Intelligence manifold and emergent alignment

Intelligence manifold

The aim of the program is to characterize an intelligence manifold that places humans, machine systems, and hybrid entities inside one common space. Axes of this manifold are characterized by sensing and action limits, communication bottlenecks, memory capacity, embodiment, and energetic budget. We hypothesize that many current AI failure modes arise because of the distance between humans and AI on this manifold. We plan to use this framework to study how the various axes affect the type of intelligence a system develops. We expect this theory to guide experiments on interfaces (between agent and environment), collective cognition, alignment, and new forms of intelligence.

This suggests a distinction between capability and distance from human constraints. Two systems may achieve similar performance (intelligence) while occupying different regions of a constraint manifold defined by sensing modalities, action affordances, energetic pressure, temporal scale, and memory budget. We propose measuring both overall competence (e.g., predictive performance, empowerment, control) and constraint proximity, because these jointly affect interpretability, collaboration quality, and failure modes (Chollet, 2019; Lieder and Griffiths, 2020). By representing intelligence as such a manifold, one may quantify overall competence as the magnitude of a point on the manifold, providing a scalar comparison between human and artificial intelligence. Human-likeness (or alienness) can be measured with a distance metric between human and AI points on the manifold.

Language and sparsity

We aim to connect this formal lens to the notion of alignment and sparsity as one phenomenon across scales. We define sparsity as an information-transfer bottleneck between parts of a system, and define alignment as the degree of influence and mutual predictability through that bottleneck. The level of sparsity fundamentally limits alignment, but alignment is also affected by distance on the intelligence manifold, i.e. the farther apart two systems are the harder for them to align. This view applies to cells in the human body, layers in a neural network, brain regions, human groups and institutions, and human–AI systems, giving us one common framework for studying coupled systems across scales.

Alignment can be thus generalized to reflect the quality of interfaces (or communication channels) between parts of a system as well as a system and its larger environment. In essence these can be treated within the same formal framework. Thinner and more lossy channels produce weaker coupling and larger alignment gaps. This gives a single formal lens that applies across scales, from cells within tissues, to brain regions within a brain, to many humans linked by language and institutions and coupled with tools such as AI. As agency / intelligence increases, alignment becomes more strongly bidirectional, because any system with enough power to shape another through a shared interface enters a regime of reciprocal influence through that same interface.

Finite shared-bridge budget

Empowerment measures how much future state can be influenced by action (Klyubin et al., 2005). Plasticity is the inward mirror and measures how much future action can be influenced by observation (Abel et al., 2025). When both flows use a shared finite bridge transcript, they obey a capacity budget.

Use the standard feedback-channel indexing $A^{T}=(A_{1},\ldots,A_{T})$ and $O^{T}=(O_{1},\ldots,O_{T})$, where $A_{t}$ is chosen after $O^{t-1}$ and before $O_{t}$.

Assume the joint law is causal and all statistical dependence between $A^{T}$ and $O^{T}$ is mediated by a specified finite bridge transcript $B$ satisfying $\mathrm{H}(B)\leq b$, so $A^{T}\perp O^{T}\mid B$. The variable $B$ is the physical or informational interface transcript being bounded; it should not include arbitrary agent memory or private randomness unless those degrees of freedom are actually transmitted through the interface. Then

$$\mathrm{I}(A^{T}\to O^{T})+\mathrm{I}(O^{T-1}\to A^{T})=\mathrm{I}(A^{T};O^{T})\leq b.$$

This theorem is a bottleneck theorem for a specified bridge. A narrow interface can spend capacity on easy outward control, leaving little capacity for evidence. It can also spend capacity on passive evidence, leaving little realized influence. A unified agent must widen the bridge, split inward and outward channels, or internalize the relevant state.

We aim to connect this formal lens to alignment and sparsity across scales. The finite shared-bridge budget gives one precise constraint on the inward and outward information flows through a specified interface. We plan to study how communication bottlenecks, alongside sensing, action, memory and energetic constraints, affect the type of intelligence a system develops and its alignment with other systems.