L1 ⚛ L1-388 ⊙ Testnet

Blind Source Separation (ICA / cocktail-party problem)

Signal Processing · Statistical independence-based demixing

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⬇ L1-388.md

# ⚛ L1 Principle — Blind Source Separation (ICA / cocktail-party problem) **ID:** `L1-388` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Signal Processing — *Statistical independence-based demixing* > **🎯 Problem class:** bilinear blind factorization · **🧮 Solution space:** independent components > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555197 --- ## 🧠 1. Introduction **Blind Source Separation (ICA / cocktail-party problem)** is a **bilinear blind factorization** whose unknown lives in **independent components** space, within the **Statistical independence-based demixing** sub-domain of **Signal Processing**. Measurements consist of acoustic pressure waves recorded by transducers via a **linear mixing** sensing mechanism. The forward operator applies, in order: L · mix · linear operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N > M) requires sparsity prior. ## ⚙ 2. Forward Model Physical chain: **x** → L · mix · linear → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.mix.linear` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.mix.linear` | L · mix · linear operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Signal Processing | | Sub domain | Statistical independence-based demixing | | Carrier | acoustic | | Problem class | bilinear_blind_factorization | | Solution space | independent_components | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 2.2 | ## 📡 4. Measurement Model Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N > M) requires sparsity prior. | Metric | Value | |---|---| | Metric | SIR_dB | | Secondary | permutation_recovery_rate | ## 📏 5. Operating Range (Ω) **Center problem class:** `instantaneous_ica` · **Forward operator:** `linear_mixing_determined` **Center point:** | Parameter | Unit | Value | |---|---|---| | M | — | 3 | | N | — | 3 | | T | — | 10000 | | Snr db | dB | 30 | | Kappa a | — | 10 | | Gaussianity | — | 0 | | Reverberation ms | ms | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | M | — | 2 – 20 | | N | — | 2 – 20 | | T | — | 500 – 200000 | | Snr db | dB | -10 – 40 | | Kappa a | — | 1 – 1000 | | Gaussianity | — | 0.0 – 1.0 | | Non stationarity | — | 0.0 – 1.0 | | Reverberation ms | ms | 0 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 dB SIR | Metric | Range | |---|---| | Sir db | 0.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **SIR_dB**, with κ = `100` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb87d084c9e96c8c7e8a5b7f3ee8fff943d311de91ac72536f677f6b3a829aff6` - **Chain tx hash:** `0xdcd8a3c56c9ef2e94ae4e1b2980a0a448b7e516246a119f7b4af40a727cc452b` - **Chain block:** `41555197` --- ## File Mapping This bundle consists of: `L1-388.md`, `L1-388.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-388.md` | Source of truth — edit this | Human or LLM | | `L1-388.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-388`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-388.md).
Regenerate L1-388.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

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L2-388-001 BSS Instantaneous-Mixing Spec (ICA benchmark family)

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📋 JSON metadata

{
  "artifact_id": "L1-388",
  "chain_block": 41555197,
  "chain_hash": "0xb87d084c9e96c8c7e8a5b7f3ee8fff943d311de91ac72536f677f6b3a829aff6",
  "chain_tx_hash": "0xdcd8a3c56c9ef2e94ae4e1b2980a0a448b7e516246a119f7b4af40a727cc452b",
  "domain": "Signal Processing",
  "hardness_fn": {
    "delta": 5,
    "kappa": 100,
    "metric": "SIR_dB",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "SIR_dB",
    "regime": "Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N \u003e M) requires sparsity prior.",
    "secondary": "permutation_recovery_rate"
  },
  "physics_fingerprint": {
    "L_DAG": 2.2,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Signal Processing",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.mix.linear",
      "int.temporal"
    ],
    "problem_class": "bilinear_blind_factorization",
    "sensing_mechanism": "linear_mixing",
    "solution_space": "independent_components",
    "sub_domain": "Statistical independence-based demixing",
    "title": "Blind Source Separation (ICA / cocktail-party problem)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "linear_mixing_determined",
      "linear_mixing_overdetermined",
      "convolutive_mixing",
      "underdetermined_mixing"
    ],
    "allowed_omega_dimensions": [
      "N",
      "M",
      "T",
      "SNR_dB",
      "kappa_A",
      "reverberation_ms",
      "gaussianity",
      "non_stationarity"
    ],
    "allowed_problem_classes": [
      "instantaneous_ica",
      "convolutive_bss",
      "nmf_bss",
      "speech_separation"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0 dB SIR",
      "forward_operator": "linear_mixing_determined",
      "input_format": "mixtures_only",
      "omega": {
        "M": 3,
        "N": 3,
        "SNR_dB": 30,
        "T": 10000,
        "gaussianity": 0.0,
        "kappa_A": 10,
        "reverberation_ms": 0
      },
      "problem_class": "instantaneous_ica"
    },
    "epsilon_bounds": {
      "sir_db": [
        0.0,
        40.0
      ]
    },
    "omega_bounds": {
      "M": [
        2,
        20
      ],
      "N": [
        2,
        20
      ],
      "SNR_dB": [
        -10,
        40
      ],
      "T": [
        500,
        200000
      ],
      "gaussianity": [
        0.0,
        1.0
      ],
      "kappa_A": [
        1,
        1000
      ],
      "non_stationarity": [
        0.0,
        1.0
      ],
      "reverberation_ms": [
        0,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Statistical independence-based demixing",
  "title": "Blind Source Separation (ICA / cocktail-party problem)"
}

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