---
slug: sparse_distributed_activation_coding
name: Sparse Distributed Activation Coding
one_liner: "A representational scheme in which each instance activates a small, content-specific subset of a much larger pool of units, so representational capacity comes combinatorially from which few units are active."
type: prime
schema_version: 2
status: density_v2_draft
categories: [computational, structural, biological]
origin_domain: computational_neuroscience
alternate_origin_domains: [machine_learning, immunology, information_retrieval]
aliases: [sparse_subset_representation, k_of_n_activation, combinatorial_sparse_code, active_fraction_coding, small_active_set_representation]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-05 generalization) — the proposed GENUS of `sparse_coding` (lift: strip the signal-processing/dictionary framing and keep only the general fact that each instance recruits a small content-specific active subset of a large unit pool). Discovered in the op-05 remaining-strata sweep 2026-07-03. Tier B (B-rest) candidate. Domain-spread flag: siblings claimed span neuroscience (grandmother-cell / sparse vs dense codes), immunology (combinatorial receptor repertoires), and information retrieval (keyword-tag sets from a large vocabulary) — three genuinely unlike representational systems. Distinctness flag: proposed distinct from `classification`/`partition` primes (which assign to ONE category; this genus activates a SUBSET and gains combinatorial capacity from the choice of which)."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Phase-C action: re-similarity-check vs `sparse_coding` (the input) and any `classification` / `partition` / `distributed_representation` / dictionary-learning prime; confirm it is a genuine genus (covers the input AND the neuroscience/immunology/tagging siblings) and not a restatement of the input, nor an alias of a distributed-representation prime; draw a subsumption edge input→candidate + sibling edges at incorporation; sync one_liner to a v1 draft per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 4
  structural_abstraction: 4
  transfer_evidence: 3
  reasoning: 'The bare structure — a large pool of candidate units, each instance represented by activating a small content-specific fraction of them, with capacity and specificity arising combinatorially from which subset is active rather than from any single unit — is a clean, medium-neutral representational form. It recurs across neural codes, immune repertoires, and tag/index systems, which is genuine breadth and high structural abstraction. Transfer sits at 3 because the sharpest formal treatments are in neuroscience and ML (sparsity, combinatorial capacity), while the immunology and tagging instances, though real, are looser. Composite 4: a strongly substrate-independent structure, above its dictionary-specific input.'
similarity_to_nearest_existing_prime:
  slug: sparse_coding
  similarity: 0.72
structural_framed:
  label: structural
  aggregate: 0.2
  criteria: {vocab_travels: 0.1, evaluative_weight: 0.05, institutional_origin: 0.3, human_practice_bound: 0.25, import_vs_recognize: 0.3}
  rationale: 'The pattern is a representational structure: a small active subset drawn from a large pool, with combinatorial capacity from the choice of active units. It carries no evaluative content, its vocabulary (pool, active subset, sparsity, combinatorial capacity) travels across neuroscience, ML, immunology, and indexing, and it is recognized as a bare structure rather than imported as a doctrine. Reads clearly structural.'
phase_b_passes_completed: []
---
# Sparse Distributed Activation Coding

## Core Idea

The genus is this bare structure: a system represents each instance by *activating a small subset of units drawn from a much larger pool*, where the active subset varies systematically with the content, so the representation's capacity and discriminating power come *combinatorially from the choice of which few units are active* rather than from the state of any single unit. The pool is high-dimensional; the active fraction is tiny; the identity of the active set is the code. The one constraint stripped from the input `sparse_coding` is the *signal-processing / dictionary-learning framing* — the input is specifically about reconstructing a signal as a sparse linear combination of dictionary atoms (an optimization over coefficients with a sparsity penalty) — whereas the genus keeps only the abstract "small content-specific active subset of a large pool" structure, dropping the linear-reconstruction and learned-dictionary commitments.

The load-bearing anatomy has three parts. First, a *large candidate pool*: many more available units than are used for any one instance. Second, *sparse per-instance activation*: each instance recruits only a small fraction, so activity is sparse. Third, *content-specific subset identity*: which units are active is a systematic function of what is being represented, so the active set carries the information. The characteristic payoff is *combinatorial capacity with cheap specificity and interference-resistance*: the number of representable instances scales with the number of ways to choose small subsets (enormous), overlapping representations share few units so cross-talk is low, and the code is energy/metabolically or storage-cheap because most units are silent. The characteristic cost/failure is the mirror: sparsity trades away *robustness of any single instance* (losing the few active units erases that representation — there is little redundancy per instance) and pushes complexity into *decoding and binding* (a downstream reader must know the subset→content map, and superposing several sparse codes risks confusable overlap if the pool or sparsity is set wrong).

Walk the claimed siblings and the lift shows across structurally-unlike systems. In *neuroscience*, sparse (near-grandmother-cell) population codes contrast with dense codes: a stimulus activates a small, specific set of cells out of a large population, and the code lives in which cells fire. In *immunology*, the adaptive repertoire represents the space of antigens by a small, combinatorially-generated set of receptor specificities drawn from an astronomically large potential pool — any one antigen engages a tiny content-specific subset. In *information retrieval / tagging*, a document is represented by a small keyword-tag set selected from a large controlled vocabulary, and the identity of the chosen tags is the representation. Neural populations, immune repertoires, and tag vocabularies are three unlike systems; each represents instances by a small, content-specific active subset of a large pool.

## Notes

**Provenance.** Produced by operator 05 (generalization / lift) as the proposed GENUS of the input prime `sparse_coding`, by stripping the dictionary/linear-reconstruction framing and keeping only the small-active-subset-of-a-large-pool representational structure. Surfaced in the op-05 remaining-strata sweep on 2026-07-03, listed as a Tier-B (B-rest) candidate in `manifest_op05_rest.yaml`. It claimed three siblings — sparse-vs-dense neural coding, combinatorial immune repertoires, and keyword-tag sets — spanning neuroscience, immunology, and information retrieval.

**For owner evaluation (keep/cut).** The case FOR: the input `sparse_coding` is tied to a specific machinery (dictionary atoms, sparse linear reconstruction, an L1/L0-penalized optimization), and the lift genuinely broadens it to representational schemes that share the sparse-subset structure without the reconstruction machinery — immune repertoires and tag sets are not dictionary reconstructions but do instantiate the genus, which is real added coverage. Substrate-independence is high and the payoff/cost (combinatorial capacity vs per-instance fragility) transfers cleanly. The specific RISKS: (1) **High similarity to the input (~0.72)** — the strongest cut signal. "Sparse coding" is already used loosely in neuroscience to mean roughly this genus, so the lift risks being a *restatement* of the input under a longer name; Kurt should judge whether the immunology/tagging siblings are coverage the input truly excludes, or whether `sparse_coding` was already meant broadly. (2) **Alias risk vs a `distributed_representation` prime** — if the corpus holds distributed / population-coding primes, this may be the *sparse* pole of that family rather than a standalone prime; the boundary (sparse subset vs dense distributed) must be drawn deliberately. (3) **Tier-B coinage** — the exact label "sparse distributed activation coding" is bespoke; the components are established but the cross-domain genus phrasing is the coinage, and "sparse" + "distributed" sit in tension (grandmother-cell-adjacent vs fully distributed) that Kurt may want tightened. **Sharp keep/cut question for Kurt: does this genus add coverage (immune repertoires, tag sets) that `sparse_coding` genuinely lacks — or is it `sparse_coding` restated, better handled by broadening that prime and, if needed, siting it under a distributed-representation parent?**

**At incorporation.** Re-run similarity against the input `sparse_coding` FIRST (0.72 makes restatement the live risk) and against any `distributed_representation` / population-coding / `classification` / `partition` prime. If it survives as distinct, draw a subsumption edge `sparse_coding → sparse_distributed_activation_coding` and sibling edges across the neural/immune/tagging instances; add a missing-edge note if a distributed-representation prime should be the parent (this being its sparse pole). If it fails the restatement test, recommend broadening `sparse_coding` instead of keeping both. Tighten the sparse/distributed tension in the name before merge. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
