Categorical AI phenomenology: A first-person approach
Authors: Robert Prentner
Organizations: Institute of Humanities, ShanghaiTech University, No. 393 Middle Huaxia Road, Shanghai, 201120, China · Association for Mathematical Consciousness Science, Geschwister-Scholl-Platz 1, Munich, 80539, Germany
This paper develops a phenomenology-first approach to artificial consciousness by reframing consciousness as the subjective experience enacted through an agent's interface with the world. We shift the methodological focus to first-person structures, modeled mathematically by categories derived from Q-networks to capture actions and phenomenological invariants. In this framework, Q-networks are conceptualized as relational interfaces encoding agent-world interaction, analogous to how the dynamical states of a computer depend on its sensory inputs, previous states, and actions. Our work provides a rigorous framework for interface consciousness to describe computational systems that embed information-processing into phenomenological structure. The approach aligns with 4E approaches to cognition by emphasizing enactive, embedded, and extended dimensions of experience. The paper thus offers a principled, relational, and phenomenological account of artificial phenomenology grounded in categorical mathematics.
Figures & tables
Figure 1: The “phenomenological hierarchy” of this paper: data about various natural and artificial information-processing systems (e.g. reaction networks, single cells, cellular collectives, brains or AIs) can be embedded into Q -networks that encode relations between actual and potential states of an agent. Q -networks can be seen as exemplars of the larger class of interfaces encoding agent-environment interaction, inherently involving embodiment. A phenomenological approach investigates how such interfaces could mediate the structural conditions for subjectivity, potentially giving rise to more complex phenomenological properties mirrored in, for example, process-unity, time-, or self-consciousness. Collectively this defines how subjective experiences are enacted through an agent’s interface with the world . (Diagram created with the help of Microsoft Copilot.)
nk
(cj,ck,⋯)
number of kernels
n=3
31
(1,1,1)
1
32
(2,1)
3
33
(3)
2
total:
3!=6
n=4
Table 1: Number of invertible kernels on n elements with at least one cycle of size k . The notation (cj,ck,⋯) indicates the sizes of cycles.
Figure 2: From A to B via C , one can compose the mapping in two distinct ways. In one case, the weight of the composite is the sum of the parts (cyan); in another, it is the maximum (orange). This flexibility illustrates how categories can accommodate different rules for composing actions. (This example has been inspired by the example of a transport-network discussed in [ Ehresmann & Vanbremeersch, 2007 ] ).
Figure 3: Illustration of the concept of colimit in a category. All mappings between objects in the pattern (colors) commute with mappings to C . Specifically, the colimit, if it exists, picks out the minimal cone C . Any mapping from the pattern to another cone C′ factors uniquely through C via a mapping from C to C′ .
Figure 4: Evolution of features over time (“third-person data”).
Figure 5: 3D embedding of the time series into a phenomenal space. Each point corresponds to a state of a Q -network; arrows indicate temporal succession.
Figure 6: Full Q -network combining temporal adjacency (gray edges) and similarity-based edges (colored). Node color encodes time index.
Figure 7: Example subnetworks for selected nodes at different similarity thresholds.
Threshold
# Max cliques
Avg clique size
# Triangles
0.98
11
2.27
1
0.84
32
3.00
16
0.74
32
3.97
9
Table 2: Motif analysis of similarity-based Q -network subgraphs across thresholds.
Figure 8: Hasse diagrams of the inclusion-category defined over the Q -network at different thresholds. Each diagram shows minimal inclusions between cliques, treated as objects of the category. As the threshold decreases, the diagrams become increasingly dense and visually complex.
Figure 9: Betti numbers as a function of threshold. These topological invariants provide phenomenological interpretations of connectedness and cyclic structure. In the example, only β0 (red) and β1 (blue) take non-zero values, standing for the presence of disconnected components and loops, respectively. The dashed vertical line marks the colimit of the filtered category, i.e. the threshold at which all components unify into a single experiential field.
Figure 10: Diagonal curve (left) and heatmap (right) showing the number of maximal cliques under inclusion functors across thresholds.
Figure 11: Generic string diagram for a strict monoidal category illustrating the idea of “process-unity.” Types (wires; experiences described by categorical structures derived from Q -networks) are transformed by processes (boxes; interpreted as transformations of these structures). On the left side, one sees a sequential composition of processes ( g∘f:X→Z ). On the right, is an equivalent diagram with the respective processes not composing sequentially but horizontally ( m∘(f⊗gT⊗1)∘p:X⊗1→1⊗Z ) 12 12 12 Here “ ∘ ” denotes sequential composition of morphisms, while “ ⊗ ” denotes parallel composition. T denotes the transpose; m and p are horizontal composites of the identity and other generic objects (“cups” and “caps” [ Signorelli et al., 2021c ] ). ; time flows from top to bottom.
Figure 12: Schematic illustration of how individual computational processes are organized under a phenomenological concept. The concept functions as a constraint on processing, not as another layer of computation, as indicated by the dotted arrows. This jointly defines the phenomenological structure of the interface instantiated by a computational system.
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