Historical Synthesizability Prior

• Historical synthesizability prior is defined as a bias leveraging empirical reaction records and experimental data to favor practically realizable molecules and materials.
• It integrates diverse data sources—from retrosynthetic precedents to thermodynamic windows—to bridge theoretical design with laboratory feasibility.
• The approach guides synthesis-aware optimization by balancing target performance with historical experimental attainability in molecular and materials discovery.

Searching arXiv for the cited papers and closely related synthesizability work to ground the article. arXiv search: "Historical synthesizability prior molecules materials synthesizability" A historical synthesizability prior is a bias, score, or probability-like criterion that favors candidates lying in the subset of design space that is consistent with prior evidence of successful realization. In the molecular and materials literature, this evidence is drawn from recorded reactions, retrosynthetic precedent, purchasable starting materials, experimental crystal databases, discovery timelines, or reported synthesis conditions, rather than from thermodynamic stability alone. The concept is not introduced as a single formal object across the literature, and several papers explicitly state that they do not define a Bayesian prior by that exact name. Nevertheless, they operationalize the same idea: synthesis-aware generation or screening should privilege structures that align with historical synthetic knowledge, historical experimental outcomes, or experimentally validated thermodynamic windows, because high in silico scores are not sufficient if the target cannot be made (Gao et al., 2020).

1. Definition and conceptual scope

In de novo molecular design, the core motivation for a historical synthesizability prior is the observation that generative models can “perform well on popular quantitative benchmarks” while still producing compounds that “are not practically synthesizable” (Gao et al., 2020). In that setting, the prior is best understood as a preference for molecules that admit a plausible retrosynthetic route to commercially available starting materials under a fixed computer-aided synthesis planning workflow. This is explicitly a historical-data-driven notion, because the workflow is trained on recorded reactions and constrained by purchasable building blocks, even though the authors state that it is “not a necessary or sufficient condition for true experimental synthesizability” (Gao et al., 2020).

In inorganic materials discovery, the same term denotes several distinct but related objects. One class of methods learns from the historical record of experimentally realized compounds and discovery dates, treating previous synthesis outcomes as empirical evidence about which hypothetical crystals are likely to be experimentally realizable (Aykol et al., 2018, Song et al., 2024, Ebrahimzadeh et al., 22 Oct 2025). Another class computes a physically grounded proxy: a finite-temperature, pressure-dependent “synthesizability window” defined by the region of $(T,p)$ space in which the target phase is the lowest-Gibbs-free-energy solid phase (Tadge et al., 26 May 2026). These approaches differ in mechanism, but all shift attention from static stability criteria to experimentally actionable attainability.

A common misconception is that synthesizability is equivalent to convex-hull stability, formation energy, or low structural complexity. The papers consistently reject that equivalence. They argue that experimentally synthesized materials can be metastable, that thermodynamically favorable candidates may remain unrealized, and that heuristic complexity scores are informative but imperfect proxies (Tadge et al., 26 May 2026, Song et al., 2024, Gao et al., 2020). This suggests that a historical synthesizability prior is not a single scalar law, but a family of synthesis-aware constraints derived from precedent, empirical realization, or equilibrium synthesis conditions.

2. Molecular generative models and retrosynthetic accessibility

In molecular generation, the most direct operationalization is the ASKCOS-based benchmark introduced for evaluating whether proposed molecules are “synthesizable” under a fixed retrosynthetic search. A molecule is counted as synthesizable if ASKCOS can find a route to commercially available starting materials using the following search limits: maximum search depth $=9$, maximum branching ratio $=25$, maximum wall time $=60\,\mathrm{s}$, maximum cumulative probability for target $=0.999$, maximum number of templates $=1000$, maximum price for starting materials $=\$100/\mathrm{g}$, and minimum plausibility$=0.1$. The search stops as soon as any pathway is found, not necessarily the best one (Gao et al., 2020).

Under this definition, random samples of 3000 molecules show large differences across datasets: MOSES, 89.8%; ZINC, 60.8%; ChEMBL, 68.3%; and GDB17, 3.5% (Gao et al., 2020). The interpretation given in the paper is that MOSES is high because it was curated to avoid problematic structures, whereas GDB17 is extremely low because it contains many enumerated theoretical molecules. For distribution-learning generators on MOSES and ChEMBL, generated samples “largely track the training set,” and no method improves synthesizability beyond the training distribution. This is presented as evidence that training-set composition itself functions as a bias toward more accessible chemistry when the source data are already more synthesizable (Gao et al., 2020).

The strongest failure mode appears in goal-directed generation. Across the hard GuacaMol objectives, the total fraction of synthesizable compounds in the top-100 suggestions is only 30.2% for ChEMBL-trained models and 32.7% for MOSES-trained models without heuristic biasing. With heuristic biasing, the ChEMBL-trained figures rise to 80.2% with SA_Score and 55.4% with SCScore; the MOSES-trained figures rise to 77.2% with SA_Score and 58.0% with SCScore (Gao et al., 2020). The paper also reports tasks where “very few or no compounds in the top 100 are synthesizable” without biasing, especially for SMILES GA and Graph GA, implying that post hoc filtering can leave no usable candidates.

Three heuristic proxies are evaluated against ASKCOS labels treated as ground truth for “synthesizable vs unsynthesizable”: SA_Score, SCScore, and SMILES length. Their reported AUC values are 0.87, 0.61, and 0.69, respectively (Gao et al., 2020). The paper stresses that agreement is “imperfect but meaningful,” because synthetic accessibility is nonlinear with respect to structure. To incorporate these proxies into optimization, the primary objective is multiplied by a normalized modifier shaped either as a Gaussian-like function or a sigmoid: $Modifier= \begin{cases} 1& \text{%%%%8%%%%}\ e^{-\frac{(x - \mu)^2}{2 \sigma}}& \text{%%%%9%%%%} \end{cases}$ and

$Modifier = 1 - \frac{1}{1 + e^{a(x-b)}}.$

Hyperparameters were tuned with 30 iterations of Tree Parzen Estimator Bayesian optimization, maximizing the fraction of synthesizable suggestions times the average objective value of the top 10 molecules from the graph genetic algorithm (Gao et al., 2020).

The resulting picture is explicitly a trade-off. Biasing almost always improves the fraction of tractable molecules, “although doing so necessarily detracts from the primary objective” (Gao et al., 2020). The practical recommendation is therefore a staged workflow: optimize without biasing, filter for synthesizability, and rerun with SA_Score bias if filtering leaves too few feasible candidates. In modern terms, this is an empirical argument that synthesis-aware optimization requires an explicit prior over historically accessible chemistry.

3. Inorganic materials: thermodynamic windows and historical discovery dynamics

For inorganic solids, one line of work replaces static hull-based screening with finite-temperature phase predominance diagrams. The method computes the Gibbs free energy as a function of temperature and reactive-gas partial pressure, then identifies the region in which a target compound is the minimum-free-energy solid phase. That region is the “synthesizability window” (Tadge et al., 26 May 2026). The thermodynamic formulation begins from

$=9$0

with fitted elemental reference energies

$=9$1

obtained from

$=9$2

At finite temperature,

$=9$3

with

$=9$4

and

$=9$5

Reactive-gas effects enter through

$=9$6

The heat capacity is fit to the HSC Chemistry Kelley form

$=9$7

The authors use DFT relaxations, FERE correction, and the MatterSim machine-learned interatomic potential for phonon-derived vibrational entropy and heat capacity, arguing that this gives a drastic reduction in computational cost relative to DFT phonons (Tadge et al., 26 May 2026).

The scope includes oxides, nitrides, sulfides, phosphides, and 48 ternary metal phosphosulfide systems. Several compounds that are metastable at $=9$8 are predicted to have finite-temperature stability windows, including $=9$9, $=25$0, $=25$1, $=25$2, $=25$3, and slightly metastable $=25$4 (Tadge et al., 26 May 2026). Binary-system validation against experimental thermochemical databases and reported synthesis conditions yields “phase-boundary temperature errors around 270 K MAE overall,” and the workflow scales to high throughput at roughly 30 core-minutes per material for DFT relaxation plus 5 core-minutes per material for MLIP phonon and thermochemical calculations (Tadge et al., 26 May 2026). The limitation is explicit: this is an equilibrium model that neglects kinetic barriers, defect stabilization, some configurational entropy, and some volatile-species effects.

A second line of work infers synthesizability from the historical evolution of a materials stability network rather than from finite-temperature thermodynamics. In that framework, nodes are stable materials, edges are tie-lines on the convex free-energy surface, and discovery time is approximated by the earliest cited structural reference in ICSD or COD (Aykol et al., 2018). The network grows from 1945 onward in 5-year increments, obeying

$=25$5

and after the 1980s its degree distribution is close to

$=25$6

The six node-level features are degree or degree centrality $=25$7 and $=25$8, eigenvector centrality $=25$9, mean shortest path length $=60\,\mathrm{s}$0, mean degree of neighbors $=60\,\mathrm{s}$1, and clustering coefficient $=60\,\mathrm{s}$2. Using a sliding window of width $=60\,\mathrm{s}$3 time steps, the model estimates

$=60\,\mathrm{s}$4

with $=60\,\mathrm{s}$5-regularized logistic regression for calibrated probabilities and random forest for classification accuracy (Aykol et al., 2018). Feature-importance analysis shows degree and degree centrality contribute about 90% of decision weight. This prior is statistical rather than first-principles: it uses discovery history as a proxy for the cumulative effects of precursors, kinetics, synthesis know-how, research attention, and related factors.

4. Learned structure-based priors from experimental records

Large-scale structure-based classifiers make the historical prior explicit by learning directly from databases of experimentally realized crystals. The CSLLM framework builds a synthesizability dataset of 140,120 crystal structures, with 70,120 positives from ICSD and 80,000 negatives selected as the lowest-CLscore structures from Materials Project, COD, OQMD, and JARVIS, using a pre-trained positive-unlabeled model from Jang et al. (Song et al., 2024). The positive class is constrained to ICSD structures with fewer than 40 atoms, fewer than 7 components, and ordered structures only. Negatives are selected from 1,401,562 structures using the threshold CLscore $=60\,\mathrm{s}$6; 98.3% of the ICSD positives have CLscore $=60\,\mathrm{s}$7 (Song et al., 2024).

Because the model is language-based, crystal structures are represented as a compact “material string”

$=60\,\mathrm{s}$8

For CaTiO$=60\,\mathrm{s}$9 (mp-4019), the paper reports a material string of length 102 characters, compared with 1817 for CIF and 1644 for POSCAR (Song et al., 2024). A LoRA-fine-tuned LLaMA-7B synthesizability classifier trained on a 9:1 split achieves 98.6% accuracy, 98.8% precision, 98.4% recall, and 98.6% F1 on the test set; LLaMA3-8B yields similar overall accuracy (Song et al., 2024). On a 1,512-structure Materials Project benchmark with phonon data, the model achieves 97.7% accuracy, reported as 106.1% better than thermodynamic-stability screening and 44.5% better than kinetic-stability screening. The paper interprets this as evidence that a learned historical prior captures synthesis pathways, precursor availability, metastability tolerance, and chemistry-specific regularities beyond $=0.999$0 or phonon stability.

SyntheFormer adopts a stricter positive-unlabeled formulation and a temporally separated evaluation. Structures in ICSD are treated as positives, while all other Materials Project entries are unlabeled rather than negative (Ebrahimzadeh et al., 22 Oct 2025). The non-negative PU loss is

$=0.999$1

and the temporal split is 2011 to August 2018 for training, September to December 2018 for validation, and 2019 to 2025 for test. The corresponding dataset sizes are 84,084 with 41,849 positives for training, 32,605 with 2,562 positives for validation, and 12,784 with 130 positives for test, with the paper noting a linear decline in synthesis rate of about $=0.999$2 per year (Ebrahimzadeh et al., 22 Oct 2025).

The representation is FTCP, a $=0.999$3 tensor spanning six components. Hierarchical feature extraction yields a 2048-dimensional feature space, reduced to 100 dimensions by Random Forest feature selection using 200 trees and maximum depth 10. The Gini criterion is

$=0.999$4

With feature selection, the model reports training AUC 0.898, validation AUC 0.629, and test AUC 0.735, compared with 0.836, 0.600, and 0.705 without feature selection (Ebrahimzadeh et al., 22 Oct 2025). Dual-threshold calibration uses $=0.999$5 for synthesizable, $=0.999$6 for non-synthesizable, and an intermediate uncertainty band; coverage is defined as

$=0.999$7

On test data, this yields 97.6% recall at about 94.2% coverage, while the triple-threshold scheme yields 90.5% recall (Ebrahimzadeh et al., 22 Oct 2025). The paper emphasizes that the model recovers experimentally confirmed metastable compounds far from the hull and assigns low scores to many thermodynamically stable but unsynthesized candidates, reinforcing the claim that a historical prior over experimental attainability is more informative than energy alone.

A related perovskite-specific formulation combines DFT descriptors with literature-derived positives and PU learning. Positive labels come from ICSD-tagged compounds and 206 unique synthesized compositions extracted from more than 1000 PDFs, for a total of 239 positives; 832 DFT compounds remain unlabeled (Desai et al., 7 Oct 2025). The descriptor set is 76-dimensional, consisting of a 36-dimensional compositional vector, a 36-dimensional elemental or molecular property vector, and a 4-dimensional phase vector, augmented by decomposition energy and band gap. The decomposition-energy formulas are

$=0.999$8

and

$=0.999$9

Using transductive bagging PU learning with SVM, random forest, and decision tree, the decision tree achieves AUC 0.908 and TPR 0.86, with best settings $=1000$0, $=1000$1, and $=1000$2 (Desai et al., 7 Oct 2025). Among 832 unlabeled compounds, only 100 are predicted with synthesizability greater than 0.5, indicating that the learned prior concentrates probability in a restricted region of chemistry rather than merely echoing stability screening.

5. Relation to dynamic historical borrowing and adjacent uses

Several papers outside chemistry use closely related logic even though they do not address molecular or materials synthesis directly. The common structure is dynamic borrowing from historical evidence when historical and current data are judged congruent, and discounting that evidence otherwise. These methods are useful for clarifying what is meant by “historical prior” in the stronger Bayesian sense.

The elastic prior for clinical trials begins with a vague prior, updates it using historical data $=1000$3, and then inflates posterior variance by a factor $=1000$4, where $=1000$5 is a congruence measure between historical and current control data (Jiang et al., 2020). For binary endpoints,

$=1000$6

or more flexibly

$=1000$7

Calibration proceeds by choosing a clinically significant difference $=1000$8, simulating congruent and incongruent cases, identifying quantiles $=1000$9 and $=\$0, and solving for $=\$1 so that $=\$2 and $=\$3, for example 0.99 and 0.01 (Jiang et al., 2020). The resulting prior effective sample size is

$=\$4

The paper’s main theoretical claim is “information-borrowing consistency”: if $=\$5 is consistent, then borrowing approaches full strength under congruence and vanishes under incongruence.

SPx, a “synthetic prior with covariates,” makes the same idea more explicit through Bayesian model averaging over three experts: direct historical borrowing, regression borrowing, and independent no-borrowing (Schwartz et al., 2024). Historical and new-trial control data are modeled as

$=\$6

with

$=\$7

The new-trial prior is

$=\$8

with

$=\$9

and prior weights

$, and minimum plausibility$0

The posterior is

$, and minimum plausibility$1

with

$, and minimum plausibility$2

In this framework, historical information is “synthesizable” with current data only insofar as the posterior supports a borrowing mechanism (Schwartz et al., 2024).

These clinical-trial methods are not methods for molecular or materials synthesizability. However, they formalize an idea that chemistry papers often use operationally rather than probabilistically: historical evidence should be borrowed strongly when it is compatible with the present candidate or present conditions, and discounted when it is not. A plausible implication is that future synthesis-aware design methods could move from heuristic penalties and learned classifiers toward explicitly calibrated historical-borrowing priors.

6. Limitations, misconceptions, and research directions

Across the literature, the principal limitation is that any historical synthesizability prior is only a proxy for true laboratory success. ASKCOS-based molecular benchmarks depend on a fixed retrosynthetic search over learned templates and purchasable building blocks, and the authors state directly that route finding under those constraints is not a necessary or sufficient condition for real synthesizability (Gao et al., 2020). Thermodynamic predominance diagrams neglect kinetic barriers and several non-equilibrium effects (Tadge et al., 26 May 2026). Discovery-network models depend on earliest citations, assumed publication delays, and the adequacy of the OQMD convex-hull network (Aykol et al., 2018). Structure-based classifiers trained on ICSD, Materials Project, or literature data inherit label ambiguity, class imbalance, database bias, and temporal drift (Song et al., 2024, Ebrahimzadeh et al., 22 Oct 2025, Desai et al., 7 Oct 2025).

A second misconception is that a historical prior must always be statistical. The surveyed literature supports at least three distinct families. The first is precedent-based retrosynthetic accessibility, grounded in reaction history and purchasable precursors (Gao et al., 2020). The second is a first-principles equilibrium prior, expressed as a stability window in experimentally relevant $, and minimum plausibility$3 coordinates (Tadge et al., 26 May 2026). The third is an empirical learned prior over the manifold of previously realized structures, trained from ICSD labels, literature-mined positives, or discovery timelines (Aykol et al., 2018, Song et al., 2024, Ebrahimzadeh et al., 22 Oct 2025, Desai et al., 7 Oct 2025). These are not interchangeable, but they address the same failure mode: screening or generation that ignores the difference between a theoretically attractive candidate and one that can actually be realized.

The research agenda stated or implied by these papers is consistent. In molecular design, future work should incorporate synthesizability more directly through better post hoc filtering with faster and more accurate CASP tools, heuristic scoring functions approximating retrosynthetic accessibility, reinforcement learning or Bayesian optimization with a CASP oracle, and fully constrained generation over synthetically accessible chemical graphs (Gao et al., 2020). In materials discovery, the comparable directions are physically grounded synthesis-window calculations, temporally faithful positive-unlabeled prediction, uncertainty-aware decision rules, and descriptor spaces that combine DFT properties with the prior existence of similar synthesized compounds (Tadge et al., 26 May 2026, Ebrahimzadeh et al., 22 Oct 2025, Desai et al., 7 Oct 2025). Taken together, these works indicate that historical synthetic knowledge is not merely auxiliary metadata. It is a substantive prior over realizable design space.