The Missing Parts
Part of the cognition series. Builds on The Parts Bin.
The 3×3 problem
The Parts Bin ended with two grids, Filter and Attend, where every cell filled with a known algorithm. That validates the axes: selection semantics × error guarantee partitions Filter cleanly, output form × redundancy control partitions Attend cleanly. No misplacements, no awkward fits.
But a grid where every cell fills on sight is a catalog, not a periodic table. Mendeleev’s grid had blanks. He predicted germanium’s density, melting point, and oxide formula before anyone found the element. I-Con (2025) did the same for Consolidate: a blank cell in their periodic table led to a new algorithm that beat the state of the art.
Can the parts bin do this? Where are the genuine blanks?
Filter: the causal row
The existing Filter grid has three rows: predicate, similarity, dominance. All nine cells are occupied. To find a blank, we need a fourth row where the selection semantics are genuinely different and at least one error-guarantee column is empty.
Causal filtering: select items by whether they causally affect an outcome. Correlation is similarity filtering. Dominance across objectives is dominance filtering. Causal means: if you intervene on this item, the outcome changes.
| Exact | Bounded | Probabilistic | |
|---|---|---|---|
| Predicate | WHERE, range query | Threshold filtering | Bloom filter |
| Similarity | Exact NN pruning | k-NN radius pruning | LSH filtering |
| Dominance | Pareto filtering | ε-dominance | Stochastic dominance |
| Causal | do-calculus gate | blank | Propensity score gate |
Causal × Exact: Given a fully identified causal graph, select items on active causal paths. The do-calculus gives the criterion; applying it as a binary gate is deterministic. This exists in theory (the backdoor criterion, the front-door criterion) but isn’t packaged as a standalone filter. Call it a do-calculus gate: pass items with nonzero causal effect under the identified model, reject the rest. The pieces exist. The assembly doesn’t.
Causal × Probabilistic: Propensity score gating. Discard items with treatment probability below a threshold. Practitioners use propensity scores for weighting (IPW), not hard gating. Truncated IPW, which discards extreme-propensity items, is a probabilistic filter. Borderline occupied.
Causal × Bounded: Filter items whose estimated causal effect exceeds a threshold, with bounded false-positive and false-negative rates. This is the genuine blank.
The pieces exist in three separate literatures. For scores: doubly robust estimators, honest causal forests, R-learners. For uncertainty: conformalized effect intervals, influence-function CIs. For the decision rule: knockoff filters, e-value procedures, class-conditional conformal risk bounds. Adjacent work in safe treatment policy learning gets close but optimizes a policy (Consolidate), not a gate (Filter).
No one has composed these into a single filter operation with the contract: strictly smaller, causal criterion, bounded error. The composition would look like:
- Score: DR-learner or causal forest → CATE estimate per item
- Bound: conformalized effect interval or bootstrap CI
- Gate: threshold on lower confidence bound, with BH/e-LOND error control
- Abstain region: items with CIs spanning zero are rejected, keeping the operator a filter rather than a policy
Real problems want it: personalized medicine (filter patients who will benefit from treatment), policy evaluation (filter interventions with causal impact), ad targeting (filter users causally affected, not just correlated with conversion).
Attend: saturated
The Attend grid fills completely. Set output, allocation, rejection — every extension tried reduces to existing algorithms. No blanks at this resolution.
Perceive: a second blank
Perceive has no grid. A first sketch:
| Fixed codebook | Learned codebook | |
|---|---|---|
| Batch | Lexical analysis, JSON parsing | BPE tokenization |
| Stream | A/D conversion | blank |
Learned codebook × Stream: Adapt the encoding as data arrives. BPE is learned offline. Recent vocabulary adaptation work is still offline: Adaptive BPE (Balde et al. 2024), PickyBPE (Chizhov et al. 2024). Generic online encoders exist — online dictionary learning (Mairal et al. 2010), Growing Neural Gas (Fritzke 1994) — but neither satisfies the Perceive contract: parseable by downstream, backward-compatible, stable enough to avoid catastrophic retokenization. This blank is less developed than the causal filter. The spec is shorter: online merge/split of codebook entries, bounded retokenization rate, predictive-utility objective. The literature is thinner. It belongs on the list but isn’t ready for a composition sketch.
What the blanks tell us
Mendeleev predicted germanium’s density before anyone found the element. I-Con predicted a new algorithm. These blanks predict something more specific: compositions. The pieces exist. The contract names what they must satisfy when assembled. The grid writes the spec.
The causal filter blank has a 4-step composition sketch, six literature entry points, and three application domains waiting. That’s not “something goes here.” That’s a build order.
Written via the double loop.