Non-decomposable (Non-linearly Separable) Functions

Mathematical formalism from connectionism where output depends on context-dependent interaction of inputs; proposed as formal requirement for ETIs.

Neighborhood — ranked by edge-count

Concepts (1)

concept

Non Linearly Separable Functions
related_tosame_as
Mathematical property where output depends on context-dependent interaction of inputs (e.g., XOR logic); proposed as formal basis for individuality transitions.

Hypotheses (1)

hypothesis

ETIs are the evolutionary equivalent of deep learning: (i) required functional relationships encode non-decomposable functions, (ii) these are enacted by basal cognition mechanisms, and (iii) conditions for deep model induction predict ETI occurrence.
gates
Overarching three-part hypothesis stated in introduction

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Non-decomposability (non-linearly separable function) is a refinement of non-aggregative interactions, necessary for collective to be non-redundantclaim0.874
Sharpens previous concepts of emergence in ETIs
Linearly Separable Functionconcept0.840
A function separable by a single linear boundary; allows independent contributions of inputs to output; computable by Perceptron
Representing non-linearly separable functions requires a network with multiple layers.claim0.805
Architectural requirement from machine learning.
Non-decomposable Collective Characterconcept0.758
A collective character that cannot be decomposed into independent contributions of particles; specifically one that is non-linearly separable
Not-Separatenessconcept0.742
The property that a living whole is at one with the world, not separate from it; the center melts into its surroundings, the boundary is fragmented or incomplete, and there is a profound connection rather than isolation—perhaps the most important property of all
Composition is non-trivial, i.e. a whole cannot be decomposed meaningfully.claim0.735
Defining property of Schrödinger compositional theory
Functional relationships required for new individuality level encode non-linearly separable functions and are enacted via information integration and collective actionhypothesis0.730
When interactions constitute non-linearly separable functions, it creates a ‘we’; what we are doing becomes a relevant variable.claim0.725
Explains how non-separability shifts identity from parts to collective.