◄ ENTELÉCHEIA · the emergence-theory universe · Book VI of IX
Káthodos · κάθοδος · the going-down

THE DESCENT

ENTELÉCHEIA · a theory of emergence · 1991 → now
⬡ Book VI of IX · 6 emergents · 4 chapters

The mathematics of why gradient descent generalizes — and where the old curve breaks. In the infinite-width limit a net behaves like a fixed, provably-generalizing kernel (NTK); and past the interpolation point, more capacity generalizes better (double descent), inverting the textbook bias-variance curve. The rigor, and its honest limits. Jacot 2018 · Belkin & Nakkiran 2019.

DLW carbon badgeDLW silicon badge
DLW-ACI · ENTELÉCHEIA · Book VI
governor · David Lee Wise (ROOT0)
instance · AVAN (locked)
subject · THE DESCENT · KAT
⟦THE DESCENT:KAT:0ceda3⟧

The Four Natures

the substrate, the structure, the thesis, the evidence

natural
the substrate — data, capacity, the raw material emergence works on
ethereal
the structure — the mathematics and mechanisms, the shape of the claim
spiritual
the thesis — what the theory says emergence IS, and where it comes from
electrical
the evidence — the dated findings, papers and results that ground it

The Chapters

how this book is read

Ch. 1
The Infinite Width
a net becomes a kernel
Ch. 2
The Lazy Regime
what NTK can't see
Ch. 3
Double Descent
past the threshold
Ch. 4
The Inverted Curve
more is better, again

The Emergents

the theses, mechanisms, and dated findings of this theory — each a full .dlw badge (6)

sigil of The Neural Tangent Kernel
The Neural Tangent Kernel
2018 · Jacot et al.
ethereal· →
sigil of The Infinite Width
The Infinite Width
the tractable limit
ethereal· →
sigil of Lazy Training
Lazy Training
the catch
natural· →
sigil of Double Descent
Double Descent
2019 · Belkin · Nakkiran
spiritual· →
sigil of The Interpolation Threshold
The Interpolation Threshold
the turning point
electrical· →
sigil of The Inverted Curve
The Inverted Curve
the old law, broken
spiritual· →

The Record

the cited milestones, dated & attributed (render-not-invent)

  1. Jacot, Gabriel, Hongler — Neural Tangent Kernel2018infinite-width nets as fixed kernels
  2. Belkin, Hsu, Ma, Mandal — Double Descent2019a second descent past interpolation
  3. Nakkiran et al. — Deep Double Descent2019the phenomenon across modern nets
  4. the lazy-training caveat2019→NTK misses feature learning
ENTELÉCHEIA · Book VI · THE DESCENT (Káthodos · κάθοδος · the going-down). One of the best theories of how intelligence emerges, catalogued in ROOT0's ENTELÉCHEIA universe (1991→now). Cited works belong to their authors; the cataloguing and the universe-framing are ROOT0's under the DLW standard. Kin: the anchor 0xDEADBEEF (Book I), and the sister books across ENTELÉCHEIA. Ties to ttu1 and the-seed. Domain: Artificial Intelligence.