Non Linearly Separable Functions

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

Neighborhood — ranked by edge-count

Frameworks (2)

framework

Multi Layer Perceptron
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Network with hidden layers capable of representing non-linearly separable functions, enabling deep model induction
Division Of Labour Game
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Game where individuals adopt complementary heterogeneous roles to maximize collective fitness; game-theoretic equivalent of non-linearly separable function

Claims (1)

claim

Shallow interaction structures cannot compute non-linearly separable functions; depth (hidden layers) is necessary for ETI-relevant individuality
supports
Assertion that deep organization is mandatory, based on connectionist theory

Concepts (7)

concept

Linearly Separable Function
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A function separable by a single linear boundary; allows independent contributions of inputs to output; computable by Perceptron
Non-decomposable (Non-linearly Separable) Functions
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Mathematical formalism from connectionism where output depends on context-dependent interaction of inputs; proposed as formal requirement for ETIs.
Evolutionary Individuality
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Property where evolution of the whole is non-decomposable function of evolution of parts; central to understanding ETIs.
Fitness epistasis
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Non-additive interactions between components affecting fitness; when non-linearly separable, it creates non-decomposable wholes.
Organismic Individuality
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Property where development and behavior of whole is non-decomposable function of component parts; distinct from genetic individuality.
Division of Labour
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Role specialization where fitness effects of particle characters reverse depending on context (e.g., germ/soma); formal game-theoretic equivalent to non-linearly separable functions.
Non-decomposable Collective Character
same_concept_as
A collective character that cannot be decomposed into independent contributions of particles; specifically one that is non-linearly separable

Hypotheses (1)

hypothesis

Functional relationships required for new individuality level encode non-linearly separable functions and are enacted via information integration and collective action
gates

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.

Representing non-linearly separable functions requires a network with multiple layers.claim0.824
Architectural requirement from machine learning.
Non-decomposability (non-linearly separable function) is a refinement of non-aggregative interactions, necessary for collective to be non-redundantclaim0.790
Sharpens previous concepts of emergence in ETIs
When interactions constitute non-linearly separable functions, it creates a ‘we’; what we are doing becomes a relevant variable.claim0.751
Explains how non-separability shifts identity from parts to collective.
How Do Nonlinearly Separable Interactions Between Components Enablequestion0.717
Non-Linear Representation Hypothesisconcept0.716
Hypothesis that information may be encoded in arbitrary non-linear subspaces of a neural network
Not-Separatenessconcept0.712
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
Non-Linear Representation Dilemmaconcept0.709
Core contribution: the impasse where lifting linearity in alignment maps makes causal abstraction vacuous, but keeping it may miss non-linearly encoded features
Non-Linear Representations in LLMsconcept0.701
Recent work identifying cases where LLM features are not one-dimensionally linear, a caveat to the linearity hypothesis.