claim

active

claim:representing-non-linearly-separable-functions-requires-a-network-with-multiple-layers

Representing non-linearly separable functions requires a network with multiple layers.

Architectural requirement from machine learning.

Source paper

extracted_from

The collective intelligence of evolution and development

(2023) · Watson, Richard · Levin, Michael

Neighborhood — ranked by edge-count

Claims (1)

claim

When interactions constitute non-linearly separable functions, it creates a ‘we’; what we are doing becomes a relevant variable.
extends
Explains how non-separability shifts identity from parts to collective.

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.

Functional relationships required for new individuality level encode non-linearly separable functions and are enacted via information integration and collective actionhypothesis0.825
Non Linearly Separable Functionsconcept0.824
Mathematical property where output depends on context-dependent interaction of inputs (e.g., XOR logic); proposed as formal basis for individuality transitions.
Shallow interaction structures cannot compute non-linearly separable functions; depth (hidden layers) is necessary for ETI-relevant individualityclaim0.818
Assertion that deep organization is mandatory, based on connectionist theory
Non-decomposable (Non-linearly Separable) Functionsconcept0.805
Mathematical formalism from connectionism where output depends on context-dependent interaction of inputs; proposed as formal requirement for ETIs.
Non-decomposability (non-linearly separable function) is a refinement of non-aggregative interactions, necessary for collective to be non-redundantclaim0.794
Sharpens previous concepts of emergence in ETIs
Networks encode structured geometric concepts that reflect external reality.claim0.794
Core claim of the paper: the right level of description for neural representations is geometric structure mirroring the world.
Linearly Separable Functionconcept0.780
A function separable by a single linear boundary; allows independent contributions of inputs to output; computable by Perceptron
Does the multi-directional nature of truth imply an underlying nonlinear representation, or is it compatible with linear separability?question0.778
Theoretical open question about the geometry of truth in LLMs raised in Discussion