-up individuation and top-down constraint. Key metrics include state entropy $H(p_i)$, mutual information $MI(p_i, p_j)$, integration $I(P) = \sum H(p_i) - H(P)$, and operational complexity $$OC(P) = \sum_{k=1}^{\lfloor N/2\rfloor} \langle MI(X_k, P - X_k) \rangle$$, over all size-k subsets $X_k$ (Weinbaum et al., 2015).
• Cluster Index: $CI(X_k) = I(X_k) / MI(X_k, P - X_k)$ measures the provisionality of a boundary; $CI \gg 1$ indicates strongly individuated subassemblages.
• Open-Ended Intelligence Approximation: $Int_t(P) = \mathcal{F}(I_t(P), OC_t(P))$, balancing integration and complexity as the signature of progressive intelligence.
• ε-Category Intelligence: For general operationalization and benchmarking, SGI leverages category indistinguishability: an agent is ε-intelligent on a category $C$ if no admissible distinguisher family $D$ can statistically separate generated samples $G_C$ from natural samples $P_C$ by more than $\epsilon$ in total variation:

$$\sup_{d\in D} \Bigl| \Pr_{x\sim P_C}[d(x)=1] - \Pr_{x\sim G_C}[d(x)=1] \Bigr| \le \epsilon$$

This unifies GAN evaluation, RL performance, and Turing-test-style human judgments under a single information-theoretic criterion (Ng, 30 Jul 2025).

3. Sense-Making and Value Emergence

In SGI, sense-making is primary—agents dynamically bring forth objects, categories, and relations via ongoing coordination, without stable pre-encoded identities. The sense-making process exhibits these phases:

1. Boundary Formation: Symmetry breaking and clustering via information metrics.
2. Fluid Identities: Provisional closures with components drifting in and out of alliance.
3. Operational Closure: Emergence of robust, quasi-autonomous subagents.

Value systems, rather than being coded externally (as explicit rewards), crystallize within this process. Proto-values manifest as local tensions and incompatibilities; as coordinative patterns stabilize, these proto-values self-organize into agent-specific values, which in turn shape future individuation and adaptation across hierarchical strata (Weinbaum et al., 2015).

4. Coordination, Exploration, and Open-Ended Learning

SGI locates intelligence not in static pattern recognition but in the capacity for dynamic, scalable coordination across heterogenous elements. Coordination analytically corresponds to the ongoing reciprocal regulation required to resolve incompatibilities without collapsing diversity. High SGI entails balancing increasing integration with nontrivial complexity, thereby avoiding both fragmentation and trivial uniformity.

Crucially, generalized exploration becomes a first-class objective (Jiang et al., 2022):

$$m^* = \arg\max_m [C(m, \pi) + \alpha_D \, Diversity(m) - \alpha_G \, Grounding(m)]$$

where $C(m, \pi)$ quantifies learning potential, $\alpha_D$ and $\alpha_G$ weight diversity and grounding (scientific relevance), and $m$ ranges over new task/data source candidates. This principle unifies supervised and reinforcement learning under active data/task acquisition, providing the machinery for open-ended task and knowledge growth—essential for scientific domains.

5. Hierarchical and Distributed Architectures

Contemporary SGI architectures draw on multi-level, agentic, and memory-augmented principles:

• Three-Level Hierarchy: Intelligence as bottom-up abstraction and top-down recall spanning (1) raw physical signals $P$, (2) information patterns $I$, (3) abstract representations $A$; operators $\psi$ and $\phi$ map $P \mapsto I \mapsto A$ (Yaworsky, 2018).
• Agentic RAG: Integration of retrieval, planning, and dynamic tool use within memory-augmented agents, structured for adaptive, compositional reasoning (Qureshi et al., 1 Jul 2025).
• Brain-Inspired Modularity: Dissociable yet orchestrated reasoners for distinct domains (vision, language, logic), persistent multi-tier memory systems, and coordination via global workspaces or message-passing (Qureshi et al., 1 Jul 2025).
• Self-Similar, Recursive Stratification: Assemblages form new layers of agents, each embedding and constraining interaction at adjacent strata, consistent with open-ended scaling of intelligence via recapitulated individuation (Weinbaum et al., 2015).

6. Evaluation, Metrics, and Open Challenges

Evaluation of SGI systems necessitates metrics that capture generalization, efficiency, and coordinative sufficiency, rather than mere peak or average performance:

• g-Index: Skill-acquisition efficiency, penalizing brute-force scaling and rewarding sample-efficient, high-performance generalization to novel tasks (Venkatasubramanian et al., 2021).
• Coherence-Aware AUC: Measures robust, balanced proficiency (non-compensatory cross-domain sufficiency) by integrating generalized means over compensability exponents $\alpha$, penalizing uneven skill profiles much more strictly than arithmetic mean (Fourati, 23 Oct 2025).
• Scientist-Aligned Benchmarks: Workflow-centric PIM-cycle tasks (deep research, idea generation, dry/wet experiments, reasoning) demand the full Deliberation–Conception–Action–Perception cycle and expose persistent limitations in current state-of-the-art LLMs (Xu et al., 18 Dec 2025).
• Operationalization: Empirical protocols emphasize falsifiability, resource constraints, and domain transfer—unifying safety, testability, and comparison across models (Ng, 30 Jul 2025).

Key open research directions include expanding semantic information measures beyond Shannon forms for richer coordination quantification; formalizing the process of value-system individuation and stabilization; realizing end-to-end hybrid architectures that blend individually specialized modules with system-level, open-ended sense-making; and formulating safe, scalable mechanisms for truly open-ended exploration and coordination across arbitrary scientific and practical domains (Weinbaum et al., 2015, Jiang et al., 2022, Xu et al., 18 Dec 2025).