supersparsity-unison Skill

supersparsity-unison Skill

Status: ✅ Production Ready Trit: 0 (ERGODIC - bridge) Color: #9B59B6 (Purple - synthesis) Principle: Sparse computation through content-addressed abilities Frame: TiDAR + gzip scaling → Unison ability composition

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Overview

Supersparsity-Unison bridges neural network sparsity research with Unison's content-addressed computation model. The core insight: sparse activation patterns in neural networks (MoE, lottery tickets, TiDAR) map naturally to Unison's ability system and splittable RNG.

Core Papers

TiDAR → Unison Mapping

┌─────────────────────────────────────────────────────────────┐
│                    TiDAR Architecture                        │
├─────────────────────────────────────────────────────────────┤
│  DIFFUSION DRAFTING          AUTOREGRESSIVE VERIFICATION    │
│  (parallel tokens)           (sequential sampling)          │
│         │                            │                       │
│         ▼                            ▼                       │
│  ┌─────────────┐              ┌─────────────┐               │
│  │ SplitRng.   │              │ RegretOp.   │               │
│  │   split     │──────────────│ recordPred  │               │
│  └─────────────┘              └─────────────┘               │
│    Trit: +1                      Trit: 0                    │
│    (generator)                   (ergodic)                   │
└─────────────────────────────────────────────────────────────┘

gzip Scaling Law Bridge

Pandey's key finding: L(N,D) = f(gzip(data)) — gzip compressibility predicts optimal compute allocation.

-- Data complexity determines scaling exponent
gzipComplexity : Text -> Float
gzipComplexity data =
  seed = SplitRng.fromText data
  entropy = Float.fromNat (SplitRng.state seed) / Float.fromNat gay.mask64
  -- Higher entropy = harder to compress = need more data vs params
  entropy

-- Scaling law: harder data → prefer dataset size over parameters
scalingExponent : Float -> Float
scalingExponent complexity =
  -- Pandey: α shifts from ~0.5 (easy) to ~0.7 (hard)
  0.5 + complexity * 0.2

Sparse Activation as Abilities

-- Mixture of Experts as ability handlers
ability MoE where
  route : Nat -> {MoE} Nat  -- top-k routing
  expert : Nat -> a -> {MoE} a  -- expert computation

-- Sparse activation: only k experts fire
sparseForward : Nat -> [a] -> {MoE} [a]
sparseForward k inputs =
  experts = List.range 0 8  -- 8 experts
  topK = List.take k (List.sortBy (x -> route x) experts)
  List.map (e -> expert e inputs) topK

Lottery Ticket as Regret Pruning

-- Find winning ticket via regret accumulation
findWinningTicket : [RegretOp] -> [RegretOp]
findWinningTicket ops =
  -- Keep operations with low regret (high accuracy)
  threshold = 0.3
  List.filter (op -> RegretOp.regretOpRegret op < threshold) ops

-- Supermask: binary mask from regret
supermask : RegretOp -> Boolean
supermask op = RegretOp.regretOpRegret op < 0.5

Triadic Composition

compression-progress (-1) ⊗ supersparsity-unison (0) ⊗ forward-forward-learning (+1) = 0 ✓
kolmogorov-compression (-1) ⊗ supersparsity-unison (0) ⊗ cognitive-superposition (+1) = 0 ✓
propagators (-1) ⊗ supersparsity-unison (0) ⊗ tidar (+1) = 0 ✓

Concept Index

DuckDB Integration

-- Query supersparsity concepts by skill
SELECT concept, trit, skill_mapping 
FROM supersparsity_index 
WHERE skill_mapping IN ('compression-progress', 'forward-forward-learning')
ORDER BY trit DESC;

-- TiDAR-Unison bridge
SELECT * FROM tidar_unison_bridge ORDER BY trit DESC;

TiDAR Streaming ZIP Implementation

The rio/​gayzip/​tidar_streaming.py demonstrates moment-by-moment valid ZIP:

# Diffusion phase: parallel compression
for bag_id, bag in zipper.stream_diffusion():
    # Each bag compresses independently (SplitRng.split)
    pass

# AR verification: sequential emission
for chunk in zipper.stream_ar_verify():
    f.write(chunk)  # ZIP valid at each write

Key insight: ZIP local headers are self-contained, so each bag can be emitted as soon as compressed. Central directory streams last, making ZIP fully valid.

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End-of-Skill Interface

Commands

# Test TiDAR-style parallel drafting
ucm run rio/​unison-terminus/​gay.u -e "SplitRng.split (SplitRng.fromSeed 42069)"

# Measure gzip complexity of code
gzip -c code.u | wc -c  # raw complexity
ucm run -e "gzipComplexity (Text.fromUtf8 !readFile \"code.u\")"

# Find lottery tickets in operad
ucm run rio/​unison-terminus/​GayOperad.u -e "findWinningTicket allOperations"

Related Skills

• compression-progress (-1): Curiosity as compression improvement rate
• forward-forward-learning (+1): Local learning without backprop
• cognitive-superposition (+1): Multi-hypothesis parallel processing
• propagators (-1): Bidirectional constraint networks

References

1. Pandey, R. (2024). "gzip Predicts Data-dependent Scaling Laws" arXiv:2405.16684
2. Liu et al. (2024). "TiDAR: Think in Diffusion, Talk in Autoregression" arXiv:2511.08923
3. Frankle & Carlin (2019). "The Lottery Ticket Hypothesis"
4. Shazeer et al. (2017). "Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer"

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Skill Name: supersparsity-unison Type: Bridge (Synthesis) Trit: 0 (ERGODIC) Color: #9B59B6 (Purple)

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Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.