Source-linked AI summary
Same Problem, Different Field: Cross-Domain Solution Import via Domain-Stripped Computational Fingerprints
Eryk Kulikowski
TL;DR
Topical and citation-based scientific tools can miss papers in different fields that solve the same computational problem. The paper distills each paper into a domain- and method-name-stripped fingerprint and uses selectable similarity to surface candidate solver imports. It reports four executed imports, including an open solver reproducing a bespoke clinical dosing engine’s output.
Problem
Topical and citation-based embeddings can miss shared computations across fields, even when those papers solve the same underlying problem.
Source: §1 · p. 1Method
A cached LLM call creates a domain-stripped mechanism skeleton and controlled computational facets, with selectable similarity retrieving candidates and facet agreement filtering them.
Source: §1 · p. 2Results
Four executed cross-domain imports include an open solver reproducing a bespoke clinical dosing estimator’s output on its reference data.
Source: §1 · p. 2Takeaways & Limitations
The fingerprint surfaces cross-domain computational isomorphisms that standard scientific embeddings miss, with the four imports demonstrating the loop as verifiable candidates.
Source: §10 · p. 10In the wild, retrieval recovers 0.619 of known twins in the top 1000, and twins ranked below the retrieved pool remain unreachable by filtering.
Source: §9 · p. 9
Abstract
from arXiv · showhide
The same underlying computational problem is solved across unrelated fields under different names: recursive Bayesian state estimation appears as a "Kalman filter" in control, "Bayesian forecasting" in pharmacokinetics, and "data assimilation" in geoscience. Topical and citation-based scientific embeddings cannot see this shared problem. We distill each paper once into a domain- and method-name-stripped faceted computational fingerprint, a free-text mechanism skeleton plus controlled computational facets. We define a tunable, facet-selectable similarity over it. The goal is solution import: surface cross-field pairs solving the same problem, so a bespoke implementation can be swapped for another field's standard, specialized solver. On a benchmark of 18 method families across 109 papers, the skeleton lifts cross-domain retrieval average precision over the abstract from 0.222 to 0.513, and the whole fingerprint reaches 0.557. Strikingly, four trained scientific embedders all fall below plain abstract+TF-IDF: they encode topical and citation similarity, the wrong signal for this task. The gain is the representation: the abstract-to-skeleton swap lifts every embedder, and the pipeline is one cached LLM call per paper plus a cheap embedder. An interventional re-skin / math-edit test shows the fingerprint tracks the computation, not the field. On a 501-paper wild corpus, known twins dominate the top of the ranking (23 of the top 30); with planted pairs excluded from the results, three blind LLM judges rate 3 of the top 5 and 8 of the top 30 pairs genuine import candidates, and 0 of 30 random ones. The human verification is the four executed imports: in one, an open standard solver reproduces a bespoke clinical dosing engine's output. We release the benchmark, the code, and the distillation prompt.
1 Introduction
The paper targets cross-field papers that solve the same computational problem, which topical and citation-based tools can miss. It distills papers into domain-stripped computational fingerprints to retrieve potential solution imports, and reports four executed imports, including a clinical dosing solver reproduction.
1 Introduction
- Topical and citation embeddings can place papers far apart even when they share a computation, leaving the relationship and solver import unreported.The introduction illustrates this with dosing mathematics that also corresponds to mixture estimation and Kalman filtering.Source: §1 · pp. 1–2
- Solution import means replacing a bespoke implementation with another field’s standard, specialized solver for the same underlying problem.An import candidate is a cross-field paper pair proposed for that swap and awaiting verification.Source: §1 · p. 2
- A cached LLM call distills each paper into a domain-stripped mechanism skeleton and controlled computational facets, over which selectable similarity retrieves and filters candidate twins.A human confirms the survivors.Source: §1 · p. 2
- The retrieve-then-filter operator combines broad fingerprint-text retrieval with facet agreement that narrows candidates, supporting a tunable precision/recall trade-off.The introduction also reports a 501-paper wild corpus: known twins account for 23 of the top 30, while blind judges rate 8 of the top 30 unplanted pairs genuine and 0 of 30 random pairs.Source: §1 · p. 2
- Four executed cross-domain imports include an open-solver reproduction of a bespoke clinical dosing estimator on its reference data.The authors frame surfaced pairs as candidates, not proof, until verified.Source: §1 · p. 2
- The curated benchmark measures retrieval given a known swappable cross-field twin; whether arbitrary papers have such a twin remains an open-world question.The wild-corpus study probes that question directly.Source: §1 · p. 2
2 Related work
Prior work bridges fields through analogy, literature-based discovery, scientific embeddings, facet-based representations, and conditional similarity. This paper instead strips domain vocabulary and method names to retrieve shared computations that papers may not state or cite.
Bridging domains: analogy and literature-based discovery
- Analogy-mining systems match purpose and mechanism over surface text, while this work strips domain vocabulary and method names to match computation.Literature-based discovery links literatures through shared concepts, whereas the targeted pairs may share no terms, citations, or concepts.Source: §2 · pp. 2–3
Scientific document embeddings
- Citation-trained scientific embeddings capture topical similarity, while the paper positions computational structure as an additional axis that text and citation clustering miss.SemCSE-Multi uses aspect-specific summaries but enriches and names within a domain rather than using cross-field disagreement as a signal.Source: §2 · p. 3
Faceted representations and method extraction
- Existing faceted representations and method-extraction systems generally use topical or task-oriented facets and citation-graph learning; this work distills domain-stripped computational facets.The representation is intended to reach independently reinvented twins that do not cite one another.Source: §2 · p. 3
LLM-generated representations and idea recombination
- Related idea-generation systems rely on author-stated links, cited concepts, or generated recombinations; this method retrieves computational isomorphisms papers do not explicitly state.Its positioning is that an LLM-written, domain-neutral skeleton can carry retrieval signal even with a bag-of-words representation.Source: §2 · p. 3
Conditional similarity and retrieve-then-filter
- Conditional similarity systems let users choose what counts as similar, but here the selected facets describe computation with domain and method names removed.The resulting precision/recall frontier runs across fields rather than within one.Source: §2 · p. 3
3 The faceted computational fingerprint
The paper represents each paper with a domain- and method-name-stripped mechanism skeleton and controlled computational facets, then uses selectable similarity to retrieve cross-field solution matches. Its design separates broad text-based retrieval from facet-based filtering, making precision and recall adjustable.
3.1 The mechanism skeleton (the retrieval signal)
- The skeleton describes what a paper computes and how, removing domain vocabulary and canonical method names so matches rely on shared mathematical structure.For the dosing example, the mechanism is estimation of a mixing distribution over latent entity parameters, rather than population pharmacokinetics or a named method.Source: §3.1 · pp. 3–4, Figure 2 · p. 4
3.2 The controlled computational facets (the filter layer)
- Six controlled computational facets plus a DOMAIN axis describe structure, data, inference, problem form, distribution, and complexity, with structure and distribution designed to support precision.DOMAIN and PROBLEM_FORM are recall drivers; the facets are not assumed to be independent, so a corrupted facet need not poison the others.Source: §3.2 · p. 4
3.3 The tunable similarity and retrieve-then-filter
- A blended alternative combines normalized fingerprint cosine and facet agreement, with the best mixing weight near α = 0.4.The paper distinguishes the distillation prompt, which improves vectors, from facet selection and aggregation, which choose a precision/recall operating point.Source: §3.3 · p. 4, §3.4 · p. 4
- Retrieve-then-filter first ranks cross-field pairs by fingerprint-text similarity, then keeps pairs agreeing on at least k selected facets, trading recall for precision as k rises.The text stage can use BM25, followed by a keyword-field facet filter; one cached distillation per paper supplies the reusable fingerprint.Source: §3.3 · p. 4
3.4 Two levers, and what is new
- The claimed novelty is a selectable conjunction of domain-stripped computational facets that traces an explicit precision/recall frontier for cross-field solution import.The paper treats the computational-isomorphism operator—high structural similarity but far apart in domain—as the operator validated here.Source: §3.4 · pp. 4–5
4 The benchmark and data
The benchmark uses a curated set of papers with complete twin labels to compare retrieval methods, and a larger corpus to examine rankings in the wild. Its families represent known swappable mathematical cores across fields, while topical distractors test whether retrieval follows computation rather than subject matter.
4 The benchmark and data
- The curated benchmark contains 109 papers across 18 method families and 92 queries with complete labels; the 501-paper extended corpus is used for the wild run.The benchmark compares retrieval methods; on the extended corpus, only planted twins are labeled, so precision and average precision are not treated as benchmark metrics.Source: §4 · p. 5
- Each family represents a mathematical core known to be swappable, making a matched bespoke implementation and standard solver an actionable import candidate.The families include distant applications such as political methodology and digital-humanities stylometry, intended to test structural rather than topical matching.Source: §4 · p. 5, Table 1 · p. 5
- Topical distractors use different mathematics in a member’s field, while name-free exemplars use a family’s method without naming it.Examples include an unnamed pharmacokinetics support-point estimator and kriging as an unnamed Gaussian process.Source: §4 · p. 5
- A positive twin is a cross-field pair sharing a family label; the curated corpus derives all such pairs, yielding 210 twins among 5,812 pairs.The extended corpus labels only planted twins, so recall of known twins is the scale measure used there; unlabeled pairs are not counted as errors.Source: §4 · pp. 5–6
5 Results: the retrieve layer
The retrieve layer represents papers by their computation rather than their field vocabulary, then uses that representation to find cross-domain papers solving the same problem. Across curated and wild-corpus evaluations, retrieval surfaces cross-field matches, while an intervention tests whether fingerprints track computation rather than topical wording.
5.2 Controlled comparison: same embedder, different input
- Under TF-IDF, replacing the abstract with the skeleton raises AP from 0.222 to 0.513, P@1 from 0.55 to 0.82, and MRR from 0.67 to 0.86.The reported paired-bootstrap intervals for the TF-IDF MRR and P@1 gains exclude zero.Source: §5.2 · p. 6
5.3 Ablation, distiller robustness, and scale
- Domain stripping adds more retrieval lift as the embedder grows more topical, reaching a significant +0.104 under citation-trained SPECTER, while its TF-IDF margin is small and uncertain.The abstract-to-skeleton gain holds across both distillers; excluding three two-member families leaves AP essentially unchanged at 0.568 versus 0.557.Source: §5.3 · p. 6, Table 3 · p. 7
- In the wild, known-twin recall is 0.619 in the top 1,000 ranked pairs versus 0.229 for the abstract; STRUCTURE-“none” skips 40 of 64 deliberately non-mathematical papers.The 501-paper wild-corpus evaluation is detection rather than a scored benchmark.Source: §5.3 · p. 6
5.4 Per-family results, distant domains, and the name-free audit
- Seventeen of 18 method families exceed cross-domain P@1 0.5, and held-out-family P@1 is 0.859 versus 0.826 with the full-corpus vocabulary.The held-out vocabulary result is reported as effectively zero-shot retrieval.Source: §5.4 · pp. 6–7
5.1 Retrieval on the curated benchmark
- Fingerprint+TF-IDF reaches AP 0.557 versus 0.222 for abstract+TF-IDF on the curated benchmark; the fingerprint tops the grid and lifts all four scientific embedders.The abstract-to-skeleton swap improves retrieval under every embedder, while dropping DOMAIN still gives AP 0.522 and DOMAIN alone scores 0.094.Source: §5.1 · p. 6, Table 2 · p. 7
5.4 Per-family results, distant domains, and the name-free audit
- Name-free exemplars retrieve cross-field twins, including a sports-analytics PageRank paper paired with an Eigenfactor paper that never says “PageRank”; 465 of 501 skeletons are name-free under the pinned list.The fully name-free exemplars retrieve a same-core twin at rank 1.Source: §5.4 · p. 7
5.5 Construct validity: candidates in the wild
- With planted pairs excluded, blind judges rate 3 of the top 5 and 8 of the top 30 surfaced pairs as genuine import candidates, versus 0 of 30 random pairs.The ranking is presented as candidate discovery for human confirmation, not proof of swaps.Source: §5.5 · p. 7
5.6 Interventional test
- For 10 papers, fingerprint cosine self-similarity is 0.72 under a re-skin and 0.46 under a math-edit, while the abstract shows 0.50 versus 0.55.The rewrites were written by a different model from the distiller; the reported interaction is +0.32, with the predicted direction for 8 of 10 papers.Source: Table 5 · p. 8, §5.6 · p. 8
6 Results: the faceted operator
The fingerprint’s core facets let users trade recall for precision on the curated benchmark, while facet agreement alone is weaker than the text representation. Adding verifiability facets to similarity hurts performance; those facets serve a separate value metric.
The precision/recall frontier
- 0.94 precision at 0.15 recall with all four facets, versus 0.18 at 0.87 when flat, on the curated benchmark’s top-1,000 retrieved pairs.Requiring two facets gives 0.28 precision at 0.68 recall; requiring all four gives 0.94 at 0.15.Source: Table 6 · p. 8, §6 · p. 8
Facet agreement alone
- On the curated benchmark, facet-only AP is 0.391 log-LR-weighted and 0.338 raw, below skeleton 0.513 and whole-fingerprint 0.557, but above abstract TF-IDF 0.222.The engineered combined similarity does not beat the plain fingerprint.Source: §6 · p. 8
Verifiability facets
- Folding verifiability facets into similarity hurts it; those facets instead feed a separate value metric.Source: §6 · p. 8
7 Analysis: representation, distiller, and embedder
The representation matters more than the embedder or distiller size: plain TF-IDF tops distilled rows, and coarse, consistent facet labels outperform finer labels on these benchmarks. The distiller ordering is bounded by family granularity and a format-control caveat.
Relative size of the levers
- Plain TF-IDF tops every distilled row, while trained embedders come closest on the free-text skeleton and fall farthest behind on the controlled-vocabulary fingerprint.The model effect is small for the skeleton, but the larger model hurts on the faceted operator.Source: §7 · pp. 8–9
Distiller granularity
- Haiku’s whole-fingerprint AP is 0.557 versus qwen3:14b’s 0.396 on the curated benchmark, despite Haiku producing 96 versus 190 mechanism-text words.The passage attributes the result to coarse, consistent labels matching across same-problem papers.Source: §7 · p. 9
- On the extended corpus, Haiku’s combined-similarity AP is 0.330 versus Opus’s 0.159, and its facet-only AP is 0.194 versus 0.031.Source: §7 · p. 9
- The family labels are deliberately coarse, so finer correct splits may score as losses; qwen3:14b was not format-controlled, making local-arm orderings indicative rather than controlled.Whether the ordering holds for finer-grained families is untested.Source: §7 · p. 9
8 Executed cross-domain imports
The paper executes four cross-domain imports, including a standard support-point solver that reproduces a bespoke clinical dosing engine on that engine’s own example data. The other three demonstrate the import mechanism on synthetic or special-case data rather than external head-to-heads.
The surfaced candidate
- The clinical dosing fingerprint links NPAG’s bespoke estimator to nonparametric mixture estimation, the same computation used by solvers in machine learning, astronomy, and nuclear physics.NPAG estimates a population parameter distribution as discrete support points maximizing joint likelihood; the tool surfaces the equivalence as an import candidate.Source: §8 · p. 9
The executed reproduction
- On NPAG’s own rifapentine example, the standard solver matches clearance to 2.5% and recovers sparse support with 15 versus 18 points; individual prediction error is 11.8%.The reproduction uses a fixed grid rather than NPAG’s adaptive grid, so the match is excellent rather than bit-exact.Source: §8 · p. 9
Actionability, and three further imports
- Three further imports reproduce causal-panel matrix completion, Gaussian-process kriging, and Needleman-Wunsch sequence alignment equivalences.The causal-panel import cuts counterfactual error by 69% on a synthetic low-rank panel; the other checks use synthetic or special-case data.Source: §8 · p. 9
- Only the vancomycin case is checked against an external reference; the skeleton flags candidates but does not perform the omitted algebra or automated verification.Source: §8 · p. 9
9 Discussion
The representation is the central contribution, with facets serving as a tunable precision filter rather than an accuracy champion. Recall limits the tool’s use as a triage aid, and the operator is scoped to literature with explicitly stated, distillable computational methods.
Contribution of each component
- The representation is the contribution; facets act as a tunable precision filter, while the operator traces the precision/recall frontier and supports clustering and rule-mining views.Source: §9 · p. 9
The recall ceiling
- The top 1,000 of 82,786 ranked pairs recover 0.619 of known twins versus 0.229 for abstracts, but 0.38 of twins rank below the retrievable pool.With planted pairs excluded, the top 30 yield 8 pairs judged genuine; recall is the binding constraint, so the tool is positioned for short-list triage rather than exhaustive search.Source: §9 · pp. 9–10
Applicability
- The pipeline applies to literature whose papers state a computable method explicitly enough to distill; qualitative and purely argumentative literatures are outside its scope.Source: §9 · p. 10
Limitations and threats to validity
- The unlabeled 501-paper corpus makes measured faceted precision a strict lower bound, but its average precision is not a score because missing positives alter hits and the positive-set denominator.The benchmark is arXiv-weighted toward fields that state mathematics explicitly, and curated families measure retrieval given that a twin exists.Source: §9 · p. 10
10 Conclusion and future work
The paper concludes that a domain-stripped computational fingerprint surfaces cross-domain computational isomorphisms missed by standard scientific embeddings, and four executed imports demonstrate the loop end to end. The same distillation can support other domain-stripped lenses, while future work includes reading a value metric from rare, high-lift facet combinations.
10 Conclusion and future work
- A faceted computational fingerprint surfaces cross-domain computational isomorphisms missed by standard scientific embeddings, and four executed imports demonstrate the loop end to end.The gain is attributed to the representation.Source: §10 · p. 10
- The skeleton carries most retrieval signal, the whole fingerprint is strongest, facet conjunctions provide tunable filters, and labels feed a classifier.The classifier uses the log-LR weighting of Section 6.Source: §10 · p. 10
- The same distillation can emit domain-stripped lenses for result verifiability, claim novelty, and method evaluation; a companion study predicts replication outcomes where citation metrics fail.Future work reads a value metric from rare, high-lift facet combinations.Source: §10 · p. 10
- The benchmark, distillation prompts, skeletons, and evaluation code are released with reproducibility metadata and archived data.Versioned link-lists and checksums reproduce the corpus from open sources; the CC-BY subset and metadata are DOI-archived, and the code is permissively licensed.Source: §10 · p. 10