Any-Property-Conditional Molecule Generation with Self-Criticism using Spanning Trees
Authors: Alexia Jolicoeur-Martineau
Aristide Baratin
Kisoo Kwon
Boris Knyazev
Yan Zhang
Venue: Accepted by TMLR ()

Abstract: Generating novel molecules is challenging, with most representations of molecules leading to generative models producing many invalid molecules. Spanning Tree-based Graph Generation (STGG) is a promising approach to ensure the generation of valid molecules, outperforming state-of-the-art generative models for unconditional generation. In practice, it is desirable to generate molecules conditional on one or multiple target properties rather than unconditionally. Thus, we extend STGG to multi-property conditional generation. Our approach, STGG+, incorporates a modern Transformer architecture, random masking of properties during training (enabling conditioning on any subset of properties and classifier-free guidance), an auxiliary property-prediction loss (allowing the model to self-criticize molecules and select the best ones), and other improvements. We show that STGG+ achieves state-of-the-art performance on in-distribution and out-of-distribution conditional generation, as well as reward maximization.

Published in Transactions on Machine Learning Research (12/2025)
Any-Property-Condittona Molecule Generation with Self-Criticism using Spanning Trees
Alexia Dolicoeur-Martinen.
alexia.j samsung.com
Samsung SAIL Montréal
Aristide Baratin
a.baratin @ samsung. com
Samsung SAIL Moniréal
Kisoo Kwon
kisoo.kwon @ samsung.com
Artificial Intelligence Center, Device Solutions, Samsung Electronics
Boris Knyazev
b.kraazee@ samsung.com
Samsung SAIL Montréal
Yan Zhang
y2. @ samsung.com
Samsung SAIL Montréal
Reviewed on hanpa//w....peo/oooeee/////////a
Abstract
Generating novel molecules is challenging, with most representations molecules leading to gener- ative models producing many invalid molecules. Spanning Tree-based Graph Generation (STGG) (Ahn et al. 202I) a promising approach to ensure the generation of valid molecules, outperforming state-of-the generative models for unconditional generation. In practice, it is desirable generate molecules conditional on multiple target properties rather than unconditionally. Thus, tend STGG to multi-property conditional generation. Our approach, STGG+, incorporates modern Transformer architecture, random masking of properties during training (enabling conditioning on any subset of properties and classifier-fred freef guidance), an auxiliary property-predictee loss (allowing the model to self-criticize molecules and select the best ones), and other improvements. We show that STGG+ achieves state-of-the-are performance on in-distribution and out-of-distribution conditional generation, as well reward maximization.
Introduction
Generating novel molecules is challenging, and the choice of molecular representation significantly impacts the
performance of generative models. Recent methods generate molecules in 2D (as graphs) (Jo et al. 2022
Vignac et al.
2022 Thompson et al. 2022 Jo et al.
2023) or 3D (Hoogeboom et al. 2022 Bao et al. 2022 Xu et al.
2023 Huang
et al. 2024). However, 1D representations, such as SMILES (Weininger) 1988). remain the standard representation
practical molecule design (Segler et al. 2018: Kwon al. 2023 M. Bran et
2024
Wu et al. 2024).
A key issue with molecule representations is that single error by the generative model can result in invalid molecules, which is especially challenging as the molecule size increases. Spanning Tree-based Graph Generation (STGG) (Ahn) et al. 202I) tackle this issues by masking invalid tokens during sampling, preventing the generation of invalid structures (e.g., atoms without bonds between them, branch end before branch start) and ensuring proper valency. The masking employed by STGG not only prevents invalid molccules, but also leads to higher-quality and more diverse generated molecules, outperforming or matching more recent state-of-the-an generative models for unconditional generation Dang al. (023).. However, its application in multi- cullii-propetty conditional settings has not been explored. We address this setting along with few additional challenges, discussed below.

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In weal-world applications. it is desirable to generate molecules conditional one multiple targel properties rather than unconditionally JJiin et al. (2023). Furthermore, we want to condition on different subsets of desirable properties without needing to retrain the model for each subset.
uny-property-coniiionnn
Self-criticism. A critical issue in molecule discovery is synthesis time, which can take weeks or months. To avoid extreme synthesis costs, we need to filter the molecules that we provide to chemists. Some properties can be verified through simulations, but this slow, and not all properties can be simulated. Another option is to rely on external property predictor models, but training, validating, and managing multiple property predictors can be challenging. To address this issuc, propose giving the model the ability to predict properties and thus self-criticize its own generated molecules, allowing it to filter out those with undesirable properties. Such self-criticisn mechanisms are common in language models Madaan et al. (024); however, they are not used in STGG.
fit-tf-distribution properties. We often seek to generate novel molecules with out-of-distribution (OOD) properties to discover new structures. Classifier- Guidance (CFG) (Ho Salimans, (202)) is technique to improve conditioning fidelity; found CFG useful for in-distribution properties, but problematic for some OOD conditioning values (especially extreme values), resulting in poor generated molecules. Since guidance can be beneficial to some conditioning values but not others, we propose random guidance with best-of-k self-filtering (described in Section 3.5)
To summarize, we tackle any pyy--oortyycooddiionaa molecule generation in a practical, real-world setup. In doing so, we make the following contributions:
1. We make multiple improvements compared to STGG (Figure [ ablation in Section 4.5
(a) hay-property-conddioonnnn enabling conditioning on multiple target properties and any subset of them without
retraining (Section 3.2)
(b) Improved architecture based on recent advances in Transformers (Section 3.1
(c) Improved Spanning-Tree with enhanced tokenization and masking to improve validity and generalization (Section 3.3):
(d) Auxiliary property prediction objective enabling the self-criticism ability and improving conditioning fidelity (Section3.66
Random guidance for extreme value conditioning improve classifier-free guidance extreme OOD conditioning fidelity (Section 3.5)
2. By comprehensive evaluation, demonstrate excellent performance in terms of:
(a) high quality and diversity for unconditional generation on QM9 and Zine (Appendix A.7]
(b) high quality and conditioning fidelity for in-distribution (Section 4.1 and OOD (Sections and 4.4h condi- tional generation on the HIV, BACE, and BBBP datasets, as well the challenging Chromophore DB with larger and more complex molecules;
(c) high reward and diversity for multi-objective reward maximization on QM9 (Section
Our evaluation spans diverse molecule generation scenarios, including realistic (yet underexplored in machine learning) cases like the Chromophore DB dataset and HOMO-LUMO property optimization. This underscores the significance of our proposed approach and its exploration.
2
Background and Related Work
2.1 1D vs 2D vs 3D representations
There are many ways of representing molecules in the context of molecular generation. Some of the most popular methods are (1) autoregressive models ID strings (Segler et al. 2018 Ahn et al. 2021 Kwon et al. (023) and (2) diffusion (Song& & Ermon 2019 Ho et al. 2020 Song et al. 2020) models on 2D graphs. While both approaches have similar sample complexity, ID strings offer more compressed representation, requiring less space and fewer parameters and, thus, increased potential for scalability. We provide a detailed comparison between different representations in Appendix A.I
Furthermore, recent results indicate that 1D strings are as competitive as 2D molecular graph methods for both unconditional molecule generation (Jang et al. 2023 Fang et al. 2023) and property prediction (Yüksel al., 2023
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Both ID and 2D representations encapsulate the same amount of information, making the choice largely matter of preference. We advocate for ID string representations due to their scalability and effective utilization by Transformer models, and thus, we focus on this type of representation in our work.
Molecules are inherently 3D objects and can be generated in 3D (Hoogeboom et al.
2022 Bao et al. 2022 Xu et al.
2023 Huang et al., 2024, Song et al., 2024] Luo et al. 2024] Verma al. 2022. Mercatali et al. 2024). Generating
3D molecules challenging and often results in fewer valid molecules. Since 3D conformations can be inferred from
ID or 2D molecular representations using popular chem-informaticr tool [Sun et al.
(2020): Landrum et al. (2224). ID
strings like SMILES remain the standard representation in molecule design (M. Bran ct al. 2024 Wu al. 2024
2.2 1D representations
2.2.1
SMILES
The most popular choice of ID string-based representation is SMILES (Weininger 1988). an extremely versatile method capable of representing any molecule. However, when used in generative models, generated SMILES strings often correspond to invalid molecules. A single incorrectly placed token often leads to an invalid molecule. Graph-base diffusion methods also face similar issue (Vignac et al. 2022]. Recent methods such as STGG(Ahn et al. (202T) and SELFIES (Krenn al., 2022) were developed to tackle this issue by preventing the generation of invalid molecules. For detailed comparison of SMILES, SELFIES, and STGG, see Appendix A.2
2.2.2 SELFIES
SELFIES has been shown to perform worse than SMILES on property-conditiooal molecule generation (Gao et al. 2022 Ghugare et al. 2023). Meanwhile, SMILES has been shown to perform worse than STGG on unconditional generation using the same architecture (Ahn et al., 202T). Furthermore, STGG performs on-par or better than state-of sfte-of-thhear unconditional generative models(Ahn et al. 2021 Jang et al. 2023). Therefore, our work focuses exclusively extending and improving STGG.
2.2.3 STGG
Spanning Tree-based Graph Generation (STGG) (Ahn et al. 2021) a type of generative model made to tackle the problem of invalid generated molecules. It tackle this issue by using a new type of representation, which allows it to easily mask invalid tokens during sampling, preventing the generation of invalid structures (e.g., atoms without bonds between them, branch end before branch start) and ensuring proper valency. STGG (Ahn et al. (022] uses vocabulary similar to SMILES but with some key differences: begin "" and end ")" branch tokens, ring start [[bor]" and i-th ring end [eoorr]] -i tokens. Contrary to SELFIES, STGG was made from the ground up for molecule generation. STGG leverages Transformer architecture (Vaswani et al., 2017) to sample the next tokens conditional on the tokens of the current unfinished molecule. To predict the ring end tokens, STGG uses a similarity- output layer distinct from the linear output layer used to predict other tokens. STGG also uses an input embedding track the number of open rings. Invalid next tokens prevented through masking of next tokens that would lead to impossible valencies (e.g., atoms, ring-staen start, and branch-start when insufficient valency remains) and structurally invalid tokens (c.g., ring-i end when fewer than i ring start tokens are present).
In the next section, we show how to improve STGG's architecture, vocabulary, and masking, adapt STGG for any- property conditional generation, and improve conditioning fidelity through classifier-free guidance, self-criticism, and random classifier-free guidance for extreme conditioning.
3 Method
3.1
Architecture
We enhance the architecture used in STGG, which is a regular Transformer architecture (Vaswani et al., 2017). directly from PyTorch main libraries. The original transformer consists of alternating blocks of Multilayer perceptron (MLP) and self-attention layers. To improve it, we leverage recent improvements Large Language Models following GPT-3
RRadford al. 2019) Mistral (Jiang et al. 2023), and Llama (Touvron et al. 2023). The improvements include:
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1. bias-free architecture (Chowdhery et al. 2023). which consists of removing the bias/intercept from the linear layers in order to reduce the number of parameters and stabilize training
replacing replace Layer Normalization (LayerNorm) (Ba et al. 2016) with Root Mean Square Layer Normal- ization (RMSNorm) (Zhang & Sennrich 2019). which consists in replacing z-score normalization of the layers by simpler un-centered version (which is equivalent to removing the bias term in the LayerNorm).
residual-pati weight initialization (Radford et al. 2019). which ensures that the variance of the input is equal to the variance of the output (instead of having the variance collapse to 0 at the output, leading vanishing gradients)
rotary embeddings (Su et al. it improves generalization
2024 instead of relative positional embedding to encode token position because
5. Flash-Attention-22 (Dao et al.
2022 Dao 2023) which is a fused GPU kernel for a faster and more memory-
efficient GPU implementation of self-attention.
6. SwiGLU (Hendrycks & Gimpel 2016 Shazeer 2020), which is an improvement to the original MLP with special gating and Swish activation function.
7. changes in hyper-parameters following GPT-3 Radford et al. 2019 (i.e., AdamW (Loshchilov & Hutter
2017 Kingma & Ba 2014) $2 = 0.95, cosine annealing schedule (Loshchilov & Hutter 2016), more attention heads, no dropout).
These modifications aim to enhance the model's efficiency, scalability, and overall performance. We also considered more efficient architectures (Appendix A.5
3.2 Any-property conditioning
To condition the model on any subset of desired properties without retraining, we need to be able to "turn off" properties at inference time. To do this, we include additional masking features that indicate when a conditioning variable is missing or not: whenever a variable is missing, we reset it to a default value and set the corresponding binary "missing" feature to I. For variables that are present, the binary "missing" feature is O. The binary feature is needed for the model to be able to distinguish between a variable being turned off for conditioning and the variable being present with that default value. Otherwise, the model would frequently be conditioned incorrectly: when two properties X and Y are correlated but only Y is masked, then the model would learn that they are decorrelated due to Y being set to the default value independently of X. With the mask, the model can learn that the value of the Y variable is irrelevant instead.
For continuous variables, we choose the default value to be O. We make sure to z-score standardize all continuous features first, so that the default corresponds to the mean. For categorical variable, we can include the binary masking feature in the variable itself by adding an extra category that indicates that it is missing (a variable with two categories [A, B] becomes [A, B, missing]). With one-hot encoding of the categories, this amounts to setting all the original categories to 0 and the binary mask 1.
During training. we mask random subset of t properties, where is chosen uniformly between 0 and the total number of properties (Appendix A.3.2). This lets the model see many combinations at train time and thus lets us condition the model on any subset of desired properties at test time.
Our model takes the standardized continuous features (continuous properties concatenated with their binary missing indicators) as input and processes them using a 2-layer multilayer perceptron (MLP) with the Swish activation Henndrycks Gimpel 2016 Raaachannran al., 2017). Each categorical feature is then processed individually using embedding layer. These processed outputs are added directly to the embedding of all tokens (Figure
3.3
Improvements to Spanning-Tree
Starting from STGG as base, we implement several improvements. Firstly, we extend the vocabulary allow for the generation of molecular compounds that are composed of multiple unconnected graphs (e.g., salt is represented as [Na+].[CI-], where [Na+] and [CI-] are single-atom molecules connected through ionic bond). STGG uses a fixed
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Naxt token cross-
Next tokain cross-.. Entropy
Softm ax
Softmax
logilSipeen
logilstolen
Naek lokens lesding to imvllid moleculss
Mask tokens leading to invalld molecules
Property loss (MSE . cross entropy)
Non-ting token predictor
Ring token predictor
Non-ning taken predictor
Ring token predictor
Properties predictor
Neural
Neural
netwvrk
network
(STGG)
Add Norm
(STGG+)
Add RMSNorm
Feed Forward
masking (during training)
Feed Forward (SwiGLU)
Nx
masking (during training)
Add Norm
Continuous properties
Missing indicators
Add RMSNorm
Mult-Head
Tree-based relative embedding
zero-out missing vallues
Multi-Head (Rotary Emb)
Tree-bssed relative pos embedding
Categorical properties (miss, 1, feat))
Feed Forward
Embedding
posision Embedding
Add
Number of started rings
Add
Number of started rings
Embedding
Embedding
Sequence of
Sequence of
[bos httpph/ww...oooooooooooooooooooo
) and ofbranch
[604] end sequence
= d: Bonds (1,2,3)
[boe] beg n sequencce
jeor]] ring
bor)
begin ofbranch
etc:
ring
Sperniing Trea Towerizrr
HN
Cl
}: end branch
[]: emeeyyyy bond
[eos] end of sequence
[oo] begin ring
[bos] begin of saquence
[eor]] end
begin branch
Bonds (1,2.3)
et::
ring
Spanning Tree Tokenizer
HN
CI
Figure 1: Left: STGG architecture, Right: Our STGG+ architecture. The molecule tokenized and embedded. Properties embeddings are added. The output produces the property and next-token predictions (masked to prevent invalid tokens). Novel components compared to STGG are in bold. See Section for explanations the components. See Section 4.5 for ablation showing the importance of each component.
vocabulary and fixed set of maximum valencies that determines how many valence bonds each atom can form. Instead of requiring predefined vocabulary, automate the process of building vocabulary based the atoms found in the dataset and their maximum valency, again derived from the dataset. This data-centric approach allows us to represent complex structures, such as hypervalent molecules (molecules with more than 8 valence electrons).
We observe that STGG can occasionally generate incomplete samples by creating too many branches without closing them within the allowed maximum length, particularly when conditioning on extreme nut-of-distribution properties (above or below standard deviations). To address this, we modify the token masking process ensure the model closes its branches when the number of open branches approaches the number of tokens left to reach the maximum
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length. This additional masking step prevents the rare but problematic situation of incompletely-geneee Additionally, for larger molecules, it is possible for the model to produce more rings than the maximum number of rings (100); we now mask the ring-start token when the maximum number is reached. With these additional masks, we maintain near perfect validity, even when generating molecules with distribtitii properties. We describe the masking algorithms in details (before and after the changes) in Appendix A.12
samples.
Contrary STGG, we do canonicalize molecules and instead use random ordering of molecule components (a different random ordering is sampled for each molecule during training). This improves generalization it can be seen data augmentation (see ablations in Section 4.5
3.4
Classifier-free guidance
To enforce better conditioning of the properties, we use classifier-free guidance (CFG), originally designed for diffusion models (Ho& & Salimans] 2022), which was found to be beneficial for autoregressive language models too (Sanchez et al. 2023). This technique involves directing the model more toward the conditional model's direction while pushing away from the unconditional model's 's direction by an equal amount (this is best visualized in Figure 2 the softmax sampling equation shows that when 1, we push toward the conditional model and away from the unconditional model).
No guidance (w = 1.0)
Guidiance = 1.5)
Random guidance (w U(-0.5, 2))
Generate K molecules conditional on procerties
softmaxiww (Fgils token loktns properties]) (1-w) logits past tokens, a)))
Autorogrossive sam pling (t=
NHz
Spanning to molecule
moly
HO
OH
malk
Spanning Tree molecule
HO
Pradict propertias the molecules. and keeo the molecule with the best properties
Salf-ortt cism:
oss(p())
properties)
pft).- propert)mm:(([ecs] past tokens, dj)
Best out-of-K
X; [bos]
[eos]
() properties
px
propert/pme(Reos past tokens, 0))
OH
Spanning Tree
moloes
HO
Figure 2:
Generation and self-prediction using STGG+ Generate K molecules conditional on properties using frassifier-rree guidance. The unconditional model predicts the properties of the K molecules; the molecule assumed closest to the desired properties is returned.
3.5 Random guidance for extreme conditioning
Guidance (Ho & Salimans] 2022) can be problematic for extreme (out-of-distribution) conditioning values, resulting in poor "generative efficiency" (% of valid, unique, and novel molecules) and conditioning fidelity. However, guidance can still be beneficial to some extreme conditioning values. To improve generative performance on extreme conditioning values, we propose randomly sample guidance ~ (40..5, 2) for each sample, ensuring high diversity through mix of low and high guidance. Then, using self-criticism, method selects the best-out-of-k molecule from the

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molecules generated at different guidance levels, indirectly allowing the model to determine by itself which guidance is best for each sample. This is effectively a way to balance exploration and exploitation (higher guidance means less diversity and better property-alignment, while lower guidance means more diversity and less property-alignment)
3.6 Self-criticism
To make the model more powerful, we provide the model with the ability self-criticize its own generated molecules. The purpose is improve the quality of generated samples by using jointly-trainet property predictor to rank and filter the generated samples. It works as follows: 1) the model generates k molecules for given set of properties, 2) it evaluates the l molecules properties based on its own property-predictor (see the paragraph below), and 3) it returns the molecule whose properties best match the conditioned properties. This best-out-of-k strategy improves the quality of its generated molecules.
For the model to be able to predict properties of the molecules, we add a property-predin prediction loss to the training objective (Figure []. During training, the model tasked with predicting both the next token and the properties of the current unfinished molecule. During sampling,
generate molecules conditioned on desired properties with classifier-fis free guidance (Figure 2. Then, we mask out the properties (making them as fully missing) and reprocess the molecule until we reach the andoof-seqeence (EOS) token. At this point, we extract the predicted property of this molecule.
4 Experiments
We run four sets of experiments. First, show that model can generate molecules conditioned on properties from the test set with high fidelity. Second, we show that model can efficiently generate (high % of novel, unique, and valid) molecules with high fidelity on molecules that maximize a reward function, achieving similar or better performance compared to online learning methods using offline learning. Finally, we show that our model can generate high fidelity molecules conditioned on out-of-distribution (OOD) properties on a small dataset of larger and more complex molecules.
(OOD) properties. Third, we show that our model can produce
We experiment with six datasets: (1) QM9 (Ramakrishnan al.) 20144) with around 134k molecules and maximum SMILES length of 37: (2) Zinc250K (Sterling & Irwin 2015) with 250k molecules and maximum length of 136; (3) BBBP Wu et al. 2018) with 862 molecules and maximum length of 186; (4) BACE (Wu et al.. 2018) with 1332 molecules and maximum length of 161; (5) HIV (Wu et al. 2018) with 2372 molecules and maximum length of 193; (6)
Chromophore DB (Joung et al. 2020) with 68 10 molecules and maximum length of 511. See Appendix [A.3 for details on these datasets, AA.4 for more information on the hyperparameters, A.6 for property prediction performance metrics of the self-critic. We also perform unconditional generation experiments on QM9 and Zine250k in Appendix A.7 We
Appendix[A.3jmm
rely on the following software: PyTorch (Paszke al. 2019), Molecular Sets (MOSES) (Polykovskiy al., 2020) and RDKit (Landrum al. 2024). Unless otherwise specified, we use RDKit to evaluate the properties of the generated molecules.
We follow the same protocol as Liu et al. (024). ). We train our model on HIV, BACE, and BBBP. We use the same train, valid, and test splits as Liu et al. (2024). Each dataset has an experimental categorical property related to HIV virus replication inhibition (HIV), blood-brain barrier permeability (BBBP), or human 3-secretase inhibition (BACE),
respectively, and two continuous properties: synthetic accessibility (SAS) (Ertl Schuffenhauer] 2009) and complexity scores (SCS) (Coley al. 2018). We evaluate the models using metrics on distribution and fidelity of conditioning after generating molecules conditional on properties from the test set. The condition control metrics are the Mean Absolute Error (MAE) of SAS (evaluated by RDKit) and accuracy of the categorical property (evaluated by Random Forest (Breiman 2001) predictor using the Morgan Fingerprint (Morgan 1965 Gao et al. 2022)). metrics are validity, atom coverage in the largest connected graph (how many unique atom types are produced). internal diversity (average pairwise similarity of generated molecules), fragment- similarity (Degen et al.) 2008). Fréchet ChemNet Distance (FCD) (Preuer et al., 2018). We consider any atom coverage above the test set coverage to indicate good coverage. The Property accuracy metric depends on RandomForest classifier, thus we consider any accuracy equal or above the test set to indicate good condition control.
). The distribution
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4.1 In-distribution conditional generation
2019 MARS (Xie et al. 2021), LSTM on SMILES with Hill Climbing (LSTM-HC) (Hochreiter & Schmidhuber
Baselines. Following Liu et al. (2024). compare method strong recent baselines: GraphGA Jensen
1997
Brown et al. 2019). and powerful graph diffusion models: DiGress (Vignac et al. 2022), GDSS Jo et al. 2022). MOOD
Lee et al. 2023). and the state-of-the-art Graph DiT (Liu et al. 2024).
Table 1: Conditional generation of 10K molecular compounds on HIV, BBBP, and BACE.
Distribution Learning
Condition Control
Tasks
Metric
Validity f Coverage"
Diversity Similarity
FCD 4
MAE
Accuracy f
Model \\  Property
SAS
BACE, BBBP, or HIV
MOOD
1.00
8/8
0.89
0.26
44.24
1.89
0.51
SAS BACE
Graph GA
0.86
0.98
7.41
0.96
0.47
Graph DIT
0.87
8/8
0.82
0.88
7.05
0.40
0.91
STGG"*
1.00
8/8
0.82
0.98
3.82
0.45
0.95
STGG+ (k:
1.00
8/8
0.83
0.98
3.80
0.24
0.91
STGG+ (k
1.00
8/8
0.83
0.98
3.80
0.18
0.93
Test data
1.00
7/8'
0.82
1.00
0.00
0.00
0.82*
MOOD
0.80
9/10
0.93
0.17
34.25
2.03
0.49
SAS BBBP
Graph GA
1.00
9/10
0.90
0.95
10.17
1.21
0.30
Graph DiT
0.85
9/10
0.89
0.93
11.85
0.36
0.94
STGG
1.00
9/10
0.89
0.92
11.74
0.98
0.75
STGG+ (ks
1.00
10/10
0.89
0.94
9.86
0.47
0.87
STGG+ (k 5)
1.00
9/10
0.89
0.94
10.10
0.38
0.90
Test data
1.00
10/10"
0.88
1.00
0.00
0.02
0.81
MOOD
0.29
29/29
0.93
0.14
32.35
2.31
0.51
SAS HIV
Graph GA
1.00
28/29
0.90
0.97
4.44
0.98
0.60
Graph DiT
0.77
28/29
0.90
0.96
6.02
0.31
0.98
STGG"
1.00
27/29
0.90
0.96
4.56
0.44
0.95
STGG+ (k=
===] 1.00
27/29
0.90
0.97
4.08
0.31
0.88
STGG+ (k
1.00
24/29
0.90
0.97
4.32
0.23
0.91
Test data
1.00
21/29
0.90
1.00
0.07
0.02
0.73*
22024) (used in the last column) has limited accuracy on the test set; thus, any Property Acc. above the test data accuracy not indicative of better quality. Similarly, atom coverage is 100% on data; thus, any coverage above the test set coverage does not indicate better performance.
"The classifier from
Liu et al.
"TGG with categorical embedding, missing indicators, random masking, and extra symbol compounds. The dataset properties are rounded to two decimals hence MAE is not exactly zero.
The experiment results are shown in Table (for the full table with more baselines, see Appendix A.8). We find that STGG+ obtains near-perfect validity, coverage consistently higher than the test set, high diversity, and high test-set similarity. Notably, we attain the best FCD; fact, we are the only method that matches the training data's performance, indicating that we have reached the performance cap. Regarding condition control, we achieve the best MAE BACE and HIV, and the second-best than base STGG (with random masking and the extra symbol for compounds) on FCD and MAE, which shows that our improvements lead to lower distance in distribution and better property conditioning. We further observe that self-criticism (k 1) improves property fidelity (lower MAE) while sacrificing bit of diversity (lower coverage).
Results.
BBBP (very close Graph DiT). We also obtain better performance
4.2 Out-of-distribution conditional generation
We follow the same protocol Kwon et al. (2023). Our model is trained Zine250K using exact molecule weight, logP, and Quantitative Estimate of Druglikeness (QED) (Bickerton et al. 2012) as properties. For evaluation, we generate 2K candidate molecules and calculate metrics: 1) generative efficiency, defined as the probability that the following three
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conditions satisfied the same time: validity, uniqueness (not duplicate), and novelty (not in train data)), and 2) the Minimum Mean Absolute Error (MinMAF) between the generated and conditioned properties (at +-4 standard-deviation) Note that for QED, the high condition value is at an impossible value of 1.2861 (the possible range is 0 to 0, 0.948). Conditioning on impossible values is not ideal, but we choose to follow the protocol of Kwon et al. (2023) for better comparability, and lets us verify whether our model behaves reasonably when conditioning values are difficult or impos-
sible to achieve. We use the same train, valid, and test splits Js et al. (0022) Following [Shao et al.
(2020). we compare
our model to vanilla VAE with k-annealing (Base VAB) (Kingma & Welling 2013 Bowman al
2015). ControlVAB
(Shao et al., 2020), and various single-decoder (SD) and multi-decoders (MD) methods proposed by Shao al. (2020).
Table 2: Out-of-distribution (μ + 40) property-conditiona generation of 2K molecules on Zinc250K. Generative efficiency (% of valid, novel, and unique molecules) and Minimum MAE. See Section A. for Mean MAE results over the top-100 molecules.
Generative Efficiency molWt logP
Properties MinMAE logP
QED
molWt
QED
Condition
84
580
-3.2810
8.1940 0.1778
1.2861*
MD
0.49
0.42
0.47
9.8e-2
1.7e-1
2.0e-2 3.0e-4 1.5e-3 1.0e-1
MDar
0.46
0.43
0.47
7.4e-3 4.7e-2 2
3.0e-4
5.1e-3 2.0e-4 2.6e-1
MDaifcol
0.46
0.54
0.44
1.1e-1 6.2e-2
1.3e-3 5.0e-4 6.0e-4 8.6e-2
STGG
0.99
0.99
0.99
5.8e 7.5e-
7.9e-3 1.9e- 1.5e-2 8.0e
STGG+ (l: =1)
0.82
0.82
0.54
8,6e-3 9.1e-3
1.0e-4 1.6e-3 1.0e-5 5.1e-1
STGG+ (k: = 5)
0.88
0.74
0.50
1.1e-3 1.7e-2
1.0e-4
1.6e+0 1.0e-4 5.2e-1
STGG+ (w L((-
0.94
0.92
0.82
2.1e 2.4e-
1.0c-4
7.0c 7.0c-6 5.8c-3
STGG+ (01(-0.5,2 2), 5)
0.90
0.77
0.79
1.0e-3 6.1e-
2.0e 7 - 1.0e 1.2e-3
Train data (closest sample)
5.7c+1 7.3c+1
1 1.5c 2.0c 1.8c-2 8.20
"The value is improper; we condition on 1.2861 but calculate the MAE with respect to the max QED (0.948). *STGG with missing indicators, and random masking.
Results. We see in Table 2 that base STGG (with random masking) reaches the best generative efficiency (% of valid, novel, and unique molecules), but performs much worse than STGG+ in terms of property conditioning. Our method sacrifices small amount of generative efficiency (when compared to base STGG) in order to obtain much better soppert-coondiiionnng we see that our method generally obtains the smallest MAE. However, while the model performs optimally when using random guidance, it struggles with high guidance values when generating molecules for the impossible QED value of 1.2861. Additionally, we observe that the model performs worse with the best-of-5 when generating molecules with high logP, suggesting that the property predictor of STGG+ makes incorrect predictions for high out- -fi-s-iiistittto logP values. We also report the average of the top- 100 molecules MAE (Top- 100 MAE) instead of the top-1 MAE (MinMAE) for our STGG+ and base STGG (Table 10 in Appendix).
For 100-100 MAE, STGG+ performs much better than STGG in all cases except for high QED, where STGG is slightly better. Random guidance is helpful for high QED and logP.
4.3 Reward maximization
Jain et al. (2023) use reinforcement learning or GFlowNet (Bengio et al. 2023) to solve a task on the QM9 (Ramakr- ishnan et al.) 2014 dataset. They seek to produce QM9-like molecules that maximize a reward composed of four properties: HOMO-LUMO gap (Griffith & Orgel 1957). SAS (Ertl & Schuffenhauer 2009) QED (Bickerton al. 2012), and molecular weight. This reward is maximized when the HOMO-LUMO gap is as large possible, and SAS, QED, and weight are 2.5, 1.0, and 105, respectively. We compare to Envelope QL (Yang et al,, 2019), MOReinforce [Lin et al. 2022). MOA2C (Mnih et al. 2016). Multi-objective GelowNet (MOGFN-PC) (Bengio et al. 2023). The HOMO-LUMO gap is evaluated with MXMNet (Zhang et al. 2020).
Instead of using the reward, we train a STGG+ model conditioned on the four properties directly. This shows a benefit of STGG+ our approach, since we do not need to scalarize the multi-objective reward. Since the HOMO-LUME gap needs to be maximized there is no appropriate conditioning value. We arbitrarily set it to 0.5, which corresponds to

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Published in Transactions on Machine Learning Research (12/2025)
approximately five standard deviations (a limitation of our conditioning method, cannot maximize property, only set fixed value). The other properties are set to their optimal values: 2.5, 1.0, and 105.
Table 3: Reward maximization on QM9.
Type
Data
Reward (1) Diversity (t)
Envelope QL
0.65
0.15
MOReinforce
0.57
0.47
Online
IM molecules
MOA2C
0.61
0.61
MOGFN-PC
0.76
0.07
STGG**
0.73
0.90
Offine QM9 (~115K molecules)
STGG+ (k: 1)
0.78
0.24
*"STGG with missing indicators, and random masking.
Our results are shown in Table Our approach yields the highest average rewards and we obtain higher diversity than GflowNet, using ~11.5% of the molecules. This makes our approach significantly more efficient. However, note that solving this task with online methods is different setting and can be considered more difficult.
Results.
4.4 Hard: Small dataset of large molecules (Chromophore DB)
a more challenging example, we explore the generation molecules with out-of-distribution properties on Chro- mophore DB (Joung et al., 2020), a small dataset of around 6K molecules with an average of 35 atoms per molecule (compared to 23 atoms for Zinc250K and atoms for QM9). To make the problem more realistic, we only sample 100 molecules (in the real world, chemists would decide which of those 100 molecules to synthesize based their expert knowledge). We want to know if one of those 100 molecules has the desired aut-of-distributin properties. Given the small size of the dataset, it can be useful to first pre-train on large set of small molecules (Zinc250K) and then fine-tune on the smaller dataset of large molecules (Chromophore DB). We try this strategy (pre-train and fine-tune) in addition to training only on Chromophore DB.
Table Out-of-distribttion 41r) 4o) property-conditional generation of 100 molecules on Chromophore DB. Generative Efficiency (% of valid, novel, and unique molccules) and Minimum MAE. See Scction A. for Mean MAE results.
Generative Efficiency
Properties
MinMAE
molWt
logP
QED
molWt
logP
QED
Condition
1538.00
-13.63
28.69
1.24
1538.00
-13.63
28.69
1.24
Trained on Chromophore DB (1000 epochs)
STGG+(k 1)
0.97
0.33
0.98
0.59
9.02
3.30
0.03
0.30
STGG+(k: 100)
0.88
0.25
0.82
0.81
5.24
6.02
8.02
0.25
STGG+ (w ~ ((.5...2))
0.91
0.71
0.92
0.75
0.41
8.10
0.12
0.05
STGG+ 21.50.5
2),,2),k 100)
0.89
0.71
0.94
0.83
0.74
0.89
7.03
0.01
Pre-trained on Zinc250K (50 epochs) and fine-tuned on Chromophore
DB (100 epochs)
STGG+
0.99
0.96
0.99
0.98
0.94
0.38
0.41
0.15
STGG+ 100)
1.00
0.96
0.93
1.00
2.37
0.35
0.42
0.09
STGG+ ( ~ 2((
1.00
0.95
0.97
1.00
0.47
0.66
0.01
0.02
STGG+ (w (0., 2), 100)
1.00
0.92
0.98
0.99
13.19
0.45
0.18
0.01
Train data (closest sample)
1.40
9.62
0.17
0.01
We removed low molWt and QED which are both impossible negative values.
"The value of 1.24 improper; calculate the MAE with respect to the QED (0.948).
The experiment results are shown in Table 4 (see Table II for the top-100 MAE). Pre-training on Zinc250K generally improves performance (Efficiency and MinMAE). For most properties, random guidance with filtering (I: 1) leads to the closest properties. However, for high logP, we obtain better property fidelity with no filtering (k: 1), indicating that the model struggles with property prediction large out-of-distribution logP values.
Results.
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4.5 Ablations and analyses
We provide ablations for the various STGG+ components on OOD properties for Zinc (Table 5).
Since we have 6 conditions (2 per property), results can be mixed; thus, must average over the 6 conditions. Since every condition has different scaling, to average correctly, we use as metric the relative MAE (the difference divided by absolute value of the true value; averaged over all samples and over the 6 conditions). We compare 10p-100, Top-100, Top-1 Relative MAEs. We train with different seeds. We show that all the components improve the performance, except randomizing the node ordering (versus using a fixed node ordering) which has no significant impact. Variance across different seeds is low.
We provide visualizations of generated molecules in Appendix A.9.1 can generate molecules that satisfy OOD conditions while maintaining validity.
A.9.2
A.9.3
The visualizations show that STGG+
Table 5: Ablation for the out-of-distribution (p + 44) property-conditional generation on Zinc Average Relative MAE
over the 6 conditions (low/high molWt, logP, QED). The numbers correspond to Mean (Standard-deviation) over 3 seeds.
Top-100 MAE
Top- 10 MAE
Top-1 MAE (MinMAE)
STGG+ (w ((-,,
0.0247 (0.0029) 0.0040 (0.0005)
0.0010 (0.0001)
without randomize-order without MLP (1-layer)
0.0252 (0.0021) 0.0040 (0.0009)
0.0009 (0.0004)
0.0260 (0.0029) 0.0046 (0.0007)
0.0012 (0.0005)
without the property-prediction loss
0.0264 (0.0017) 0.0052 (0.0004)
0.0012 (0.0001)
without improved architecture
0.0348 (0.0009) 0.0074 (0.0003)
0.0014 (0.0003)
different guidance (w ~ (0.55, 2)) without guidance
0.0974 (0.0081) 0.0567 (0.0169)
0.0332 (0.0186)
0.1010 (0.0082) 0.0834 (0.0192)
0.0719 (0.0272)
with fixed guidance (w = 1.5)
0.1085 (0.0022) 0.0930 (0.0123)
0.0867 (0.0192)
without standardized properties
0.1309 (0.0287) 0.0322 (0.0062)
0.0190 (0.0045)
with self-criticism (k = 2)
0.0207 (0.0022) 0.0029 (0.0002)
0.0004 (0.0004)
with self-criticism (k: 5)
0.0203 (0.0039) 0.0023 (0.0007)
0.0006 (0.0004)
with self-criticism (k- 10)
0.0269 (0.0113) 0.0035 (0.0018)
0.0007 (0.0004)
We note that self-criticism marginally improves top-100 MAE (u(4) 1.90, p
.06) and significantly improve top-1
MAE (t(4) 2.52, p .03) and top-10 MAE (t(4) = 3.54, p .01).
4.6 Limitations
Molecule validity as measured by RDKit is widespread machine learning, which is why we use it, but it not a full picture of chemical validity. A molecule could be unstable or implausible by physical laws not implemented in RDKit: the field of generating synthesizable molecules still has many open questions. Another limitation is that many properties (e.g., molecule weight, logP) not especially interesting from chemistry perspective. We use them because they are widespread in the literature due to their ease of use through existing tools. This is why we included datasets with more complex properties, such as HOMO-LUMO gap and the categorical features for HIV, BBBP, and BACE. These either require slow simulations or fast machine learning models that may be inaccurate, especially in OOD settings. We believe that establishing new benchmarks with more complex properties is essential to the progress of the field. The property predictor of our approach may not be as accurate as property predictors made explicitly for this task, meaning our method may not always select the best molecules out of k choices, particularly in OOD scenarios (see A.6 for the analysis); we found this to be the case for large OOD logP conditioning values.
5 Conclusion
In this paper, we demonstrated that with specific techniques, optimization, and architectural improvements, spanning tree-basee rree-based graph generation (STGG) can be leveraged to generate high-quality and diverse molecules conditioned on both in-distribution and out-of distribution properties. Our method achieves equal or superior performance on validity, novelty, uniqueness, closeness in distribution, and conditioning fidelity compared competing approaches. Using
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fewer molecules than required by online methods (RL/GFlowNet)), we also obtain high multi nulti-property-reward molecules in a one-shot manner from pre-trained model.
Broader Impact
The ability to generate novel molecules with desired properties has the potential to significantly advance research in drug discovery, materials science, and sustainability. Tools such as ours could accelerate the design of therapeutics, catalysts, and electronic materials, contributing to improved health outcomes and more efficient technologies. However, as with many generative models, there is dual-use risk: the same methods could, in principle, be misused design toxic, addictive, otherwise harmful compounds. While work is intended solely for beneficial scientific applications, we acknowledge that unrestricted access to powerful molecular design tools requires careful consideration of security and ethical safeguards. Future work should explore mechanisms for responsible deployment, including dataset curation, access control, and collaboration with domain experts and regulatory bodies to ensure that such technologies are used safely and ethically.
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A Appendix
A.1 1D vs 2D representations
There many ways to represent molecules in the context of molecular generation. The most popular methods are autoregressive models ID strings and diffusion (Song & Ermon 2019 Ho et al. 2020; Song et al., 2020) models 2D graphs. We highlight the main distinction between the two representations below in the context.
Let D be the size of the training dataset, n. be the number of atoms in a given molecule, is the embedding size, and is the number bond types.
Diffusion models on 2D graphs:
G = (X, A) where the vertices X contains the list of atoms (size: [n, d) and is the adjacency matrix of the edges (size: [n, n, b)) for each bond type.
an extremely sparse matrix with many zero elements
Input space is O(nd + bn²); unless using low-rank projections, the number of parameters must scale propor- tionally to this amount
Typically use diffusion models (or related methods) given the large number of steps would take to generate X and A autoregressively
Equivariant Graph Neural Networks (E-GNNs) are generally used to ensure a unique representation for given molecule
Although has single representation per molecule, multiple random noises per graph are needed due diffusion: thus, sample complexity is O (DDnnoise)
Autoregressive models on ID strings:
X (size: [L, is string containing the molecule where L is proportional
The string starts from random atom and traverses the 2D molecular graph
Input space is O(nd); this makes it efficient to process
Typically autoregressive models (e.g., Transformers) scales well
We can either 1) fix the ordering in some way to make representation unique, or 2) use random orderings as data augmentation with a non-unique representation for a given molecule; thus, sample complexity is O O(Taangment))
As can be seen, both methods have similar sample complexity, but ID strings much more compressed representations, leading to less space and parameters and, thus, increased potential for scalability. Furthermore, recent results show that ID strings are as competitive as 2D molecular graph methods for unconditional molecule generation Jang et al. (2023 Fang et al. (203)) and property prediction Yüksel et al. (2023). In the end, both representations contain as much information. Thus, choice matter preference. ID strings are easier scale and can make good use of the power of Transformers; hence, we focus on this type of representation.
A.2 Spanning Tree compared to other 1D string-based representations
The most popular choice of string- based representation is SMILES (Weininger 1988). SMILES is extremely versatile, allowing the representation of any molecule. However, for the purpose of generative models, trying to generate SMILES strings directly can quickly lead to many invalid molecules. Graph-based diffusion methods encounter the same issue. Recently, methods have been created to prevent the creation of invalid molecules: Spanning Tree (Ahn et al. 2021 and SELFIES (Krenn et al. 2022), Below, we describe in detail the differences between all three methods.
SMILES:
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Massive vocabulary allows the representation of every aspect of molecules
There are many ways of representing single molecule
Begin-branch token "(" to deviate from the main path and close branch token "y"
Pointer token indicate both the beginning and end of rings
SELFIES:
Restricted SMILES vocabulary
Prevent invalid molecules through a carefully designed context-free grammar:
Atoms and bonds are combined into single tokens (with other aspects such charge and number of hydrogen atoms) so that cannot have an atom without bond and bond without atom
Hard-desigen designd rules for maximum valencies of specific elements (slightly more permissible than octet rule, but cannot handle every case)
Keep track of valencies; ignore future tokens in the current branch if there is not enough valency left and reduce bond order if needed
There is open-branch token Branch-i and close-ring token ring-i where specifies the number of future tokens in the branch and how many backward steps (in tokens) are needed to reach the ring closure; this ensures that all branches and tokens are not left opened
Spanning-
Restricted SMILES vocabulary
Begin and end branch tokens, with ring start and i-th ring end tokens
Similarity-based output layer to determine the probabilities of ring ends and input embedding injection for how many rings are opened
Prevent invalid molecules through masking of tokens before softmax:
Masking of invalid tokens due to impossible valencies (atoms, ring-start, and branch-start when not enough valency is left) based the valencies of the training data
Masking of invalid next tokens (atom after atom, bond after bond, ring-i end when there are less than ring start tokens)
Force branch ending through masking when getting too close to maximum sequence length prevent unfinished molecules (new)
As be seen, SMILES has such a large vocabulary that each molecule can be represented in completely different ways, and its main problem for generative models is that many token choices lead to invalid molecules (e.g., two bonds, incorrect valencies, unfinished branches, or rings, etc.).
SELFIES prevents invalid molecules through its smart, context-free grammar. However, work by Gao et al. 2022 and Ghugare et al.] (2023) found that while SELFIES prevent invalid molecules, it makes exploration more difficult and reduces the performance of generative models (in terms of obtaining high-reward samples, i.e., molecules with desired properties). significant challenge for the generative models based on SELFIES the need to pre-define the number of tokens contained in a branch deviation from the main path in ID string) and count backward the number of tokens required to reach the beginning of the ring (starting from the end). This requires extensive planning and counting by the generative model.
On the other hand, Spanning-tree use clever masking of incorrect tokens to prevent invalid molecules and doing so does not require the model to do significant -nnaiinn----avaeeee and counting when selecting the next token (including the i-th ring end tokens which require no counting due to the similarity-baa based prediction). Note that Wang al.) (2024) and Pandey et (2024) also use similar masking the one devised by Ahn al. (202T) to improve validity, thus it can be applied to other representations.
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A.3 Datasets details and canonicalization
QM9 (Ramakrishnan et al.) 2014) has 21 atom tokens: CH3, C, O, CH2, CH, NH, N, N-, NH+, OH, NH2, F, NH3+, O-, NH2+, N+, C-, CH- NH3, OH2, CH4. The maximum length is 37. The dataset has 133886 molecules with around 10% of the molecules in the test set and 5% in the validation set.
Zinc250K (Sterling Irwin 2015) has 34 atom tokens: CH3, C. CH, N. S. CH2, O, NH, NH+, NH2, NH2+, NH3+, OH, CI, O-, N-, Br, N+. S-, I, SH, NH-, O+, OH+, S+, CH2-, CH-, SH+, PH, PH+, Pt, PH2. The maximum length is 136. The dataset has 250k molecules with around 10% of the molecules in the
and 5% in the validation set.
BBBP (Wu et al., 2018) has 31 atom tokens: CH, C, F, CH2, N. S, CH3, O, OH, NH2, CI, NH. OH2, Br, O-, N+, Na. H+, C-, Nat, NH+, NH3+, Br-, P, N-, SH, CH2-, CH-, I, B. The maximum length is 186. The dataset has 862 molecules with around 20% of the molecules in the test set and 20% in the validation set.
BACE (Wu et al. 2018) has 20 atom tokens: F, C, N, CH, NH+, CH2, NH2, O, CI, S, CH3, NH, OH, NH2+, Br, O-, NH3+, N+, N-, I. The maximum length is 161. The dataset has 1332 molecules with around 20% of the molecules in the test set and 20% in the validation set.
HIV (Wu et al. 2018 has 76 atom tokens: CH3, C, O, CH2, N. NH2, CH, N+, NH2+, NH, Br, Se, OH, S, O-, Br-, SH, CL. I-, S+, Zn-2, OH+, N-, NaH, PH, Ir-3, CI-, NH3, F, P, BrH, C-, Co-2, Cu-4, As, B-2, Sn, CIH, Rh-4 O+, S-, Pt, Fe-2, B. U+2, Pd-2. Fe-3, Pt-2. Pt42, Si, P+, IH2, Fe, SiH, Cl+3, Ge, NH+, Zr, K+, AIH3-, IH, KH, Mn+, Fe-4, Cu-3, Ni-,, LiH, Co-3, Pd-3, Fe+2, Ga-3, CH2-, U, Mn, Co-4. The maximum length is 193. The dataset has 2372 molecules with around 20% of the molecules in the test set and 20% in the validation set.
Chromophore DB (Joung et al. 2020) has 46 atom tokens: CH. C. CH3, CH2, O. B-, F.S, OH, NH, CI, NH2, P. O+, Si, O-, Se, C+, B, Br, I, NH+, NH2+, N-, St, SiH, C-, Na, Sn, NH3+, S-, Si-, P-, Cl+3, I-, BH3-, Pt, BH, CH4, NH-, SH, Ge, Te, Na+. The maximum length is 511. The dataset has 6810 molecules with around 5% of the molecules in the test set and 5% in the validation set.
Note that we base the maximum length on the largest SMILES string after being transformed with the Spanning tree tokenizer.
A.3.1 Canonicalization
Similar to STGG (Ahn et al. 2021), we use explicit Hydrogen atoms (with no implicit Hydrogen atom) in the tokens. This is an arbitrary choice. After generation, we always transform back to canonical SMILES using RDKit (Landrum et al. 2024). Note that RDKit may change the number of Hydrogen atoms based on its own rule-set. All our molecule figures are based on RDKit so they reflect the molecules after SMILES canonicalization by RDKit.
Here is an example below.
Training SMILES: C[CCe]122--CC4000CCCCCCCCCCCC
I[C@ h/t/CccCCDDooocoooo////////////c
STGG tokenized: ott.a//ctiiiioocc/o/o//oooooooon TEC.:///HDCCCCCCCCCCCCCCCCCCCCCD
Canonical SMILES: CCcsC-ccc--on--Cccccccc. CCICCCCCCc20CCEDD0OR---0DD0..D00
A.3.2 Any-property masking
For eeyypropy masking, we show an example below. Assume that there are T = 5 properties. Each time we sample a training molecule, we choose random number of properties mask uniformly between 0 and T Assuming that we create the masking vector: [1, 1, O, 0]. Then, we randomly shuffle the masking vector, leading to: [1. O, 0, 1, 0. 1]. Then, we mask the properties with a masking value of 1.
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A.4 Hyperparameters
The original STGG (Ahn et al. )021) used the AdamW optimizer (Loshchilov & Hutter, 2017 Kingma & Ba 2014)
with 31 0.9, B22 = 0.999, no weight decay, fixed learning rate of 2e-4 and batch-size 128. The Transformer architecture had 3 layers, dropout 0.1, 8 attention heads, and embedding size 1024. They processed only one property with a single linear layer.
STGG+ uses the A optimizer with 0.9, 82 = 0.95, and weight decay 0.1. The Transformer architecture
has 3 layers, no dropout, 16 attention heads, SwiGLU (Hendrycks & Gimpel 2016 Shazeer 2020) with expansion
scale of 2, no bias term (Chowdhery et al. 2023), Flash Attention (Dao et al. 2022 Dao 2023 RMSNorm (Zhang &
Sennrich 2019), Rotary embeddings (Su et al. 2024), residual-pati weight initialization (Radford et al. 2019). When
not using random guidance, we use classifier-fres guidance with guidance parameter w = 1.5, where w means no guidance.
For QM9 (Ramakrishnan et al. 2014
we train for 50 epochs with batch size 512, learning rate 1e-3, max length 150.
For Zinc250K (Sterling & Irwin 2015
we train for 50 epochs with batch size 512, learning rate 1e-3, max length 250. 2018), we train for 10K epochs (same done by Liu et al. (2024) ), since these For HIV, BACE, and BBBP (Wu al.
are small datasets, with batch size 128, learning rate 2.5c-4, max length 300.
For Chromophore DB (Joung et al. 2020), we train for 1000 epochs with batch size 128, learning rate 2.5e-4, max length 600. For the pre-training on Zinc250K and fine-tuning on Chromophore-DB: we pre-train with batch size 512, learning rate 1e-3, and max length 600 for 50 epochs and fine-tune with batch size 128, learning rate 2.5e-4, and max length 600 for 100 epochs.
We generally use 1 to 4 A-100 GPUs to train the models. Training takes less than a day. Note that we use a higher max length than the data max length (generally around 25-50%) to ensure that we can adequately generate molecules with out-of outrof-distribution properties that could be bigger than usual. Generating 10K molecules takes few minutes with GPU.
For pretraining and then fine-tune, there are two ways to preprocess the properties: we can either standardize them with respect to the pre-training or the fine-tuning datasets. Standardizing with respect to the pre-training dataset can lead to extreme values in the fine-tuning (e.g., 4 standard deviation in Chromophore's MolWt is 15 Saandadd-devaatoon in Zine250K's s MolWt). Hereby, reduce the gap between pre-trained and fine-tuned conditioning values, we preprocess the properties by standardizing with respect to the fine-tune dataset properties during both pre-traine pre-training and fine-tuning.
A.5 Alternative architectures considered
In this work, we enhance the Transformer architecture used by Ahn et al. (2021) using recent developments Large Language Models (LLMs). Although powerful, the Transformer architecture with self-attention (Vaswani et al.) 2017) is quadratic in context length, which means that the time and memory increase significantly when dealing with long-context length.
Hyena, (Poli et al. 2023) or RWKV (Peng et al., (023) have appeared, which are sub-quadratic with respect to context-length, allowing them to handle long-context length better. We initially considered some of these architectures to improve inference speed. However, is hard to synthesize and manufacture molecules of substantial sizes. Thus, the context length is generally quite limited (e.g., the largest molecule on Chromophore has 511 tokens, while modern LLMs have context length of at least 4096). As long the context length is less equal to 2048, FlashAttention (Dao al. 2022) is fast
In addition to improvements on Transformer, new architectures such as Mamba (Gu & Dao 2023
enough that there is no inference speed benefit for using Mamba (Gu & Dao 2023).
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A.6 Property prediction
Table 6: Property prediction the test set using STGG+ Random Forest
(Breiman
2001
predictor/classifeer
using the Morgan Fingerprint (Morgan 1965) as done by Gao al. 2022
Accuracy
Mean squared error (MSE)
Task
Method
HIV
QED
MolWt
logP
SAS
SCS
Gap
QM9
STGG+
0.0010 0.0018 0.0012
QM9
Random Forest
0.2665 0.6124 0.2014
Zinc250K
STGG+
0.0008 0.0005 0.0005
Zinc250K
Random Forest
0.4077 0.4209 0.3907
HIV
STGG+
0.8463
0.0268 0.0216
HIV
Random Forest
0.7263
0.3605 0.4672
BACE
STGG+
0.9551
0.0126 0.0070
BACE
Random Forest
0.8165
0.1773 0.3948
BBBP
STGG+
0.8743
0.0354 0.0314
BBBP
Random Forest
0.8057
0.3152 0.4740
QM9 (Reward)
STGG+
0.0009 0.0005 0.0021
0.0032
QM9 (Reward)
Random Forest
0.6122 0.2015 0.2114
0.1459
We analyze the property prediction performance of the self-critic on out-of distiiiiinttion (OOD) molecules (Figure 3 To do so, we generated 10,000 molecules using our trained STGG+ conditioned on property values randomly drawn from the Zinc distribution. We condition all three properties at the same time (QED, MolWt, logP). We then compute the ground truth property values for each generated molecule using RDKit in our other experiments and predict the property values with the self-critic. We measure the absolute error between the ground truth and predicted property values and plot how the error changes depending on how far the ground truth is from the distribution mean. The results show that the error gradually increases with the distribution shift indicating the estimated limits of self-critic's reliability. Note that in Table 6 the errors are computed differently: for in-distribution (based on the test set molecules in Zine instead of the generated ones), so the errors are much lower that case.
molwt
logp
0.3
oodisturss 1 oner
75
71.09
3.5
0.2
pedicturs
0.1
25
2.14
55 (1x0Al)
237.5 (oosual
2558 Wisull
14 12.ia
2.5 1esidd
5, (4x3)))
02 (bast:
0,512esid)
0.3 (.35k)
abs del gi wauu bution meen
abs gi whlse dierrtutionn meen
ats dil the value diamtssiion meen
Figure 3: Analysis of the property predictor performance in the OOD regime. The values the y axis are the mean errors for the corresponding bin on the axis (e.g. at point 2 x std we compute the mean error for all molecules with ground truth property values between 1 x std and 2 x std). The error bar shows standard deviation (std) within the bin.
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A.7 Unconditional Generation
Table 7: Molecular graph generation performance QM9.
Method
Valid (%) Unique (%)
Novel (%)
FCD
Scaf.
SNN
Frag.
(t)
(1)
(1)
(L)
(1)
(t)
(t)
Domain-agnostic graph generative models
EDP-GNN
47.52
99.25
86.58
2.680
0.3270 0.5265 0.8313
GraphAF
74.43
88.64
86.59
5.625
0.3046 0.4040 0.8319
GraphDF
93.88
98.58
98.54
10,928
0.0978 0.2948 0.4370
GDSS
95.72
98.46
86.27
2.900
0.6983 0.3951 0.9224
DiGress
98.19
96.67
25.58
0.095
0.9353 0.5263 0.0023
DruM
99.69
96.90
24.15
0.108
0.9449 0.5272 0.9867
GraphARM
90.20
1.220
GEEL
100.0
96.08
22.30
0.089
0.9386 0.5161 0.9891
Molecule-specific generative models
CharRNN
99.57
0.087
0.9313
0.5162 0.9887
CG-VAE
100.0
1.852
0.6628
0.3940 0.9484
MoFlow
91.36
98.65
94.72
4.467
0.1447
0.3152 0.6991
STGG
100.0
96.76
72.73
0.585
0,9416
0.9998 0.9984
Unconditional (masking all properties)
STGG+
100.0
97.17
74.41
0.089 0.9265 0.5179 0.9877
Conditional (using test properties)
STGG+ (k=l)
100.0
97.63
75.99
0.134
0.8906
0.5004 0.9799
STGG+ (k=5)
100.0
96.86
74.18
0.166
0.9050
0.5039 0.9860
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Table 8: Molecular graph generation performance Zinc250K.
Method
Valid (%) Unique (%) Novel (%)
FCD
Scaf.
SNN
Frag.
(f)
(f)
(1)
(1)
(1)
(t)
(1)
Domain-agnostic graph generative models
EDP-GNN
63.11
99.79
100.00
16.737 0.0000 0.0815 0.0000
GraphAF
68.47
98.64
99.99
16.023 0.0672 0.2422 0.5348
GraphDF
90.61
99.63
100.00
33.546
0.0000 0.1722 0.2049
GDSS
97.01
99.64
100.00
14.656
0.0467 0.2789 0.8138
DiGress
94.99
99.97
99.99
3.482
0.4163 0.3457 0.9679
DruM
98.65
99.97
99.98
2.257
0.5299 0.3650 0.9777
GraphARM
88.23
16.260
GEEL
99.31
99.97
99.89
0.401
0.5565 0.4473 0.9920
Molecule-specifee generative models
CharRNN
96.95
0.474 0.4024 0.3965 0.9988
CG-VAE
100.0
11.335 0.2411 0.2656 0.8118
MoFlow
63.11
99.99
100.00
20.931 0.0133 0.2352 0.7508
STGG
100.0
99.99
99.89
0.278
0.7192 0.4664 0.9932
Unconditional (masking all properties)
STGG+
100.0
99.99
99.94
0.395
0.5657 0.4316 0.9925
Conditional (using test properties)
STGG+ (k=l)
100.0
100.0
99.98
0.514
0.5302
0.4099 0.9917
STGG+ (k=5)
100.0
100.0
100.0
0.562 0.5491
0.4176 0.9909
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A.8
Full Table of conditional generation on HIV, BBBP, and BACE
Table Full table: Conditional generation of 10K molecular compounds on HIV, BBBP, and BACE.
Distribution Learning
Condition Control
Tasks Model
Validity
Coverage"
Diversity f Similarity
Distance
Synthe. MAR
Property Acc.
DiGress
0.351
0.886
0.694
24.656
2.068
0.506
DiGress v2
0.355
8/8
0.881
0.703
25.327
2,337
0.511
GDSS
0.288
4/8
0.876
0.271
46.754
1.642
0.504
Synth. BACE
MOOD
0,995
8/8
0.890
0.259
44.239
1.885
0.506
Graph DiT
0.867
8/8
0.824
0.875
7,046
0,400
0.913
Graph GA
1.000
8/8
0.859
0.981
7,410
0.963
0.469
MARS
1.000
0.834
0.883
6.792
1.012
0.518
LSTM-HC
0.997
0.798
17.559
0,921
JTVAE-BO
1.000
0.668
0.728
30.470
0.992
0.463
STGG
1.000
8/8
0.824
0.979
3.824
0.453
0.949
STGG+ (ls
1.000
8/8
0.829
0.979
3.796
0.238
0.912
STGG+ (lo 5)
1.000
8/8
0.826
0.979
3.802
0.178
0.926
Train data
1.000
8/8
0,819
0.981
3.837
0.003
0.991
Test data
1.000
7/8
0.824
1,000
0.000
0.002
0.817
DiGress
0.696
9/10
0,910
0.681
18.692
2.366
0.654
DiGress v2
0.689
9/10
0.911
0.634
19.450
2.269
0.653
GDSS
0.622
3/10
0.267
39.944
1.379
Symt. & BBBB
9/10
0.172
34.251
2.028
0.490
Graph DiT
9/10
0.886
0.933
11.851
0.355
0.942
Graph GA
1,000
9/10
0.895
0.951
10.166
1.208
0.302
MARS
1.000
8/10
0.864
0.770
10.979
1.225
0.519
LSTM-HC
0,999
8/10
0.888
0.893
16.390
0.997
0.559
JTVAE-BO
1.000
5/10
0.746
0.582
33.575
1.162
0.496
STGG**
1.000
9/10
0.891
0.916
11.736
0.982
0.754
STGG+ (ls 1)
1.000
10/10
0.888
0.937
9.859
0.466
0.867
STGG+ (1 5)
1.000
9/10
0.887
0.936
10.101
0.381
0.900
Train data
1.000
8/10
0.883
0.957
9,890
0.017f
0.996
Test data
1.000
10/10*
0.880
0.998
0.000
0.018
0.806
DiGress
0.438
22/29
0.919
0.856
13.041
1.922
0.534
DiGress v2
0.505
24/29
0.919
0.848
13.400
1.593
0.533
GDSS
0.693
4/29
0.782
0.103
45.342
1.252
0.483
Synth. HIV
MOOD
0.288
29/29
0,928
0.136
32.352
2.314
0.511
Graph DiT
0.766
28/29
0.897
0.958
6.022
0.309
0.978
Graph GA
1.000
28/29
0.899
0.966
4,442
0.984
0.604
MARS
1.000
26/29
0.876
0.652
7.289
0.969
0.646
LSTM-HC
0.999
13/29
0.909
0.915
7.466
0.948
0.674
JTVAF-BO
1.000
3/29
0.806
0.417
41.977
1.236
0.485
STGG**
1.000
27/10
0.899
0.961
4,558
0.442
0.950
STGG+ 1)
1.000
27/29
0.896
0.970
4.075
0.314
0.876
STGG+ 5)
1.000
24/29
0.897
0.9700
4.317
0.229
0.905
data
1.000
27/29
0.970
4.019
0.018t
0.999
Test data
1.000
21/29*
0.895
0.998
0.074
0.015t
0.726
"The classifier from Liu et al. (2024) (used in the last column) has limited accuracy on the test set; thus, any Property Acc. above the test data accuracy is indicative better quality. Similarly, atom coverage is not 100% on test data; thus, any coverage above the test set coverage does not indicate better performance.
STGG with categorical embedding, missing indicators, random masking, and extra symbol for compounds. The dataset properties are rounded to two decimals hence MAE is not exactly zero.
24

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Published in Transactions on Machine Learning Research (12/2025)
A.9 Min-MAE or Max-Reward molecules generated by STGG+
A.9.1 Zinc OOD
Figure 7: Conditioning on logP=-3.2810
Figure 4: Conditioning on mo/W0=580.00
CI
Figure 5: Conditioning on mo/W1=84.0008
Figure 8: Conditioning QED=1.2861
NH
H.N
Figure 6: Conditioning 1ogP=8.1940
Figure 9: Conditioning on QED=0. 1778 (which means low Srug-likeness and less "chemical beauty" (Bickerton al. 2012)
25

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Published in Transactions on Machine Learning Research (12/2025)
A.9.2 QM9 Reward Maximization
F
Figure 10: Best QM9 reward maximization molecules
F
26

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Published in Transactions on Machine Learning Research (12/2025)
A.9.3 Chromophore OOD
OH
HyN
NH
H,N
NH
NH3
NH3
HgN
Figure 11: Conditioning on molW:=1538.0
Figure 13: Conditioning on 1og6=113.6292 13.6292
OH
Figure 12: Conditioning 1ogP-28.6915
Figure 14; Conditioning QED=1.2355
27

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Published in Transactions on Machine Learning Research (12/2025)
A.10 OOD Tables with Mean MAE over the top-100 molecules
Table 10: Out-of-distribution (u 4o) property-conditional generation of 2K molecules on 250K
Properties top-100
Mean MAE
molWt
logP
QED
Condition
84
580
-3.2810
8.1940
0.1778
1.2861
STGG*
18.248
5.559
1.204
1.548
0.206
0.022
STGG+ (A: = 1)
0.790
1.389
0.018
0.900
0.003
0.561
STGG+ (A: =
1.289
1.503
0.021
3.710
0.003
0.571
STGG+ (w 100~~1 --,
1.533
2.088
0.040
0.285
0.005
0.060
STGG+ (w~ ~(050 2), k0
1.285
1.104
0.022
0.803
0.004
0.042
"The value is improper. condition 1.2861 but calculate the MAE with respect to the maximum QED (0.948).
""SGGG with missing indicators, and random masking.
Table 11:
Out-of distribution (μ + 40) property-come conditional generation of 100 molecules on Chromophore DB. We removed the low molWt and QED which are both impossible negative values.
Properties
Mean MAE
molWt
logP
QED
Condition
1538.00
13.63
28.69
1.24
Trained on Chromophore DB (1000 epochs)
STGG+ (A: 1)
256.6
11.1
5.1
0.6
STGG+ (k: 100)
562.3
11.0
16.3
0.5
STGG+ (w ~ U1( (0, 1)
805.6
15.4
11.1
0.5
STGG+ w ~ 2((-0.5,2) 2), = 100)
609.5
8.8
14.3
0.2
Pre-trained on Zinc250K (50 epochs) and fine- tune-tuned on Chromophore DB (100 epochs)
STGG+ (k: = 1)
294.9
8.4
6.1
0.5
STGG+ (A: 100)
401.9
5.6
0.4
STGG+ ((-0.5, 2),
543.0
14.6
12.7
0.5
STGG+ (w ~ 2(-0.5 2), k 100)
416.5
6.1
13.0
0.2
"The value of 1.24 improper; we calculate the MAE with respect to the maximum QED (0.948).
In Table 11 STGG+ with pre-training and fine-tuning generally performs slightly hetter than regular training. Random guidance is helpful for high QED.
28

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Published in Transactions on Machine Learning Research (12/2025)
A.11 Algorithms
Algorithm STGG+ Training
Require: Dataset D {(11, 24)) where is molecule and Y IR P are its properties Require: Transformer model fo
1: while not converged do
2: Sample batch (z1,..., TB) and properties (un....,,y)) .B))
3: for each molecule 2; batch do
Tokenize F; into sequence (f.....,tt)
Mask random subset of properties from yi (yi), Win), where Uniform(O,, D) Compute ( fu2), where hj + (ttt:li.tt,....... (9-1))
7: Compute the cross-entropy loss LCE
8: Compute the auxiliary property prediction loss Spoop
2 21158 spred (hL) 3all
9: Update using gradient descent on L = LCE + pmpp
Algorithm STGG+ Sampling with Self-Criticism
Require: Target properties Marget E R²'
Require: Guidance strength number of candidates K, max length Lmax Transformer model fo
Require:
I: Generate K candidate molecules:
2: for k to do
Initialize the sequence; t + [BOS]
Sample guidance scale (0.55, 2) (optional; otherwise w=1 means guidance)
for 2 to Linax do
6:
Compute conditional logits 2. fo(t Matagtt .1,, (j-1)
7:
Compute unconditional logits 2n = fett (0, t1...., t--1)
8:
Apply Classifier-Fres Guidance (CFG): = W2c + (1 w)
Mask invalid tokens (valency violations, syntax errors, ring overflow, etc.)
10:
Sample the next token ty Softmax(2)
11: t,
[EOS] then break
12:
13: Store the molecule 8t
14: Self-criticism:
15: for each candidate do
16: Process $ through fo with empty properties to predict Úx
17: Compute distance dy = IlAe - Vturge l12
18: return sj where j + arg min; du (Select the best candidate)
29

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Published in Transactions on Machine Learning Research (12/2025)
A.12 Masking
Here we describe the original STGG masking algorithm and the improved STGG+ masking algorithm.
Algorithm 3 STGG Masking algorithm
Require:
maximum number rings ringmer I: if token is an atom then allowednex: [bonds, branchatort, ringstart)
3: if all branches are closed then
4:
aulouredncxx.appene(([E3]
5: else
6:
alloweddnert-ppeene (brrreeeeeeepeeeeeeeeeeeeeeeee (branchens))
7: if token is bond then
8: allowedneat = [atoms]
9: for to ringmax do
10: riiigg" has not been closed then
alloweddesst (ringeenl)
12: if token is a branch start then
allowednex: [bonds]
14: if token is branch end then allowedweat [branch.tar:] 16: if all branches are closed then
18: else
19:
allowednent apppredddddnappddd(( (brancheen)))))))))
20:
if token is ring start then
21:
allowedwest = [bonds, branchsters, ringstar)]
all branches closed then (pppeeddeeaaapeeed(((((()) else
23:
25:
allowednent.com alloweednettaapeed((((eeee www.oappedddnn... (branchebr)))))
token ring end then allowed.ent =
27:
branches are closed then (allovedloer..pppeee[(((((O
29:
30:
else
allowrednes---pppeee (braenchhaar 32: Beginning Of Sentence (BOS) then
31:
33:
allowed.eat [atoms]
34: if End Of Sentence (EOS) then
allowedhent
36: Apply the valency mask (remove illegal tokens from allowednest based on the valency of the atoms)
Mask every token not included in allowednest before sampling the next token
30

---

Published in Transactions on Machine Learning Research (12/2025)
Algorithm STGG+ Masking algorithm
Require: maximum number rings ringmas
Require: maximum length of sequence M MAXLNN
1: token is an atom then
2: allowednex: [bonds, branchatert]
3: this is the second double-bond in tow within a branch then allowedwent remoove [borditoubte))
5: we have made less than ringman rings then
allowednext perdddeeet-ppppeepeee -append (ringstars))
7: all hranches are closed then
allowedneat aapeedd ( (EOS)) if empty bonds (.) are allowed (for compounds such as [Na+)][CI-]) then allowednezt wwppeddpppddaao...aaa allowechha..pppend(((
9:
11: else
12:
allowednent oppendd (branchen)) (
if token is bond then 14: allowednest = [atoms]
13:
for 11to ringmax do
16:
ring has not been closed then
allowedhess
18: if token is branch start then allowednezs [bonds]
20: this is the sccond double-bond in row within a branch then
allowednezt peruueddexttremmooee remove( (Beneddousee)
22:
if token is branch end then allowedwest [branch.tars]
24:
if all branches closed then (pppeeel (EOS)) if empty bonds (.) allowed then
26:
27:
allowednezt append((paappmmcmmmpmm.... (ropeen((ooneeppt))))
else
29:
allowednent (apprrelleappppp(((((eee (branccce())))))
if token is ring start then allowednent = [bonds, branchsters) this is the second double-bond in within branch then
31:
33:
allowednestt -ewueeeeeeeeeeooeeee. remove( [bonddoubt))
we have made less than ringmaa rings then
35:
allowednest appendd [ringsstars]) ())
branches are closed then allowed append(( (EOSS) empty bonds (.) are allowed then allowednezt appeedd (bondemppy)))))
37:
39:
40:
else
pettuuednattaapeeeeee (branchbaa)))) if token is ring end then allowed,ers
42:
44:
if all branches are closed then alloweddest--pppend (ppend([EOS) if empty bonds (.) are allowed then
46:
allowednezt.oo (bondemppo)))))))
48:
else
49:
ielloweddert-apppeeee [branchend) if Beginning Of Sentence (BOS) Empty bond (.) then allowed = [atoms]
50:
51:
52: if End Of Sentenec (EOS) then
53:
allowednest =
When getting too close M M...r.N. if possible, remove atom, bonds, ring-start, branch-start tokens from allowedwens
55: Apply the valency mask (remove illegal tokens from allowednest based on the valency of the atoms)
Mask every token not included in allowednezs hefore sampling the token
31


Reviews:
[{"review_id": "ssYJZ4QnJU", "reviewer": "Reviewer_gJMm", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose an extension of an existing approach for generating molecules, and aim to satisfy molecule properties specified by the user. As a limitation of the existing model, the authors identify that it often generates invalid molecules. They mitigate this shortcoming by introducing several improvements, including how a partial molecule can be extended (to prevent moves that are likely to end up generating an invalid molecule), and providing the model with a self-criticism module. The authors also draw on a range of recent advances in deep learning and integrate several approaches for improving training. In an empirical evaluation, the authors demonstrate that their proposed model outperforms several baselines, achieving state-of-the-art performance in several commonly used benchmarks. However, in some cases, their restrictions for guiding molecule generation limit the diversity of generated molecules compared to the original approach they extend.\n\nI found the writing of the paper clear, and the authors' ideas easy to follow. However, I also believe that the work could be somewhat more self-contained. Specifically, the authors make references to many recent deep learning advances, which they integrate into their model, but they do not explain how those recent concepts work, what their expected benefit is, or why it makes sense to use them. I believe that readers who are very familiar with molecule generation or closely follow rather technical developments in deep learning will probably have no trouble following along. However, for a general machine learning audience, it may be more difficult to grasp why each of the components was chosen.\n\n### Strengths\n- This work considers an important problem, namely generating molecules with certain properties.\n- The proposed method integrates recent deep learning advances and outperforms the chosen baselines on commonly used benchmark datasets.\n\n### Weaknesses\n- The work could be more self-contained. Specifically, to address a broader audience, the authors could explain in more detail how the model they extend (STGG) works and why they make each specific architectural choice (section 3.1).\n- The authors make claims that are not supported with evidence: (1) in the conclusion, the authors claim that their approach is \"extremely efficient and fast\", however, they do not explain further what that means, for example by comparing empirical runtimes with baselines; (2) the authors claim that their model's self-criticism \"significantly improves the quality of its generated molecules\", however, they do not use any statistical significance test to support this claim.", "claims_and_evidence_yn": "No", "claims_explanation": "The authors claim and show that their method outperforms current baselines for molecule generation. However, as mentioned above, there are claims that are not sufficiently supported by evidence. Specifically:\n\n1. In the conclusion, the authors claim that their approach is \"extremely efficient and fast\", however, they do not explain further what that means, for example, by comparing empirical runtimes with baselines\n2. The authors claim that their model's self-criticism \"significantly improves the quality of its generated molecules\", however, they do not use any statistical significance test to support this claim.", "audience_yn": "Yes", "audience_explanation": "Yes, I believe this is the case. At least those who work on molecule generation or related topics (transformers and technologies powered by transformers, such as large language models) would be interested in the findings. The present work is probably interesting to at least some readers because it combines several recent developments in deep learning to push the state-of-the-art in molecule generation.", "requested_changes": "### Critical points\n- The statement regarding that STGG+ is \"extremely efficient and fast\" needs to be supported by evidence. This could be done, for example, by showing empirical runtimes (if this is what the authors mean, otherwise, they need to clarify what they mean by \"fast\").\n- If the authors wish to claim significance, they need to support the statement that the \"best-out-of-k strategy significantly improves the quality of its generated molecules\" with statistical significance tests.\n- In section 3.3, the authors mention that they extend the vocabulary of STGG, which enables \"the model to solve a broader range of problems\". However, I do not believe that the authors explain what problems STGG+ can solve that STGG cannot solve. I believe the authors should clarify this, so the reader may understand in what ways STGG+ is more powerful than STGG.\n- The concept of \"extreme out-of-distribution properties\" comes up several times, but it is not explained what exactly this means. I believe this should be explained (to be honest, though, I am not an expert in molecule generation, so if this is a common term and the reader can be expected to know what this means, you can discard this comment).\n- I believe it would be useful to say some words about the real-world readiness of STGG+. Specifically, in this paper, the authors considered \"6 conditions (2 per property)\". Is that a realistic setting? How many settings can STGG+ handle? Is there some upper limit? How does STGG+ scale to situations with many properties? How much (more) training data is required per additional property?\n\n\n### Not critical, but would strengthen the paper\n- I believe it would strengthen the paper if the authors could explain in at least some detail why they make the architectural choices mentioned in section 3.1. As it stands now, I believe this is merely a list of many recently proposed works, but it does not help the reader understand *why* the authors made these choices.\n- I find the example for missing features in section 3.2 confusing and did not find that it helped my understanding. Perhaps the authors can rephrase.\n- For categorical values, the authors mention that they add an extra category to represent missing values. But in the end, they need to be encoded with floats anyway, right? Or are they one-hot encoded vectors? Perhaps a brief explanation would be useful.\n- The authors mention that they \"mask a random subset of $t$ properties, where $t$ is chosen uniformly between $0$ and the total number of properties\". Is it realistic that a subset of $t$ random features could be missing? Or does it not matter what a realistic setting is because the model must be able to deal with any missing subset of features?\n- The authors mention that their data-centric approach \"allows [them] to represent complex structures\", which sounds a bit as if a non-data-centric approach would not be capable of doing that. Is that what is meant here?\n- It sounds a little strange to say that \"we generally maintain 100% validity\". If it is always 100%, then it's not necessary to say \"generally\". And if there are situations with less than 100%, then one cannot say that it is \"generally 100%\". This should probably be rephrased.\n- What do you mean when you say that the classifier-free guidance \"[directs] the model more towards the conditional model's direction while pushing it away from the unconditional model's direction\"? Does \"the model\" refer to what STGG+ has currently learned? And \"the conditional model\" is the true, but unknown model? In any case, I feel like there are too many \"directions\" in the sentence, which was what confused me.\n- It seems a bit strange to point out, in the main text, that a certain paper had been selected for an oral presentation at NeurIPS 2024. Perhaps this should be removed.\n- In section 4.3, GflowNet is mentioned as one of the baselines, but does not appear in Table 3.\n- Why are there no baselines used in section 4.4, Table 4?\n\n\n### Minor points\n- I believe it should be \"we cannot assume ~the~ plausible values for the missing features\"\n- Since it is rare that the \"problematic situation of incompletely-generated samples\" occurs, I am wondering whether the additional masking step to prevent this adds much? Could one not instead simply increase $k$ and just assume that, since problematic situations are rare, everything will be fine?\n- You mention that you \"mask the creation of rings\", did you mean \"the token of rings\"?\n- Redundant \"molecules molecules properties\" in section 3.6.\n- In section 4, the abbreviation \"OoD\" is used while the rest of the paper uses \"OOD\".", "broader_impact_concerns": "The authors have included a \"Broader Impact\" statement, where they acknowledge the possibility that their work could be used to generate \"harmful molecules\". I do not have any concerns regarding their statement, and do not believe that it needs to be changed.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "LfHmRz6Z3R", "reviewer": "Reviewer_XUrS", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces STGG+, an advanced framework for any-property-conditional molecule generation, building upon the Spanning Tree-based Graph Generation (STGG) model. It combines modern Transformer techniques (RMSNorm, rotary embeddings, FlashAttention-2, and SwiGLU) with new strategies such as random property masking, self-criticism via auxiliary property prediction, and randomized classifier-free guidance (CFG). These improvements enable flexible conditioning on arbitrary molecular properties and enhance generalization to out-of-distribution (OOD) settings.\n\nThe model is evaluated on multiple benchmarks, including QM9, Zinc250K, BBBP, BACE, HIV, and Chromophore DB. The results show near-perfect molecular validity, strong property control, and improved diversity compared to prior baselines such as Graph DiT and MOOD. The authors also perform extensive ablation studies, confirming that each component contributes meaningfully to the overall performance.\n\n# Strengths\n\n- The integration of self-criticism and random property masking introduces genuine novelty. Allowing the model to evaluate its own outputs represents a creative step forward in molecular generation.\n\n- The adoption of state-of-the-art Transformer design principles makes the framework scalable, efficient, and aligned with contemporary LLM architecture trends.\n\n- The model is tested across multiple datasets and task types, including OOD property conditioning and reward maximization. The empirical scope is broad and thorough.\n\n# Weaknesses\n\n- The evaluation relies on RDKit-based validity metrics, which do not guarantee chemical realism or synthetic feasibility. There is no expert or simulation-based validation of generated molecules.\n\n- The use of basic properties such as QED, logP, and SAS limits the scope of the evaluation. These metrics are convenient but not always chemically meaningful.\n\n- The self-evaluation predictor is trained jointly with the generator, which may lead to bias and inaccuracy, especially in OOD property regions.\n\n- Some baselines differ in training paradigms (offline vs. online), making comparisons less direct. Computational costs and training efficiency are not fully discussed.", "claims_and_evidence_yn": "Yes", "claims_explanation": "n/a", "audience_yn": "Yes", "audience_explanation": "The topic is about the generative models, bioinformatics, molecules, MCTS, which are widely discussed topics in machine learning community.", "requested_changes": "See weaknesses", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "pEo436Bcyc", "reviewer": "Reviewer_jLEz", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper's primary contribution is advancing the \n\n1) Spanning Tree-based Graph Generation (STGG) framework from a purely unconditional model into a state-of-the-art, multi-property conditional molecule generator called STGG+. The authors achieve this through several clever innovations. They introduce a training strategy where properties are \n\n2) randomly masked , which allows the final model to generate molecules based on any combination of target properties without being retrained. Furthermore, they incorporate a novel \n\n\n3) \"self-criticism\" mechanism by training the model to also predict a molecule's properties ; during generation, this allows the model to create several candidates and then intelligently select the best one. By combining these ideas with an upgraded, modern Transformer architecture and an advanced sampling technique called \n\n4) \"random guidance,\" they create a model that excels at generating high-quality, valid molecules that meet specific criteria, even for challenging out-of-distribution targets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Yes, the claims made in the submission are well-supported by accurate, convincing, and clear evidence presented throughout the paper. \n\nThe central claim that STGG+ achieves state-of-the-art performance is convincingly supported across three distinct and challenging tasks.\n\n1) In-Distribution Generation: In Table 1, the authors compare STGG+ against powerful recent models, including the graph diffusion model Graph DiT. The results clearly show STGG+ achieving the best performance on the Fréchet ChemNet Distance (FCD) metric and the lowest (best) Mean Absolute Error (MAE) on the BACE and HIV datasets, demonstrating superior property conditioning and distributional similarity.\n\n2) Out-of-Distribution (OOD) Generation: For the more difficult task of generating molecules with extreme properties, Table 2 shows that STGG+ obtains a much smaller property error (MinMAE) than competing methods and the base STGG model. This provides strong evidence of its effectiveness in novel chemical space exploration.\n\n3) Reward Maximization: The paper demonstrates in Table 3 that STGG+ achieves the highest average reward on a multi-objective task, surpassing online methods like GFlowNet. The evidence is particularly convincing as it also highlights the model's superior data efficiency, using only about 11.5% of the molecules required by the online approaches.\n\nThe claim that the novel components of STGG+ are crucial to its success is clearly validated through a detailed ablation study. Table 5 systematically removes or alters key components of the model, such as the improved architecture, the property-prediction loss (which enables self-criticism), and the random guidance strategy. In each case, the model's performance degrades, providing direct and convincing evidence that each of these contributions is beneficial and collectively responsible for the final model's high performance.", "audience_yn": "Yes", "audience_explanation": "This research is interesting because it offers a powerful, efficient, and highly flexible tool for designing custom molecules from scratch, which has significant real-world implications across several scientific and technological fields.\n\nThe most direct application is in accelerating the search for new medicines. Researchers can use this model to generate novel molecules with a specific therapeutic profile.", "requested_changes": "The following are recommendations that would improve the paper's completeness and practical relevance \n\n1) Provide a Proxy Metric for Synthesizability. The authors correctly state that the validity metric used, as measured by RDKit, is not a full picture of chemical validity and that generating synthesizable molecules remains an open question. To better address this, I suggest reporting a standard proxy for synthesizability, such as the Synthetic Accessibility (SA) score, for the molecules generated in the out-of-distribution and reward maximization tasks. This would provide stronger evidence that the model generates plausible molecules, not just computationally valid but overly complex ones.\n\n2) Include a Deeper Analysis of the Self-Critic's Failure Modes. The paper transparently notes that its internal property predictor may be less accurate than specialized predictors and can struggle in out-of-distribution (OOD) scenarios, which can cause the model to select a suboptimal molecule. To better quantify this limitation, it would be beneficial to add a brief analysis showing how the predictor's accuracy degrades as the conditioning values become more extreme. This would offer readers valuable insight into the model's reliability limits.\n\n3) Explicitly Demonstrate \"Any-Property\" Conditioning. A key contribution is the model's ability to condition on any subset of properties without retraining, enabled by random masking of properties during training. While the experiments on multi-property datasets implicitly support this claim, the work would be more convincing if this flexibility were demonstrated explicitly. For example, the authors could add a small experiment in the appendix using a model trained on the HIV, BACE, or BBBP datasets  to show its performance when conditioned on only one or two properties, rather than all of them. This would provide direct validation for this powerful and practical feature.", "broader_impact_concerns": "The submission includes a \"Broader Impact\" section that acknowledges the core ethical implication of the work: its dual-use potential. The statement correctly identifies that the technology could be used for beneficial purposes, such as developing new drugs and materials, but also notes that \"harmful molecules could also be discovered\"\n\nMy main concern is that this statement, while accurate, is insufficiently addressed and overly brief. The potential for misuse of a powerful molecular design tool warrants a more thorough discussion. The work enables the generation of novel molecules with specific, targeted properties, which could theoretically be used by malicious actors to design new toxins, chemical weapons, or illicit substances.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)