From asi
Explains latent-latency duality linking compression in latent spaces to response times via spectral gaps and mixing times. Provides Python code for encoders, decoders, and dynamics. Useful for AI model optimization tradeoffs.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 0 (ERGODIC - mediates space ↔ time)
Analyzes neural network training dynamics using Langevin SDEs per Moritz Schauer's approach, measuring temperature control, Fokker-Planck convergence, mixing time, and discretization effects.
Optimizes ML inference latency via model compression, distillation, pruning, quantization, caching strategies, and edge deployment patterns.
Deep-dives into ML/AI topics by fetching official docs and GitHub sources via KB or web tools, for explaining concepts, comparing approaches, or surveying frameworks like 'how does X work?' or 'X vs Y'.
Share bugs, ideas, or general feedback.
Trit: 0 (ERGODIC - mediates space ↔ time)
Bundle: core
Status: ✅ New
LATENT (Space) ↔ LATENCY (Time)
↓ ↓
Compression Speed
↓ ↓
Representation Response
↓ ↓
dim(z) τ_mix
Core Theorem: Good latent representations minimize latency.
t_response ∝ 1 / compression_ratio(z)
The spectral gap (λ₁ - λ₂) connects both domains:
| Domain | Spectral Gap Role |
|---|---|
| Latent | Separation of clusters in representation space |
| Latency | Mixing time τ_mix = O(log n / gap) |
From Ramanujan graphs (optimal expanders):
gap ≥ d - 2√(d-1) [Alon-Boppana bound]
τ_mix = O(log n) [Logarithmic mixing]
# Encoder: Observable → Latent
z = encode(x) # dim(z) << dim(x)
# Decoder: Latent → Reconstructed
x̂ = decode(z)
# Bidirectional loss
L = ||x - x̂||² + β·KL(q(z|x) || p(z))
# Fokker-Planck: Distribution evolution
∂p/∂t = ∇·(∇L(θ)·p) + T∆p
# Mixing time from Hessian
τ_mix ≈ 1 / λ_min(H)
# Gibbs equilibrium
p∞(θ) ∝ exp(-L(θ)/T)
τ_latency = f(dim_latent, spectral_gap, temperature)
Specifically:
τ_response = (dim(z) / gap) × log(1/ε)
Where:
- dim(z) = latent dimension
- gap = spectral gap of computation graph
- ε = target accuracy
From MCP_OPTIMAL_TRANSITIONS.md:
| MCP Server | Latency | Latent Cost | Energy |
|---|---|---|---|
gay | ~10ms | 0.1KB context | LOW |
tree-sitter | ~50ms | 1KB context | LOW |
exa | ~1s | 3KB context | HIGH |
firecrawl | ~2s | 10KB context | HIGH |
Optimal triad: gay → tree-sitter → marginalia (560ms, 5 energy)
From worlding_skill_omniglot_entropy.py:
class BidirectionalCharacterLearner:
def __init__(self, char_dim: int = 28, latent_dim: int = 64):
self.char_dim = char_dim
self.latent_dim = latent_dim # Compression ratio: 784 → 64
def encode_character(self, image: np.ndarray) -> np.ndarray:
"""READ: Image → Latent Code (learn what the character means)"""
# Latency: O(dim_latent)
pass
def generate_character(self, latent_code: np.ndarray) -> np.ndarray:
"""WRITE: Latent Code → Image (learn how to express the character)"""
# Latency: O(dim_output)
pass
Compression: 784 → 64 = 12.25× compression
Expected Latency Reduction: ~12× for downstream tasks
Training latency depends on reaching Gibbs equilibrium:
Stopped Early: t < τ_mix → Poor latent representation
Fully Converged: t > τ_mix → Optimal latent representation
↓
Minimal inference latency
From fokker-planck-analyzer:
def check_convergence(trajectory, temperature):
# Mixing time from loss landscape geometry
τ_mix = 1 / λ_min(Hessian(loss))
# Check if training exceeded mixing time
if training_steps > τ_mix:
return "CONVERGED: Good latent representation"
else:
return f"EARLY STOP: Need {τ_mix - training_steps} more steps"
| Skill | Trit | Role |
|---|---|---|
fokker-planck-analyzer | -1 | Verifies convergence (latency) |
latent-latency | 0 | Mediates space ↔ time |
compression-progress | +1 | Generates compressed representations |
Conservation: (-1) + (0) + (+1) = 0 ✓
def optimize_latent_for_latency(model, target_latency_ms):
"""
Find optimal latent dimension for target latency.
Relationship: latency ∝ dim(z) / spectral_gap
"""
current_dim = model.latent_dim
current_latency = measure_latency(model)
# Target dimension
target_dim = int(current_dim * (target_latency_ms / current_latency))
# Retrain with smaller latent space
return retrain_model(model, latent_dim=target_dim)
def predict_mixing_time_from_latent(latent_structure):
"""
Estimate training latency from latent space properties.
"""
# Spectral gap of latent similarity graph
gap = spectral_gap(latent_similarity_matrix(latent_structure))
# Mixing time bound
n = latent_structure.n_samples
τ_mix = np.log(n) / gap
return τ_mix
def route_with_ramanujan(nodes, message):
"""
Route through network with optimal latency.
Ramanujan graphs achieve t_mix = O(log n).
"""
# Build routing graph with Ramanujan property
G = build_lps_graph(nodes, degree=7) # (7+1)-regular
assert spectral_gap(G) >= 7 - 2*np.sqrt(6), "Not Ramanujan!"
# Route via non-backtracking walk
path = non_backtracking_path(G, source, target)
# Expected latency: O(log n) hops
return path
From security applications:
Detection latency = O(log N) / gap
For Ramanujan (gap = 1/4):
N = 1000 nodes → detection in ~37ms
N = 1M nodes → detection in ~74ms
# Analyze latent-latency tradeoff
just latent-latency-analyze model.pt
# Optimize for target latency
just latent-optimize --target-ms=100
# Measure spectral gap of latent space
just latent-spectral-gap embeddings.npy
# Predict mixing time
just predict-mixing-time --hessian=H.npy
# Route with Ramanujan optimality
just ramanujan-route --nodes=1000
CREATE TABLE latent_latency_metrics (
model_id VARCHAR PRIMARY KEY,
latent_dim INT,
spectral_gap FLOAT,
mixing_time_estimate FLOAT,
inference_latency_ms FLOAT,
compression_ratio FLOAT,
is_converged BOOLEAN,
created_at TIMESTAMP DEFAULT NOW()
);
-- Query: find optimal models
SELECT model_id, latent_dim, inference_latency_ms
FROM latent_latency_metrics
WHERE is_converged = true
ORDER BY inference_latency_ms ASC
LIMIT 10;
fokker-planck-analyzer (-1) ⊗ latent-latency (0) ⊗ compression-progress (+1) = 0 ✓
ramanujan-expander (-1) ⊗ latent-latency (0) ⊗ agent-o-rama (+1) = 0 ✓
spi-parallel-verify (-1) ⊗ latent-latency (0) ⊗ gay-mcp (+1) = 0 ✓
fokker-planck-analyzer - Convergence verificationlangevin-dynamics - SDE-based learningramanujan-expander - Spectral gap optimizationcompression-progress - Intrinsic motivationmcp-tripartite - Energy-latency tradeoffsSkill Name: latent-latency
Type: Theoretical Bridge
Trit: 0 (ERGODIC - space ↔ time mediation)
Core Equation: τ_response = dim(z) / gap × log(1/ε)
Status: ✅ Available
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.