--- license: apache-2.0 task_categories: - feature-extraction - question-answering tags: - structure-mapping - analogical-retrieval - zero-lexical-overlap - predicate-lattice - retrieval-benchmark - rare-events - reasoning - sma pretty_name: Structure Synthesis Benchmark (SSB) --- # Structure Synthesis Benchmark (SSB) ## Dataset summary The **Structure Synthesis Benchmark (SSB)** is a zero-lexical-overlap structural retrieval benchmark designed to test whether a retrieval system matches on **relational structure alone**, with no surface vocabulary shared between the query and the target analog. SSB is part of the SMA-1 evaluation suite (paper: *"Structure-Mapping Agentic Memory"*, Ayaz Khan, 2026, under review at *Nature Machine Intelligence*). **Headline result (from `reports/confirmatory/ssb_summary.csv`, seeds 41 and 43, n = 100 per seed):** | Method | Forced-choice r@1 | Library r@1 | |---|---|---| | SMA (structure-mapping) | **1.000** (SD 0.000) | **0.895** (SD 0.007) | | BM25 | 0.000 (SD 0.000) | 0.000 (SD 0.000) | | TF-IDF Dense | 0.000 (SD 0.000) | 0.000 (SD 0.000) | Cliff's δ = 0.895, p_Holm = 0.0004 (paired bootstrap, 10 000 resamples). --- ## Dataset construction ### Core principle: disjoint per-triple vocabularies Each benchmark triple (base, target, distractor) uses **independently sampled random functor names** so that the query and its true analog share **zero surface vocabulary**. The only bridge is a **declared predicate lattice**: the query functor and the analog functor are mapped to the same abstract concept in the lattice, and retrieval requires ascending at most δ = 2 hops (penalised by ρ^distance = 0.95^hops). This construction directly operationalises Gentner's systematicity principle: a system that matches on surface co-occurrence will score every candidate equally (zero lexical signal); only a system that ascends the predicate lattice to find structural correspondences will score the true analog higher. ### Previous (broken) construction — what we fixed Prior versions used a `far_` / `near_` prefix naming trick: the same functor vocabulary was reused across triples, and the "far" analog was simply the renamed version. This was circular — the benchmark unknowingly told the system which triple was the analog. The current generator eliminates this entirely: - Each triple receives a fresh randomly-sampled vocabulary (UUID-derived functor names with no shared substrings). - Distractors are star-rewired (provably non-isomorphic to chain-structured analogs for width ≥ 3) so a correct matcher cannot accidentally score a distractor 1.0. - The MAC screening stage uses the ancestor-closure feature vector (blueprint §2.7) so lattice-bridged vocabularies intersect at screening; the Lemma-2 bound remains admissible with ancestor features. ### Generation parameters (frozen at prereg-v1) | Parameter | Value | |---|---| | Lattice ascension depth δ | 2 hops | | Ascension penalty ρ | 0.95 per hop | | Structural width | ≥ 3 (chain structure) | | Vocabulary collision probability | < 10⁻⁶ (UUID-space) | | Seeds used in confirmatory runs | 41, 43 (n = 100 each) | | Seeds used in development / calibration | 29, 31 | --- ## Dataset splits | Split | Purpose | Seeds | n triples | Status | |---|---|---|---|---| | `dev` | Calibration (rho dial) | 29, 31 | 200 | Released | | `test` | Confirmatory evaluation | 41, 43 | 200 | Released | | `forced_choice` | One analog + one distractor per query | all | see above | Released | | `library` | Query against a pool of 24 indexed cases | all | see above | Released | The **forced-choice** split presents each query with exactly one true analog and one star-rewired distractor; r@1 = 1 means the system always ranks the analog first. The **library** split presents each query against a 24-case indexed library; r@1 measures whether the structural match tops the library ranking. --- ## Intended use SSB is intended as a **diagnostic test** for retrieval systems that claim to match on relational structure rather than surface similarity: 1. **Structural retrieval systems** (structure-mapping engines, SME-style, predicate-lattice-based) — the benchmark was designed to reward these. 2. **Ablation studies** — a system that degrades from structural to surface retrieval should drop from r@1 ≈ 1.0 to r@1 ≈ 0.0 on SSB. 3. **Unit testing** — the forced-choice split is included in the SMA-1 test suite as gate G4 (`test_macfac_lattice_bridges_disjoint_vocabularies`). SSB is **not** intended as a benchmark for: - General-purpose information retrieval (no natural language; no text documents) - Semantic similarity (there is no semantic content — functors are arbitrary symbols) - Knowledge graph completion (no real-world entities or relations) --- ## Limitations and caveats 1. **Synthetic by construction.** SSB uses randomly generated functor names and artificially constructed predicate lattices. Performance on SSB does not directly predict performance on real-domain retrieval tasks (see the 5-domain agentic suite in the SMA-1 paper for real-domain evaluation). 2. **The lattice is declared, not learned.** The predicate lattice used by SMA is supplied at evaluation time. A system without a compatible lattice (e.g. pure BM25, dense RAG) will score 0.000 by construction — the benchmark is a test of whether the mechanism exists, not how well it generalises to unseen lattices. 3. **Chain structure only.** The current generator uses chain-shaped base cases (linear predicate chains). Richer topologies (trees, DAGs) are not yet in the benchmark. 4. **Small n.** Confirmatory evaluation uses n = 100 per seed × 2 seeds = 200 triples. Statistical power is sufficient for the observed effect sizes (δ = 0.895) but marginal tests may lack power. 5. **Development contamination risk.** The calibration seeds (29, 31) were used to set the rho = 0.95 dial; confirmatory seeds (41, 43) were reserved and never inspected during development. The protocol is documented in `configs/preregistration.md`. --- ## Source repository ``` https://github.com/ayazkhan27/sma-1 ``` Generating script: `scripts/confirmatory_battery.py --task ssb` Confirmatory outputs: `reports/confirmatory/ssb_{rows,stats,summary}.csv` Gate test: `tests/test_macfac.py::test_macfac_lattice_bridges_disjoint_vocabularies` --- ## Citation ```bibtex @software{khan2026sma, author = {Ayaz Khan}, title = {SMA-1: Structure-Mapping Agentic Memory}, year = {2026}, license = {Apache-2.0}, url = {https://github.com/ayazkhan27/sma-1} } ``` --- ## License Apache-2.0. See `LICENSE` at the repository root. Benchmark construction uses no third-party data; all functor names are randomly generated. The predicate lattice is fully synthetic.