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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

LEARNING FUNCTION · π⁰

This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.

Consciousness researchdocumented formula
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eq-5a4cb2006847a5mathematical expression
π0=Entmaxα(r)whereα∈(1,2]π⁰ = Entmax_α(r) where α ∈ (1, 2]

Read the equation

This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

  1. Read π⁰ as the quantity being defined or updated by this relation.

  2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

  3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

Read the surrounding source passage
STAGE 0: STRUCTURAL SPARSITY (Entmax)
π⁰ = Entmax_α(r)     where α ∈ (1, 2]

Unlike softmax, Entmax produces EXACT ZEROS for low-relevance substrates

Softmax([3, 1, 0.5, 0.1]) = [0.73, 0.10, 0.06, 0.04]  ← nothing is zero
Entmax₂([3, 1, 0.5, 0.1]) = [0.89, 0.11, 0.00, 0.00]  ← true sparsity
Exact original notation
π⁰ = Entmax_α(r)     where α ∈ (1, 2]

Related builds

Sources & provenance

01
Complete_Consciousness_Equation_Notes_RAW.txt
line 6240 · Jul 21, 2026
π⁰ = Entmax_α(r) where α ∈ (1, 2]
02
Pasted text(3).txt
lines 236–300 · Jul 21, 2026
π⁰ = Entmax_α(r) where α ∈ (1, 2]

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