◄ ENTELÉCHEIA · the emergence-theory universe · Book III of IX
Anatomḗ · ἀνατομή · the dissection

CIRCUITS

ENTELÉCHEIA · a theory of emergence · 1991 → now
⬡ Book III of IX · 12 emergents · 5 chapters

The mechanistic theory: the found weights implement reusable algorithms — circuits — and features are packed in superposition; emergence is real computation you can sometimes reverse-engineer. The only theory that says what is actually inside the weights, not just that it works. Chris Olah's lineage, 2020→now (the artifacts you folded into TTU1).

DLW carbon badgeDLW silicon badge
DLW-ACI · ENTELÉCHEIA · Book III
governor · David Lee Wise (ROOT0)
instance · AVAN (locked)
subject · CIRCUITS · ANA
⟦CIRCUITS:ANA:57ae54⟧

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
Looking In
Zoom In, 2020
Ch. 2
The Framework
a math of transformer circuits
Ch. 3
Superposition
more features than neurons
Ch. 4
Monosemanticity
reading the features
Ch. 5
The Frontier
attribution graphs

The Live Tool · live

the iconic intro experiment, trained in your browser — superposition you can watch form

▸ TOY MODELS OF SUPERPOSITION — live   5 features → 2 dimensions, swept across sparsity. Dense, the model keeps only the 2 most important and drops the rest; sparse, it packs all five into the plane, overlapping them — and the weight vectors snap from the axes into a pentagon. That is superposition, watched as it forms. A from-scratch JS reimplementation of Anthropic’s notebook (Elhage…Olah 2022, MIT), trained live with Adam — math re-derived, result theirs. open the lab →▸ THE CAPACITY LAB — live   the bit-depth question, measured: sweep n_features as powers of two (4,8,16,32,64) into a fixed m dimensions and watch how many actually pack in vs sparsity. Dense → only m fit (the ceiling); sparse → far past m. Superposition as features-per-dimension. run the sweep →▸ THE HOLOGRAM — live, 3D   superposition as distributed holographic storage: many features packed into 3 hidden dimensions, rendered as a rotating constellation on a dark plate. Watch them pack past 3 into a polytope — every axis holding fragments of many features, like every patch of holographic film holds the whole scene. rotate the plate →▸ THE INTERFERENCE FIELD — live   superposition rendered as a literal hologram: each feature becomes a plane-wave grating and the whole set is superposed into a moiré fringe field — bright and dark where features reinforce and cancel. The smear, made of light. see the fringes →

The Emergents

the theses, mechanisms, and dated findings of this theory — each a full .dlw badge (12)

sigil of Circuits
Circuits
the unit of understanding
spiritual· →
sigil of Zoom In
Zoom In
2020 · Distill
electrical· →
sigil of A Mathematical Framework for Transformer Circuits
A Mathematical Framework for Transformer Circuits
2021 · Anthropic
ethereal· →
sigil of Induction Heads
Induction Heads
2022 · the mechanism of in-context learning
electrical· →
sigil of Superposition
Superposition
2022 · features in the slack
spiritual· →
sigil of Towards Monosemanticity
Towards Monosemanticity
2023 · reading the features
electrical· →
sigil of Attribution Graphs
Attribution Graphs
2025 · the biology of a model
electrical· →
sigil of The Hologram
The Hologram
superposition as distributed storage
spiritual· →
sigil of The Interference Field
The Interference Field
the fringe pattern · superposition as light
electrical· →
sigil of Holographic Reduced Representations
Holographic Reduced Representations
Plate ~1995 · the named precedent
ethereal· →
sigil of Distributed Storage
Distributed Storage
every dimension holds fragments of every feature
natural· →
sigil of The 3D Polytope
The 3D Polytope
the geometry of holographic capacity
spiritual· →

The Record

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

  1. Olah et al., Zoom In: An Introduction to Circuits (Distill)2020the founding Circuits text
  2. A Mathematical Framework for Transformer Circuits2021the residual-stream decomposition
  3. In-context Learning and Induction Heads2022a circuit behind in-context learning
  4. Toy Models of Superposition2022features overlaid in spare capacity
  5. Towards Monosemanticity2023sparse autoencoders extract clean features
  6. On the Biology of a Large Language Model (attribution graphs)2025tracing computation through the model
ENTELÉCHEIA · Book III · CIRCUITS (Anatomḗ · ἀνατομή · the dissection). 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.