MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Authors: Peter Eckmann
Dongxia Wu
Germano Heinzelmann
Michael K Gilson
Rose Yu
Venue: ICML 2025 poster (2025)
Keywords: drug discovery
multi-fidelity learning
active learning
Primary area: applications->chemistry_physics_and_earth_sciences

Abstract: Current generative models for drug discovery primarily use molecular docking as an oracle to guide the generation of active compounds. However, such models are often not useful in practice because even compounds with high docking scores do not consistently show real-world experimental activity. More accurate methods for activity prediction exist, such as molecular dynamics based binding free energy calculations, but they are too computationally expensive to use in a generative model. To address this challenge, we propose Multi-Fidelity Latent space Active Learning (MF-LAL), a generative modeling framework that integrates a set of oracles with varying cost-accuracy tradeoffs. Using active learning, we train a surrogate model for each oracle and use these surrogates to guide generation of compounds with high predicted activity. Unlike previous approaches that separately learn the surrogate model and generative model, MF-LAL combines the generative and multi-fidelity surrogate models into a single framework, allowing for more accurate activity prediction and higher quality samples. Our experiments on two disease-relevant proteins show that MF-LAL produces compounds with significantly better binding free energy scores than other single and multi-fidelity approaches (~50% improvement in mean binding free energy score). The code is available at https://github.com/Rose-STL-Lab/MF-LAL.

MF-LAL: Drug Compound Generation Using Multi-Fidelityy Latent Space Active Learning
Peter Eckmann' Dongxia Wu
Germano Heinzelmann Michael K. Gilson 34 Rose Yu'
Abstract
1. Introduction
Current generative models for drug discovery pri-
Generative models for de novo drug design have gained significant interest in machine learning for their promised ability to quickly generate new compounds for specific ap- plications. However, generating compounds with real-world biological activity remains a f'undamental challenge (Handa et al., 2023; Coley et al., 2020). One of the main difficulties is the computational evaluation compound- ppotteinnnnn bind- ing affinities. The generated compounds are often highly novel, activity predictor trained with existing exper- imental data is insufficient due poor out- out-of-distribution generalization (Chatterjee et al., 2023; Ji et al., 2022). In- stead, physics-based methods that model 3D interactions between compound and target are commonly used.
marily use molecular docking guide the generation of active compounds. How- ever, such models are often not useful in prac- tice because even compounds with high docking scores do not consistently show real-world exper- imental activity. More accurate methods for ac- tivity prediction exist, such molecular dynam- ies based binding free energy calculations, but they are too computationally expensive to use in generative model. To address this challenge, we propose Multi-Fidelity Latent space Active Learn- ing (MF-LAL), a generative modeling frame- work that integrates a set of oracles with varying cost-accuracy tradeoff's. Using active learning, train surrogate model for each oracle and use these surrogates to guide generation of com- pounds with high predicted activity. Unlike previ- ous approaches that separately learn the surrogate model and generative model, MF-LAL combines the generative and multi-fidelity surrogate models into single framework, allowing for more accu- rate activity prediction and higher quality samples. Our experiments two diseasc-relevant proteins show that MF-LAL produces compounds with significantly better binding free energy scores than other single and multi-fidelity approaches (~~ 50% improvement in mean binding free en- ergy score). The code is available https:/ // gi thub. htthuuuucoom//ccm Rose- LLL-Iaa/MF
oracle to
Due to speed, molecular docking is the prevalent physics- based method to evaluate novel compounds by generative models (Eckmann al., 2022; Jeon & Kim, 2020; Lee et al., 2023; Noh et al., 2022; Fu et al., 2022; Peng et al., 2022; Guan et al., 2023a;b). However, docking is relatively poor predictor of activity (Pinzi & Rastelli, 2019; Handa et al., 2023; Coley et al., 2020; Feng et al., 2022), so it would be desirable to apply more accurate binding free energy calculation techniques (Pinzi Rastelli, 2019; Feng et al., 2022). These techniques, based on molecular dynamics sim- ulations, are currently considered the most reliable approach to predict affinity (Moore et al., 2023; Cournia et al., 2021). However, they have not been used by generative models due to their high computational cost (Thomas et al., 2023), with a single compound-pree protten pair taking hours to days to simulate on powerful computer (Wan al., 2020). Thus, neither docking binding free energy techniques alone can guide the real-world application of generative models.
DDepartment of Computer Science and Engineering, UC San Diego, La Jolla, California, United States Departamento de Física, Universidade Federal de Santa Catarina, Brazil 'Deparment of Chemistry and Bigchemistry, UC San Diego La Jolla, Califor- nia. United States "Skaggs School of Pharmacy and Pharmaceuti- cal Sciences, UC San Diego, La Jolla, California, United States. Correspondence Peter Eckmann <peckmann@ ucsd.edu>> Michael Gilson <mgilson @ health. www.althuus..cduu... Rose <roseyu ucsd.edu>.
Multi-fidelin surrogate models aim to fuse multiple data sources as oracles spanning a range of accuracy and cost Bfernández-Goding 2023). are frequently learned us- ing an active learning approach, where model selects or generates queries that it most uncertain about to send to chosen oracle (Ren et al., 2021). The results from the oracle then added to the training data of the model. We will focus on "query synthesis" approaches (Angluin, 1988), where the model generates its own queries to send to the oracles, speeding up learning compared to approaches that
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
query oracles with samples from fixed candidate set (Guo al., 2021; Zhu & Bento, 2017; Morand et al., 2022).
desired properties (Paul al., 2021). Early works (Jin et al., 2018; Cóómez-Bombarelii al., 2018; You al., 2018) focus on properties such as the octanol-water partition coefficient (logP) or quantitative estimate of drug-likeness (QED), which are of very limited practical utility (Coley et al., 2020; Xie et al., 2021). More recently, there has been an understanding that the binding affinity to a targeted protein is much more relevant for practical drug discovery (Xie al., 2021; Eckmann al., 2022; Fu et al., 2022).
Combining docking (low fidelity) and binding free energy (high fidelity) using multi-fidelity surrogate models holds promise to make generative models more practical. Yet, the use of multi-fidelity methods in drug discovery has been limited. Prior work from (Hemandez-Gauu Garcia et al., 2023) uses generative model to generate query compounds with high acquisition function values computed by a separate multi-fidelitty surrogate model. However, since we want to generate query compounds to send to oracles at multiple fidelity levels, the distribution of optimal query compounds may differ across fidelities. A separate generative model is not aware of such differences across fidelity levels, hence it cannot send queries to the multi-fidelity oracles efficiently.
One approach to guide generative models in optimizing compound binding affinity is to use an oracle for compound evaluation. This oracle can be applied to reinforcement learning (Jeon & Kim, 2020; Fu et al., 2022; Mazuz et al., 2023), VAFs (Eckmann et al., 2022; Noh et al., 2022), ge- netic algorithms (Spiegel & Durrant, 2020; Fu et al., 2022), diffusion models (Lee et al., 2023; Hoogeboom et al., 2022; Wu et al., 2024; Zhou et al., 2024), or other generative frameworks (Zhu et al., 2024). All of them use docking software, such as AutoDock (Morris et al., 2009), as the oracle, because it is the only reasonably fast option. How- ever, docking known to be inaccurate (Pinzi & Rastelli, 2019), and compounds with high docking scores do not consistently show experimental activity (Handa et al., 2023; Coley al., 2020; Feng et al., 2022).
We aim to address the problem of multi-fidelity genera- tion with Multi-Fidelity Latent space Active I Learning (MF- LAL), an integrated framework for compound generation using multi-fidelity active learning. Instead of separating the generative model and surrogate model, we perform sur- rogate modeling and generation together at each fidelity level using sequence of hierarchical latent spaces. This improves the quality of generated queries because there is separate latent space and decoder specialized for each fi- delity, and improves surrogate modeling because each latent space can be organized for predicting at just that level. Infor- mation is shared between fidelity levels using networks that map from lower to higher fidelity latent spaces. We use both docking and binding free energy methods as oracles in our multi-fidelity environment to achieve favorable trade-off between cost and accuracy. In summary,
Molecular dynamics based binding free energy calculations are much more accurate than docking (Moore et al., 2023; Cournia et al., 2021), but have not yet been applied to de novo generative drug design due to their high computational cost (Thomas et al., 2023). While Ghanakota et al. (2020) use binding free energy calculations in combination with molecular generative model, they focus on the optimization of known lead compound. This allows them to rely on much cheaper relative binding free energy calculations, as opposed to the absolute binding free energy (ABFE) calcu- lations needed for de novo design (Cournia et al., 2017).
We introduce a novel fidelifi generative model- ing framework, ME-LAL, which integrates data from multiple fidelity levels to generate high-quality sam- ples at the highest fidelity (binding free energy).
Structure- generative models are trained on 3D struc- tures of pootein-ligand pairs, and aim to predict 3D ligand that fits in a given protein pocket with high binding affin- ity. Techniques include autoregressive generation (Peng et al., 2022) and diffusion modeling (Guan et al., 2023a:b). Despite not needing an oracle like docking during the gen- eration process, the generated compounds are still evalu- ated with docking as a post-processing step. This means structure-basse generative models do not avoid the issue of inaccurate binding affinity prediction.
We employ an active learning approach with novel query generation technique that ensures compounds generated at higher fidelities also scored well at lower fidelities, improving the quality of generated samples.
We evaluate MF-LAL and state-of-the-art baseline methods on a real-world task of optimizing the binding free energy of compounds against two risease-relevant human proteins, and find that MF-LAL generates com- pounds with significantly better scores than baselines (~ 50% improvement in mean binding free energy).
2.2. Multi-fidelity surrogate modeling
2. Related Work
Multi Multi-fidelity modeling methods aim to fuse multiple data sources of variable accuracy and cost (Fernáádez--odiieg 2023), and are widely used in scientific fields for surrogate modeling and uncertainty quantification (Brevault et al., 2020). A popular choice of surrogate model is a Gaussian
2.1. Molecular generative models
Generative models in drug discovery have gained much interest for their ability to quickly generate compounds with
2

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
process (GP), which performs well in low data settings and produces well-calibrated uncertainty estimates (Brevault et al., 2020). One such technique to apply GPs to multi- fidelity modeling is described by Wu et al. (2020), where a downsampling kernel is used to output predictions at each fidelity level. Other multi-fidelity surrogate modeling ap- proaches utilize neural processes (Yating & Lin, 2020; Wu et al., 2022: 2023: Niu et al., 2024) and ordinary differential equations (Li et al., 2022b) an alternative to GPs.
property of interest, where the accuracy and cost of the predictions increase with the fidelity level k. We have a multi-fidelity dataset D consisting of K distinct sets of moleeule-activity pairs, one for each fidelity, D (121")
(+) yi JE....... {a yK N.) Each v/ fa( (*) is the result from querying oracle fx with molecule 1.0 The molecules are drawn from unknown distribu- tions .P.....PP.. We aim to approximate these distribu- tions using generative models p01.... ..,.....g with parameters o 0x. Note that pi # ... # pk. meaning we must learn separate generative models for each fidelity level, as opposed to previous approaches that learn a single genera- tive model for all fidelities.
(1) N₁
(0) (0)
Multi-fidelity models are frequently trained in an active learning fashion, where one uses an estimate of a model's uncertainty to most efficiently acquire more datapoints from an oracle (Ren et al., 2021). In the multi-fidelit setting, this means iteratively querying across both the sampling space and each different fidelity oracle (Li et al., 2022a; Hemandez-GGarcia et al., 2023). Traditional active learning involves selecting from a fixed candidate set with the high- est acquisition function value to query oracles with, which limits the training set to only existing samples. It also limits how much the model can learn with each query, since the maximally informative sample may not present in the candidate set. Query synthesis approaches (Angluin, 1988) have been proposed avoid this problem by using genera- et al.
Latent representation. To learn the generative models, we first learn an encoding of the input molecule to the lowest fidelity latent space. Specifically, we use a single probabilistic encoder qe parameterized by e that encodes a molecule æ into mean and variance vectors μ1 and o The latent vector Z1 NN(H,, 01), corresponding to the first (lowest) fidelity, is sampled from the resulting dis- tribution. Since we want separate latent space at each fidelity level, we define set of probabilistic networks hg, (zı)...., hhx-_, (Zx-1) with parameters E......kk11 that pass information between latent spaces. Specifically, heg takes the vector Zy as input and outputs a mean and variance vector in the subsequent latent space, Px+1: T++1- We sample from this distribution to obtain latent vector 7 i.e. Zk++1 ((P++1, Tk+1). We also define set of probabilistic decoder networks pe, (-Iz),.... ,.............. (-Izx) to reconstruct the original molecule x from the latent vectors. The use of a specialized decoder for each fidelity level im- proves reconstruction quality compared to previous methods that only use one, thus making the generated samples more tailored for their fidelity level.
tive model to generate new queries. Hernandez-Gare (2023) have applied these ideas to drug discovery problems by training a generative model to optimize the acquisition function computed by a separate multi-fidelity surrogate model, which does not take into account the different distri- butions of optimal query compounds at each fidelity.
3. MF-LAL
We introduce Multi-Fidelity Latent space Active Learning (MF-LAL), an integrated framework for compound gen- eration using multi-fidelity Bayesian active learning. An overview of our framework shown in Figure 1. We encode molecules into a hierarchy of latent spaces (left panel), one for each fidelity, and learn surrogates that predict the oracle output based on the latent vectors (middle panel). These oracles are used to reverse optimize in the latent spaces to generate new compounds with high predicted scores. The generated molecules are fed to an oracle at a chosen fidelity in an active learning loop, the output of which used to re-train the latent representation and surrogate models (right panel). After training, we use the surrogates to reverse optimize in the highest fidelity latent space and generate compounds with high property scores at the highest fidelity. See Figure 2 for a diagram of the network architecture, and Appendix A for further details of the model.
We represent molecules using SELFIES strings (Krenn et al., 2020). The encoder and decoder of MF-LAL are fully- connected neural networks that use a flattened, one-hot en- coded SELFIES string. See Table 3 for comparison with other encoder and decoder designs.
Surrogate modeling. In order to generate molecules with high property scores, we aim to learn differentiable surro- gates fi...., fx that approximate the oracles and use them for reverse optimization in the latent spaces. Each surrogate fu maps from its corresponding latent vector zy to an esti- mate of fs. We use gradient-based optimization to find a point in given latent space that has high property score predicted by the surrogate ('reverse optimization"). which can then be decoded to molecule (Gómez-Bonie Bombarelli et al., 2018). The hg. networks, which pass information between latent spaces, allow us to re-use information learned about the molecule's 's binding properties at lower fidelities to aid
3.1. Learning multi-fidelity latent representations
Problem setup. A multi-fidelity environment consists of a set of oracles (f fxk that predict a
3

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Multi-fidelity latent representation
Surrogate model
Bayesian active learning
Predict oracle output at each fidelity
Collect training data to feed back to model
Z
AutoDock4
Encode molecule into hierarchical latent spaces
Reverse optimize in latent space for novel molecule generation
K
Z K
Generated molecules used to query oracles
K
decode
Figure 1. Overview of Multi-Fidelity Latent space Active Learning (MF-LAL). Left: molecules are encoded into hierarchy of latent spaces. Middle: surrogate models predict the oracle outputs based on the latent vectors, and reverse optimization is performed in the latent spaces to generate high scoring compounds, Right: generated molecules are sent to the oracles and the results used to re-train the latent representation and surrogate models.
in prediction at the higher fidelities without having to re- learn it using large amounts of high-fidelity data. This is because training the surrogate models organize each latent space (Tevosyan al., 2022) for property prediction at that level, and so the latent vectors contain information about the binding properties useful for predicting the oracle output that can then be passed to higher fidelities. Additionally, the use of separate latent spaces for each fidelity level, as opposed to previous approaches that use only a single latent space shared across all levels, improves surrogate modeling performance because each latent space can be organized for prediction just that level.
Algorithm Active learning for MF-LAL
Require: multi-fidelity dataset D consisting of set of initial training examples, number of compounds to gen- erate to generate at lower fidelities M
1: + 1
while computational budget is not exceeded do train model on data D (Eq. 2) ggnerateHighhoorigMMosii M, 1) (Algo-
4:
I
rithm 2)
5:
query f1(()) and save result in
6:
Dj - Dp U ((1,,))
7:
if < K and Exs (zx) < 7h then
k k
We use stochastic variational Gaussian process models (SVGPs, (Hensman et al., 2015)) with hyperparameters Ax, (which define the mean and covariance ker- nels of the GP) for the surrogates. We chose SVGPs for their speed of training and ability to train with minibatches. Specifically, fi is given by fk Gm(mx, (r), Σx, (z, .²)) where m(x) and E(x, x²) are the mean and covariance ker- nels of the SVGP. To train the model, we jointly minimize the evidence lower bound (ELBO) (Kingma & Welling, 2014) of the latent encodings and marginal log likelihood (MLL) of the GP models (see Appendix A. for the full loss equation). While the loss only evaluated at fidelity k, it backpropagated through to all lower fidelities. Addition- ally, in our implementation, loss using the ELBO (Hensman et al., 2015) for improved scalability.
end if
10: end while
efficiently query the oracles, allowing us to make fewer queries to the most expensive oracles. As show in Algorithm 1, our active learning cycle consists of first generating a molecule to query at a chosen fidelity, querying the oracle to obtain the property score, appending the result to the dataset, and then retraining the model. We repeat the process until some computational budget is reached.
Similar to (Kandasamy et al., 2016), we start with only querying the oracle at the lowest fidelity level k = 1 and increase to higher fidelities when the model's uncertainty falls below certain thresholds. We use the posterior vari- ance, Exa- of the GP surrogate fa to measure the model's uncertainty. Specifically, during active learning, we repeat- edly generate latent vector Z at fidelity k that decodes to query compound. If Σx, (2x) "ik, where Y is the uncertainty threshold (which we treat as hyperparameter), then we permanently increment & by one for all subsequent queries. Otherwise, & remains the same. Once at the highest fidelity, we keep running active learning until some compu-
approximate the MIL GP
3.2. Bayesian active learning for sample-efficient training
Training multi-fidelity surrogate model requires significant computational resources, especially to gather data at the highest fidelity level. Instead of passively collecting training data, we develop a Bayesian active learning approach to

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Reconstruction
Predict Inear regression score
Reconstruction
Predict docking score
Reconstruction
Prodict binding free energy
Decoder
f
Decoder 2
Decoder K
fx
40
Z-1
figs
h2
ZK
Input molecule
Encoder
Figure 2. Diagram of ME-LAL architecture. An input molecule is encoded into the first latent space 21 using neural network. The networks .... Aex transform points in 3ı to the higher fidelity latent spaces. Each latent space has an associated decoder, which reconstructs the original molecule, and a GP surrogate model for that fidelity level.
tational budget is reached. We use this stepwise approach to ensure all surrogates have enough training data to make ac- curate predictions in high property areas of the latent spaces, thus leading to high property compounds being generated.
of the chemical space explored by the high fidelity oracles, reducing the computational cost wasted on non-promising areas and making the use of high-cost oracles feasible. also means the higher fidelity latent spaces encode a more limited distribution of compounds, improving the quality of samples generated from those latent spaces. Indeed, we show that the likelihood term is critical for strong perfor- mance (Table 3).
We generate query molecules from the latent space using the upper confidence bound (Auer, 2002) the acquisi- tion function. The method use to generate molecules is described later in Section 3.3. To ensure that generated compounds remain similar to the training set of drug-like molecules, we also add an L2 regularization term on the latent vector. The acquisition function thus given by
To compute the likelihood of point z (0) at fidelity k. first generate set of M high-scoring compounds at fidelity k - 1. Next, we map those points to a sum of Gaussians in the kth latent space using heg 1 giving us a set of M pa- rameters {(u) of ) We then measure the likelihood of point Z in the generated sum of Gaussians distribution (see Appendix A. for mathematical details). This guar- antees that the compounds generated in latent space k are also likely to have been generated in k - 1 with high scores. Thus, we effectively reduce the size of the chemical space that must be explored at fidelity k to only compounds that have already shown promise at the lower fidelities.
azz (3) k)) x (z( + SEAs (z(2)
(z) |z
(1)
where & is a point in latent space lt and B is an exploration hyperparameter. m and Σ are the mean and covariance kernels of the GP surrogate. We set B 1 during active learning, and B 0 after during inference only focus on the most promising compounds.
3.3. Generating molecules with high property scores
The full generation algorithm is detailed in Algorithm In our implementation, we vectorize optimization across all M latent space points simultaneously. In order to encourage diversity in generated compounds, we also add term to the generation objective that measures the average pairwise cosine similarity between the M points (Appendix A.
Our goal is generate compounds at fidelity k that max- imize some generation objective. To accomplish this, we perform gradient-basee based optimization to find a point ((( in the ktth latent space that maximizes the generation objec- (8) tive, and then decode z into a molecule using pe.- For our generation objective, we do not want to simply maxi- mize Se, but instead the upper confidence bound (Eq. 1) to ensure exploration during active learning. addition, we also introduce novel likelihood-basse term to the gener- ation objective that encourages the model to only sample compounds at higher fidelities that also scored well at the lower fidelities. Specifically, when generating molecule at fidelity k. we maximize the likelihood that the molecule would also be generated at fidelity l - 1 with a high prop- erty score. This additional term greatly restricts the area
4. Experiments
4.1. Experimental setup
We define multi-fidelity environment for binding affinity which uses four oracles, each of which takes molecule as input and outputs an estimate of its binding affinity with increasing accuracy:
Linear regression (f1). Simple linear regres-
5

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M) MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Algorithm 2 MF-LAL molecule generation procedure
We target the BRD4(2) and c-MET proteins (PDB SUFO and 5EOB), both of which are implicated in human cancer development, although through different biological mech- anisms. We chose these targets because ABFE is already well-validated on them and known to have good agreement with experimental data (Heinzelmann & Gilson, 2021). See Appendix for further experimental details and analysis of the oracles, including experiments confirming that our higher fidelity oracles are more costly yet more accurate distinguishing experimental actives from inactives.
Require: fidelity k to optimize compounds for, explo- ration/exploiatioon hyperparameter 3, number of com- pounds to generate at lower fidelities M
1: procedure GENNRATEHHCHSSOORNNGNOON
M,
2: procedure GETTOPLATENNPONNTSS 3)
3: for i in 1..M do k for gradient-based optimization
4: initialize ( ~ (O, I) as a starting point
5:
k then find z that maximizes Eq. 1 via gradi-
(8)
6:
Each model is provided with an initial dataset of random ZINC250k (Irwin et al., 2012) compounds queried at each fidelity (see Appendix B for further details). To compare models, we run each in an active learning loop using a fixed computational budget of days, and then generate 15 unique compounds the highest fidelity predicted to have the best scores. We then run these compounds through ABFE and compare their scores. Based on the real-world use case of our method, and following other works (Lee et al., 2023; Luo et al., 2021; Fu et al., 2022), we focus particularly on the properties of the top generated compounds. This is be- cause drug campaigns would take only the top compounds generated and use them as starting points for further opti- mization, so the binding affinities of the top compounds are the most relevant for measuring performance. See Ap- pendix C for additional results showing the oracle-predicted binding energy of the generated query compounds over the active learning process, and the reconstruction accuracy for each fidelity decoder during training.
ent descent
7:
else
8:
k- 1 2 k-
getTopLatentPoing Pontss - 1, M, 3)
9:
for j in 1. do
10:
Pi k
(1)
(1)
ha
(2
(
11:
end for find 2/
12:
that maximizes Eq. + Eq. 3
via gradient descent end if
13:
14:
end for return 2
(M)
15:
16:
end procedure
(1)
..... z (M)
17:
zi
18:
for i in M. do
20 po, (-Iz()) (1)
19:
20:
end for
21:
return 21)) (M) if k- < K else (1)
> only
need one compound at highest fidelity
22:
end procedure
4.2. Basclines
We compare MF-LAL with the following baselines:
sion model trained on experimental data from the BRD4(2VcMET target from BindingDB (Liu et al., 2007) to predict the K₁, measure of binding affinity. Morgan fingerprints are used to represent the molecule.
SF-VAE (only ABFE / only docking) (Gómez- Bombarelli et al., 2018). Uses a simple single-fidelity GP as an activity surrogate model that is used to guide optimization in the latent space of vanilla VAE, repre- senting a simple single-fidelity approach. This consists of two separate baselines, one where the GP is trained only on ABFE data and one where it is trained on only docking data.
2. AutoDock4 (/2) (Morris al., 2009). Uses 3D geo- metric and charge information from the protein and compound to estimate the binding energy.
3. Ensembled AutoDock4 (fz) (Morris et al.. 2009). Same as above, except we dock the compound into the binding pockets of 8 BRD4/5 c-MET cocrystal struc- tures that were solved with different known ligands, and then take the minimum predicted energy. This en- semble approach is generally more accurate than using a single protein structure (Amaro et al., 2018).
REINVENT (only ABFE/ oolyy/nlyya docking) (Olivecrona et al., 2017). An RL-based molecular generation tech- nique which we use to optimize ABFE. and separately, docking score. Represents a simple single-fidelity ap- proach using a modern generative model.
4. Absolute binding free energy (ABFE) (f4) (Heinzel- mann & Gilson, 2021). A binding free energy method applicable to de novo drug discovery that uses molec- ular dynamics simulations to accurately predict the binding energy.
RGA (only docking) (Fu et al., 2022). A genetic algorithm-basee method that uses 3D neural network on both the protein and ligand to prioritize mutations and crossovers. The docking score is used as the reward function, making it single-fidelity method.
6

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
VAE 4x SF-GP. Uses vanilla VAE model for molecule generation and four independent GP surro- gates for activity prediction, one for each fidelity, all using the single latent space as imput. To be contrasted with MF-LAL, which uses multiple connected latent spaces instead of a single one.
(2)4
-12.0 kcal/mol
-11.3
-10.2
C-MET
VAE+ MF-GP. Similar to above, except using a single multi-fidelity GP model activity surrogate (Wu al., 2020) instead of four independent single-fidelity GP models.
-13.9 kca//mol
-12.9
-7.9
Figure 3. Visualization of MF-LAL generated molecules. The top 3 molecules and associated ABFE scores shown for both the BRD4() (top row) and c-MET (bottom row) targets. The compounds diverse and relatively drug-like.
ME-AL-GFN (Hernandez-Garcia et al., 2023) GFlowNet generative model used optimize the pre- dicted score from a multi-fidelity GP model. This baseline represents the state of the art in multi-fidelity generation, where generative and surrogate models are separated.
4.3. Results
Table reports the average and top 3 ABFE scores of 15 compounds generated by MF-LAL, as well as those gen- erated by the baseline methods, following active learning for 7 days. We ran each method separately for two targets, BRD4(2) and c-MET, For MF-LAL and the most compet- itive baseline for each target (evaluated by lowest mean ABFE score), we evaluated an additional 25 compounds (to- 40) for improved robustness, which shown in Table 2. We also report the number of active scaffolds, which means the number of generated compounds that are active and have less than 0.4 Tanimoto similarity to any other active compound. We defined active as < -8.2 kcal/mol (< 1uM activity) for BRD4(2) and < -6.8 kcal/mol (< 10μM activity) for c-MET based on the affinities of compounds from previous works that investigate these targets (Liu et al., 2007; 2017; Naguib et al., 2024). Specifically, Liu al. (2017) consider BRD4(2) inhibitors active when they have submicromolar activity, and Naguib al. (2024) state that "potent activity" against c-MET is achieved with a 12 μM inhibitor. The number of active scaffolds metric closely reflects the goal of early-stage drug discovery, which is to identify diverse set of highly active compounds.
ME-AL-PPO (Hernandez-Garciaa et al., 2023). Same as above except using the PPO RL algorithm instead of a GFlowNet as the generative model.
MF-GP + ZINC250K. Active leamnnng using a multi- fidelity GP model (Wu et al., 2020) with a fixed can- didate set consisting of ZINC250K compounds (Irwin et al., 2012). This baseline represents a non-query synthesis approach to multi-fidelity active learning.
Pocket2Mol (Peng al., 2022). 3D structure- based drug design model that takes protein pocket as input and outputs a 3D molecule via diffusion. Unlike the other methods, does not use any binding affinity oracle during generation.
DecompDiff (Guan et al., 2023b). Same type of model above, but makes additional improvements to the generation process by decomposing generation into scaffold and motif stages.
We filtered generated compounds such that all had QED (Bickerton et al., 2012) 0.4, SAscore (Ertl & Schuffen- hauer, 2009) < 4, and no rings with > 7 atoms. 55% of all compounds generated for BRD4(2), and 68% for c-MET, fulfilled these criteria. We also only allowed compounds that fit these criteria to be queried during active learning. We filtered compounds that did not meet the criteria after gener- ation, instead of performing multi-objective optimization, because most generated compounds from single-objective optimization already had QED/SAscore in the range of typ- ical drug compounds (Bickerton et al., 2012; Ertl & Schuf- fenhauer, 2009). Following this filtering step, the mean QED of generated compounds for BRD4(2) (c-MET) was 0.59 (0.63), SAscore was 3.6 (3.5), and diversity (1 - mean pairwise Tanimoto similarity) was 0.81 (0.83).
TAGMol (only docking) (Dorna et al., 2024). 3D structure-based diffusion model that conditions gen- eration on the protein pocket. A property predictor is introduced to guide the diffusion process towards ligands that have high predicted affinity. In our case, the property predictor is a single-fidelity predictor of the docking score.
The first three baselines are single-fidell fidelity methods, where we use both only ABFE and only docking the single fidelity. The next five baselines, as well as MF-LAL, are multi-fidelity. Pocket2Mol and DicompDiff do not utilize any oracle during generation. Evaluation of generated com- pounds from all baselines is done with ABFE

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Table 1. Evaluation of 15 generated compounds at highest fidelity. The mean and top ABFE values are shown for 15 compounds sampled from each method after active learning for days. active seafs." " is the number of compounds ("scaffolds") that are active << 8.2 kcal/mol for BRD4(2) and < -6.8 for c-MET) and have < 0.4 Tanimoto similarity to any other active compound.
METHOD
BRD4(2) ABFE (KCAL/MOL)
C-MET ABFE (KCAL/MOL)
# ACTIVE
ACTIVE
MEAN SD
SCAFS.
COUNT
1ST
2ND
3RD
MEAN + SD
SCAFS.
COUNT
1ST
2ND
3RD
SF VAE (ONLY ABFE)
-0.9 2.7
0
15
-5.7
2.9
229
-.2 3.0
15
-..4
-3,9
SF- VAE (ONLY DOCKING)
-3.1
0
15
-6.1
-5.3
-4.8
-2.8 +
3.4
15
-5.9
-5.8
-5.1
REINVENT (ONLY ABFE)
-3.9
2
15
-8.7
-8.3
-8.2
+
0
15
-6.5
-5.8-5.1
REINVENT (ONLY DOCKING)
+..1
15
-11.0
-6.2
-5.7
-.0
15
-8.0
-6.8 -5.9
RGA (ONLY DOCKING)
3.9
O
15
-7.8
-7.0
-6.8
-2.1
O
15
-6.0
-5.5
VAE + SF-GP
3.1
O
15
-8.0
-5.5
-5.3
2.5
15
-6.3
-5.9
VAE + MF-GP
-1.3
0
15
-4.9
-2.0
-3.3
15
-9.7
-6.0-4.2
MF-AL-GFN
-2.5 2.2
0
15
-6.5
-5.8
-5.1
-3.1 1.8
0
15
-5.5
-4.5
MF-AL-PPO
+.5
15
9.2
-65
-.2
.4.2
15
-6.6
-5.8
MF-GP+ ZINC250K
3.9
15
-5.
-4.7
-4.5
2.9
-63
5.8 5.8
POCKET2MOL
-4.3 3.8
15
-9.8
-8.7
-8.0
2.2
4.2
15
-4.5
-3.9
DECOMPDIFF
-2.7 4.0
15
-8.9
-8.1
-7.5
-1.9
6.4
15
-8.0
-5.1
TAGMOL (ONLY DOCKING)
-1.9 3.0
0
15
-8.1
-7.6
-6.9
-3.5
3.3
15
-7.0
-5.6-5.1
MF-LAL (OURS)
-6.2 + 3.9
6
15
1.200-10.29..
-6.7 3.1
4
15
-12.9
-7.9
Table Evaluation of 40 generated compounds highest fidelity. For MF-LAL and the most competitve baseline (Table ran ABFE on an additional 25 generated compounds for increased robustness. refers to < 0.05.
METHOD
BRD4(2) ABFE (KCAL/MOL)
C-MET ABFE (KCAL/MOL)
# ACTIVE
# ACTIVE
MEAN + SCAES. COUNT
1ST
2ND 3RD
MEAN SD
SCAFS. COUNT
1ST
2ND
3RD
MF-AL-PPO
-4.3 + 2.6
40
-8.5
-6.6
-5.8
MOC
-4.6 3.8
40
-9.8
-9.8
-9.3
MF-LAL (OURS)
6.3* -6.3* 3.7
8* 40
-12.0
-11.3
-7.1 110.
100.2
3.0
6*
40
-12. -7.9
We find that the average ABFE scores of the compounds generated by MF-LAL, as well as those of the top three compounds, are significantly better (lower kcal/mol) than the corresponding scores of compounds generated by the baseline methods for both targets. The difference in aver- age ABFE score (predicted binding free energy) between MF-LAL and the top baseline is -1.6 kcal/mol for BRD4(2) (p 0.03) and -288 kcal/mol for c-MET (p 0.001), which are significant margins (see Appendix B.3 for details on the statistical tests). Additionally. MF-LAL generates sig- nificantly more active scaffolds than the most competitive baseline (p < 0.05 for both targets), and the mean ABFE score of the top compounds from MF-LAL is significantly lower than the mean ABFE score of the top 3 compounds from baseline methods (p 0.05 for both targets). Thus, method outperforms both single and multi-fidelity tech- niques, well as 3D structure-basse based methods (Pocket2Mol (Peng et al., 2022), DicompDiff (Guan et al., 2023b), and TAGMol (Dorna et al., 2024)) that do not use any binding affinity oracle. This suggests MF-LAL most capable at generating compounds with real- world activity, since ABFE scoring is the gold standard prediction method. Note, too,
that the multi-fidelity techniques other than MF-LAL per- formed mostly similarly to the single-fidelity methods. This suggests that successfully taking advantage of multiple fi- delities requires an architecture which, like that used in MF-LAL, tailored to generating compounds for multiple fidelity oracles.
The molecular structures of the top 3 compounds generated by MF-LAL for both targets shown in Figure 3. The compounds are structurally diverse, and none of them have close similars in the training set or in large datasets like Pub- Chem (Kim et al., 2023). This shows the ability of MF-LAL to generate promising and novel structures. There are some similar ring structures across the compounds generated for c-MET, but this not necessarily undesirable it shows the model has found high-property region of chemical space. The scaffold may be promising starting point for development of empirical structure- -entturr-aatiiity relationships and lead optimization by medicinal chemists. Additionally, the mean pairwise Tanimoto similarity among the 40 gener- ated compounds 0.2 for both targets, further indicating that method generates structurally diverse set.
8

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Table Ablations on model architecture. The mean and top ABFE-computed energies are shown for 15 compounds sampled from each method after active learning for 7 days.
METHOD
BRD4(2) ABFE (KCAL/MOL)
C-MET ABFE (KCAL/MOL)
# ACTIVE
# ACTIVE SCAFS.
MEAN SD
SCAFS.
1ST
2ND
3RD
MEAN +
1ST
2ND
3RD
MF-LAL (OURS)
-6.2 = 3,9
12.0
10.22
-9.8
1.7
4
-12.9
-7.9
-7.7
-FID. 1
66.1 0.7
-7.7
-7.6
-7.4
-6.0 1.1
1
-8.8
-7.0
-6.0
FID. 2
-..1
-8.5
-6.5
-6.0
-
2
-8.0
-7.3
-6.1
FID. 3
4.2
-9.2
-5.9
-5.7
4.2
-9.8
-7.1
-6.1
FID. 4
-2.4 3.2
-8.6
-4.3
-3.4
-3.1
4.0
-7.6
-6.7
-5.1
w/o LIKELIHOOD TERM
4.1
-11.9
-9.7
-9.0
-3.8 3.7
2
-10.9
-7.7
-6.3
TRANSFORMER ENC/DEC
-6.1 6.1
-11.5
-9.9
-9.0
2.9
2
-11.6
-7.6
-6.5
GCN ENC/DEC
-5.9
-0.99
10.11
-9.0
-6.1
1
-11.1
-7.5
-6.5
Table reports results from various ablations of the MF- LAL architecture (using 15 compounds sampled from methods). We experimented with removing each fidelity level individually, removing the likelihood term from the generation objective, and replacing the fully-connected coder/decoder networks with a Transformer (Vaswani et al., 2017) and graph convolutional network (GCN for encoder and inner product decoder as described by Kipf & Welling (2016)). The results show that all fidelities contribute to performance. Removing the likelihood term greatly reduced the performance of our method, showing that the approach of only querying compounds at higher fidelities that also scored well at lower fidelities is critical for strong perfor- mance. Replacing the culnecco encoder/decoder with a Transformer had little effect on performance, so we used the simpler fully-connected version. Finally, changing the molecular representation to a graph and replacing the fully- connected encoder/decoder with GCNs (Kipf & Welling, 2016) resulted in slightly worse performance.
molecules and increasing the unpredictability of the surro- gate outputs. We also note that by design, MF-LAL may miss scaffolds the highest fidelity that have strong binding if the lower fidelity oracles did score that scaffold well. We consider this necessary tradeoff to make the search for good compounds at the highest fidelity computationally tractable. Finally, it should also be noted that our experi- mental setup of evaluating each method after a fixed run time of week may lead to high variance in the results, because each method has not been trained to convergence. While this most accurately reflects real-world usage, may mean the ABFE values of the top generated compounds are somewhat variable between runs. Future work could include using a reaction reaction-aware generative model that generates more synthesizable molecules (Horwood & Noutahi, 2020).
Impact Statement
Similar other works that apply machine learning drug discovery, our work is subject dual use (Urbina et al., 2022). There is potential for societal benefit, by helping develop new drug compounds to treat disease. However, there also potential for harm, such as to generate new chemical weapons. Fortunately, the latter places a whole additional set of requirements on compounds (e.g. skin- absorbable volatile and subject to inhalation), so this problematic direction does not appear to be imminent.
5. Discussion and Conclusion
We present Multi-Fidelity Latent space Active Learning (MF-LAL), an integrated framework for generative and multi-fidelity surrogate modeling. Our experiments show that MF-LAL generates compounds with significantly higher activity, predicted by gold-standard binding free energy oracle, than other single and multi-fidelity ap- proaches. Thus, MF-LAL shows promise as way to gen- erate compounds with real-world binding while incurring a reasonable computational cost.
A Acknowledgments
This work was supported in part by NSF Grants #2205093, #2146343, #2134274, CDC-RFA-FT-23-0066 the U.S. Army Research Office under Army-ECASE award W91 MONNF-07-R-0003--10 the U.S. Department Of Energy, Office of Science, IARPA HAYSTAC Program, DARPA AIE FoundSci and DARPA YFA. MKG has an equity inter- est in and is a cofounder and scientific advisor of VeraChem LLC.
Limitations of our approach include limited set of ora- cles and potential lack of synthesizability of the generated compounds, since SAscore is known to be imperfect (Sko- raczyński et al., 2023). The SVGP technique we use for our surrogate models is known to overestimate the posterior vari- ance far away from the inducing points (Bauer et al., 2016), potentially biasing our method towards out-of-distribution

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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
A. Model details
The encoder, decoder, and networks are all 3-layer feed-forward networks with ReLU activations and 512-dimensional hidden layer. Each latent space has 64 dimensions. Molecules are represented using SELFIES strings (Kremn et al.. 2020), and fed the network using flattened one-hot encoding representation. The loss on the latent encodings is the ELBO, which is the sum of the KL divergence and the cross-entropy loss of the reconstruction.
The surrogate models consist of a 4-layer deep kernel (Wilson et al., 2016) to encode the input and Matern kernel for the covariance function. To accelerate training, we use an approximate GP trained with the ELBO loss (Hensman et al., 2015).
At each active learning step, we train the whole model from scratch until convergence with the Adam optimizer using a learning rate of 0.0001. For the molecule generation procedure using gradient-based optimization, we use the Adam optimizer with a learning rate of 0.1 for 100 epochs.
A.1. Training details
Given a training molecule a and associated oracle output y at fidelity k, we minimize
Po (I, Zk.) g(zn (x)
+ / pDullieeeaDD(AAeeee)a))
L(o, Ex 2, (g((ax)))))) log
(2)
4o [Z (r)
=
where g(zx|12) (a:)
heg (Zk-)
else
where the first term is equivalent to maximizing the ELBO and the second is the MLL of the GP. While the loss is only evaluated at fidelity k, it backpropagated through to all lower fidelities.
For the likelihood term of the generation objective, maximize the likelihood of a point z in latent space k. This is equivalent to maximizing the probability density function evaluated at that point:
M
(z - 14 (-04)
P ( 14 o -
Σ j=l
1
cxp
(3)
20)
Additionally, we add diversity term to the generation objective. We aim to minimize the following function:
M
s(zx i=
( Z
(4)
M
where (AA, is the cosine similarity between vectors A and B.
B. Experimental details
All experiments conducted server with 8 RTX 2080 Ti GPUs. For model and each baseline, we performed random hyperparameter search with 20 trials using only the first 3 fidelities, and took the set of hyperparameters with the best generated samples at fs following 3 hours of active learning. We excluded ABFE from the hyperparameter search due to computational cost, and just used the same set of hyperparameters for all subsequent experiments using all 4 fidelities. We note that ME-LAL was somewhat sensitive to choice of hyperparameters, especially the KLDDfrconstrruttio ratio for the decoders and the diversity coefficient used during generation. Thus, we advise users of MF-LAL to conduct a hyperparameter search similar the method we used before applying MF-LAL to a new of oracles.
Each model provided with initial dataset of random ZINC250k (Irwin et al., 2012) compounds evaluated each fidelity. Each fidelity had 5 random compounds selected, except for the first fidelity, where we supplied 200,000 compounds and associated oracle outputs. This was because we wanted a large dataset of compounds to train the encoder and decoder at the first fidelity level, ensuring that generated compounds were reasonable, and running fi was almost instantaneous. For the more expensive oracles, however, we let active learning generate compounds to query to most efficiently use computational resources.
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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
B.1. Oracles
For all oracles, we estimated the cost (for the baselines that require it) using the average run time over 10 samples with random input compounds. We also computed the ROC-AUC (shown below) of each oracle for the BRD4(2) and c-MET targets to confirm that the higher cost oracles are more accurate. To do this, presumed inactive compounds for BRD4(2) and c-MET, and then ran each oracle on all of the compounds. The actives were retrieved from the BRD4(2)c-MET target from BB with K; < 10pM, and the inactives were generated using DUD-E (Mysinger et al., 2012). As expected, for both targets, the ROC-AUC increases with higher fidelity, as well as the computational cost. This shows that the higher cost oracles are indeed more accurate, and so the hierarchy of fidelities we use sensible and applicable multi-fidelity learning.
generated dataset of 32 known active and
Linear regression (cost: 0.1s, ROC-AUC BRD4(2): 0.59, e-MET: 0.68) We used BRD4(2) and, separately, e-MET data from Bi (Liu et al., 2007) to train simple linear regression model. The input to the model was 2048-bit Morgan fingerprints, and the output the experimental binding energy in K,, converted to kcal/mol.
AutoDock4 (cost: 4s, ROC-AUC BRD4(2): 0.73, c-MET: 0.72) We prepared the AutoDock4 grid files using AutoDock- Tools (Morris et al., 2009). Arbitrary ligands were prepared using obabel (O'Boyle et al., 2011) with pH 7.4 and gasteiger partial charges. We used AutoDock-GPP SSantos-Marting et al., 2021), GPU-accelerated version of AutoDock4, for all computation. For each ligand, we performed 20 random restarts and selected the minimum predicted energy.
Ensembled AutoDock4 (cost: 44s for BRD4(2) and 68s for c-MET, ROC-AUC BRD4(2): 0.80, c-MET: 0.80) Same as above, except we used the minimum energy from 8 separate AutoDock4 runs using the same ligand and each of the following protein crystal structures (listed as PDB IDs): 5ues, 5uet, Suev, 5uez, 5uf0, 5uvs, 5uvy, 5uv2 for BRD4(2), and 2wd1, 4deg, 4dei, 4rlv, 5eob for c-MET
Absolute binding free energy (ABFE) (cost: 9:20hrs, ROC-AUC BRD4(2): 0.92, e-MET: 0.89) We use the Binding Affinity Tool (BAT.py) implementation (Heinzelmann & Gilson, 2021) for absolute binding free energy calculation, available https: / github...b//../// com/ Gieiineeeeeieeeeeeeeeeeee wwweiinzeemaann.e..m Btt.//AA.ppp....... py. For BRD4(2), we use the short tevb calculations. which were introduced recently to reduce computational cost (Heinzelmann et al., 2024). For c-MET, but we found we could reduce simulation times for all components to 30% of their original amounts and still retain strong performance. All molecular dynamics simulators are run with AMBER with GPU support. As BAT.py requires starting pose for the ligand, we used the pose generated from AutoDock4. We additionally wrote custom scripts to parallelize molecular dynamics runs across all available GPUs.
the standard SDR method,
B.2. Baselines
The details of each baseline are as follows:
SF-VAE (only ABFE/ only docking) (Gobee--Bombarllii et al., 2018). The VAE encoder and decoder, and GP surrogate, are set up similarly to those in MF-LAL. The upper confidence bound is used as acquisition function.
REINVENT (only ABFE/ / only docking) (Olivecrona et al., 2017). Used the code available at https://gitthb. can//aarcusslliveeroon/aaaa INNNEN
RGA (only docking) (Fu et al., 2022). Used the code available wtt.hb/.....fir///ggttt.o..../te reinforced-genetie caattiicalgrrihhn
VAE + 4x SF-GP. The VAE encoder and decoder, and GP surrogates, are set up similarly to those in MF-LAL. We also use the same acquisition function and generative procedure as MF-LAL for this baseline, except without the need to map points between latent spaces.
VAE + MF-GP. We use the Multi-Fidelity Max Value Entropy acquisition function for selecting compounds during active learning (Takeno et al., 2020), and a linear truncated fidelity kernel (Gardner et al., 2018) 88) for the GP surrogate.
MF-AL-GEN (Hermandez-Gann Garcia et al., 2023) Used the code available at https: //gittttubbh com/
nikita- 0209 //m//mmf--mm al--aa--- -fnf.
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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
ME-AL-PPO (Hernandez-Garciaa al., 2023). Provided in the same codebase as the referenced above.
MF-GP + ZINC250K. We use the Multi-Fidelity Max Value Entropy acquisition function for selecting compounds during active learning (Takeno et al., 2020), and a linear truncated fidelity kernel (Gardner et al., 2018) for the GP surrogate. All ZINC250K (Irwin et al., 2012) compounds are provided as the candidate set.
Pocket2Mol (Peng et al., 2022).
Used the code available at
Pocket2Mol.
DecompDiff' (Guan et al., 2023b). Used the code available https:://gttnab.ccm//ytettt DecompDiff.
TAGMol (only docking) (Dorna et al., 2024). Used the code available at https::///// httt:p://ggthub..coo wtt.:icc...//occcllllloooe TAGMo1. We used the singlc-objective gradient guidance model for optimizing binding affinity.
B.3. Statistical tests
To compare the mean ABFE score of generated compounds from each method, we used a standard Student's t-test. We also used a standard t-test for the mean of the top 3 generated compounds from each method. For these tests, we used the entire set of 40 compounds if we had in the top compounds among the methods that had 40 compounds. For comparing the number of active scaffolds, used a binomial test to compare the proportion of distinct active compounds among the total generated compounds. For this test, we cannot directly compare the samples of 40 compounds with the samples of 15 compounds, because we expect the number of active scaffolds to plateau as we generate more compounds (meaning proportion test across samples with different sizes is not valid). Therefore, the p-value we report for number of active scaffolds only compares MF-LAL with the top baseline. However, we found that limiting all methods 15 generated compounds still showed statistically significant results favoring ME-LAL
them for given method, otherwise used 15. We only analyzed the differences
C. Additional results
C.1. Oracle outputs during active learning
Fidelity Fidelity
-6.5
Oracle-predicted binding energy (kcal/mol)
-7.0
-7.5
M
-8.0
-8.5
-9.0
-9.5
Active learning cost
Figure Oracle outputs during active learning. The y-axis shows precceedrd binding energy generated query compounds, and the x-axis shows active learning progress.
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MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning
Figure C.I shows the oracle-predicted binding energy of the compounds generated during the ME-LAL active learning process. We only show fidelities 2 and 3, because fidelity is already supplied with large initial dataset so there is little improvement in the query quality during active learning, and fidelity does not show any noticeable improvement due to relatively small number of queries made. For fidelities 2 and 3, we observe marked improvement of the predicted binding energy over active learning, showing that MF-LAL successfully learns what makes a compound favorable at each fidelity level.
C.2. Reconstruction accuracy
0.9
Fidelity
h
Fidelity
Fidelity
0.8
Fidelity
Reconstruction accuracy
0.7
0.4
0.3
0.2
10
20
30
40
50
60
70
80
Active learning steps
Figure 5. Reconstruction accuracy during active learning. The y-axis shows the proportion of training set compounds that were successfully reconstructed using decoder, the x-axis shows the active learning iteration.
Figure C.2 shows the reconstruction accuracy of the decoders during active learning. Reconstruction accuracy is the proportion of compounds that were exactly reconstructed, meaning every SELFIES character is identical to the input. The decoder corresponding to the highest fidelity latent space achieves the overall highest reconstruction accuracy, which likely because it only has to decode from a very limited compound space. The lowest fidelity decoder has the worst reconstruction accuracy, because decodes the most varied set of compounds. Nonetheless, the reconstruction accuracies are relatively high across all decoders, meaning MF-LAL successfully learns the mapping from latent space back molecule at all fidelities.
17


Reviews:
[{"review_id": "OSc2vj4sli", "reviewer": "Reviewer_URfo", "summary": "This paper introduces, MF-LAL,  a generative algorithm for drug discovery based on biological activity rather than docking. Rather than conditioning on molecular docking, the authors propose a pipeline to generate molecules based on molecular dynamics-based binding free energy. As MD-based free energy calculations are prohibitively expensive, MF-LAL uses multiple oracles at varying fidelity levels to z. The authors also present a sample of efficient training to minimize the high-fidelity data required. The active learning-based method generates molecules based on the acquisition function over the hierarchical latent space and expands the dataset. Optimized molecules are then generated using gradient-based optimizations to find extrema in the latent space at some fidelity.\n\n## Update After Rebuttal\n\nI have read the rebuttal and decided to keep my score.", "questions": "", "limitations": "", "rating": 3, "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": "We thank the reviewer for their helpful feedback and positive comments about the work.\n\n> **Q1:** The training details including the supplement are sparse and disjointed. It is not easy to understand how exactly the model is trained. I know space is limited, but even an algorithm in the supplement in addition to the loss function would help\n\n**A1:** Thank you for the suggestion, we will consolidate all training details into a single section and add a training algorithm to the Appendix in the updated draft.\n\n> **Q2:** One concern would be that such an optimization causes adverse effects on the fidelity not being trained.\n\n**A2:** The loss function we use while training considers molecules from all fidelity levels 1...K, regardless of the current level k. In other words, while k dictates which fidelity data we will add to the dataset, the entire dataset is used to train the model regardless of k. This ensures that training at level k does not degrade performance at the other fidelity levels. Analyzing the reconstruction accuracy, and the accuracy of the surrogate models, confirms that they retain their performance when other fidelities are being trained.\n\n> **Q3:** The usual generation quality measures such as validity, diversity, and synthesizability are not presented\n\n**A3:** Among the generated compounds for both targets following filtering, the diversity (1 - mean pairwise Tanimoto similarity) is 0.81 for BRD4(2) and 0.83 for c-MET. The synthesizability (mean SAscore) is 3.6 for BRD4(2) and 3.5 for c-MET. The drug-likeness (mean QED) is 0.59 for BRD4(2) and 0.63 for c-MET. The validity is 100% for both targets, because we use SELFIES strings that guarantee validity. These metrics are in the range of typical drug compounds, so we consider them satisfactory. We will include these numbers in the updated draft.\n\n> **Q4:** Since all the baselines don’t have statistically significant results, it is a bit concerning to compare the results\n\n**A4:** As reported in Section 4.3, compounds generated by MF-LAL had better ABFE scores than all baseline methods at a statistically significant level (see Appendix B.3 for statistical details). Specifically, the difference between both the mean ABFE scores of all generated compounds, as well as the scores of the top 3 compounds, is significant between MF-LAL and each baseline for both targets. For the “# of active scaffolds” test, MF-LAL also produced significantly more active scaffolds than other baselines. Since MF-LAL shows statistically significant improvements over baseline methods, we do not think these comparisons are concerning.\n\n> **Q5:** Substructure similarity is measured with Tanimoto distance of Morgan fingerprints which does not capture 3D information.\n\n**A5:** If the reviewer is referring to the similarity metric we used to compute the number of active scaffolds, we do not think that capturing 3D information is critical in this case. Scaffold similarity, which is what we measure in our paper, is the most commonly used diversity metric by medicinal chemists and strongly relates to the overall structural diversity of a set of compounds [1]. Additionally, measuring the 3D shape diversity is a difficult task, and is not commonly done by practitioners [1].\n\n[1] Galloway et al. “Diversity-oriented synthesis as a tool for the discovery of novel biologically active small molecules.” Nature Communications 2010.", "claims_and_evidence": "* A key component of the active learning method present is the threshold calculation in algorithm 2 line 7 $\\sigma_{\\lambda_k}(\\cdot)$ must be well calibrated in order for the active learning to work.  \n* The reconstruction accuracy of the decoder is quite small and not very robust", "methods_and_evaluation_criteria": "* The training details including the supplement are sparse and disjointed. It is not easy to understand how exactly the model is trained. I know space is limited, but even an algorithm in the supplement in addition to the loss function would help, especially for  \n* The hierarchical latent space is interesting and optimizing at a single fidelity updates the latent space in all fidelities \n* One concern would be that such an optimization causes adverse effects on the fidelity not being trained.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "- The usual generation quality measures such as validity, diversity, and synthesizability are not presented \n- Since all the baselines don’t have statistically significant results, it is a bit concerning to compare the results", "relation_to_broader_scientific_literature": "The authors tackle a very important problem of sample efficient training of surrogate modeling. It is usually prohibitively costly to acquire the amount of data usually needed for deep learning models. So a method that maximizes sample efficiency is hugely important in the specific field of drug discovery but also beyond to other scientific domains.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "* The retrieval component of the pipeline is very similar to fuzzy search algorithms and semantic search algorithms and is not particularly novel. \n* Substructure similarity is measured with Tanimoto distance of Morgan fingerprints which does not capture 3D information. \n* The authors have many baselines and discuss potential drawbacks due to the lack of experimental samples", "other_comments_or_suggestions": "* Line 114 Col 2: querying oracle k –> querying oracle f_k\n* Line 209 Col 2: We use the posterior variance of the GP surrogate $\\sigma_{\\lambda_k}(\\cdot)$ –> We use the posterior variance, $\\sigma_{\\lambda_k}(\\cdot)$, of the FP surrogate $\\hat{f}_k$", "questions_for_authors": "N/A", "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": "", "extra_scores": {}}, {"review_id": "V5smLnrPPE", "reviewer": "Reviewer_rMi8", "summary": "This paper introduces a new approach for generating drug candidates, called MF-LAL. The proposed method utilizes a variational autoencoder with multiple latent spaces arranged hierarchically to accommodate different fidelities. The first level employs a regression model trained to predict activity on known compounds. The second and third levels are based on molecular docking to one or several protein structures, respectively. The final level focuses on absolute binding free energy (ABFE) prediction, which is the most computationally intensive model for estimating binding to the target protein. Compounds are generated using an active learning method with query synthesis. The acquisition function relies on surrogate models trained on data already collected from various fidelities. Initially, molecules of the lowest fidelity are generated until uncertainty falls below a predefined threshold. Subsequently, the model begins generating molecules from the next level of fidelity. This process continues for seven days. The results show that MF-LAL can generate molecules with the best ABFE, outperforming single-fidelity and single-latent-space models.\n\n## update after rebuttal\n\nThe Authors addressed all my comments. I decided to maintain my positive score.", "questions": "", "limitations": "", "rating": 3, "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": "We thank the reviewer for their helpful feedback and positive comments about the work.\n\n> **Q1:** There are no details on how GCN was implemented for generating molecules.\n\n**A1:** We will include details of our GCN implementation in the Appendix in the updated draft. Briefly, we used a three-layer graph convolutional network with one-hot encoded atom types for the encoder, and an inner product decoder as described in Kipf and Welling 2016.\n\n> **Q2:** The SELFIES representation is used to ensure that the string representation can be decoded to molecules, but rather heavy filtering criteria are applied (QED > 0.4, SA < 4, no rings with at least seven atoms) - what percentage of the generated compounds match these criteria for the tested models?\n\n**A2:** Among all compounds generated after training with active learning, 55% for BRD4(2) and 68% for c-MET fulfilled the filtering criteria. We find these percentages high enough such that there is no need to do multi-objective optimization, especially because generation is very fast so discarding 25-50% of the generated molecules is not problematic. We will include these numbers in the updated draft.\n\n> **Q3:** It is unclear whether the number of active scaffolds and the results of the top compounds are computed from all 40 compounds or just 15.\n\n**A3:** The number of active scaffolds and the top 3 compounds in Table 1 are computed from all 40 compounds (for MF-LAL and the top baselines). Based on this and other comments from reviewers, we will make two separate tables in the updated draft reporting results on both 15 and 40 compounds for clarity. See the response to Reviewer QauA for the MF-LAL results on only 15 compounds, including the top compound scores and the number of active scaffolds.\n\n> **Q4:** the initially generated compounds prior to filtering could be assessed in terms of validity, synthetic accessibility, and drug-likeness.\n\n**A4:** Prior to filtering, the mean SAscore of generated compounds is 3.9 for BRD4(2) and 3.6 for c-MET. The mean QED is for 0.48 BRD4(2) and 0.50 for c-MET. The validity is 100% because we used SELFIES strings, which are guaranteed to be valid. We will include these numbers in the updated draft.\n\n> **Q5:** How were thresholds -8.2 and -6.8 kcal/mol chosen for the two tested targets? Was it based on reference compounds or balance of the activity classes in training regression model for the lowest fidelity?\n\n**A5:** The thresholds were chosen based on reference compounds from previous works that investigate BRD4(2) and c-MET (see lines 368-373, left side). We roughly picked these thresholds based on the typical experimental affinities of the best binders analyzed in these works. For BRD4(2), Liu et al. 2017 (see paper for citation) explore various BRD4(2) inhibitors and generally consider compounds active when they have submicromolar (<1 $\\mu$M) activity, which is the cutoff we used in our paper. For c-MET, Naguib et al. 2024 states that “potent activity” is achieved with a 12 $\\mu$M inhibitor, so we set our activity cutoff to <10 $\\mu$M. We will include these details in the updated draft.\n\n> **Q6:** The choice of the decoder architecture seems nonstandard. Text representations such as SMILES and SELFIES are usually generated in the autoregressive fashion. Have you tried using RNNs? Was the transformer trained also to predict all characters at the same time, or autoregressively?\n\n**A6:** Both Transformers and RNNs have indeed been used in such applications. We chose to only test the Transformer architecture, however, because it has demonstrated very similar or slightly superior performance relative to RNNs on molecular generation tasks [1, 2]. Our Transformer was trained to predict characters autoregressively using the standard Transformer decoder architecture.\n\n[1] Chen et al.”Molecular language models: RNNs or transformer?” Briefings in Functional Genomics 2023.\n\n[2] Xu et al. “REINVENT-Transformer: Molecular De Novo Design through Transformer-based Reinforcement Learning.” arXiv 2024.", "claims_and_evidence": "The claims in the paper are supported by experimental results.", "methods_and_evaluation_criteria": "The method is explained clearly, and the selected evaluation metrics for the two biological targets effectively demonstrate the value of the proposed model. However, the choice of the decoder architecture is nonstandard and is compared only with non-autoregressive methods (more details in Questions For Authors). There are no details on how GCN was implemented for generating molecules. Moreover, I am curious about the validity of the generated compounds. The SELFIES representation is used to ensure that the string representation can be decoded to molecules, but rather heavy filtering criteria are applied (QED > 0.4, SA < 4, no rings with at least seven atoms) - what percentage of the generated compounds match these criteria for the tested models?", "theoretical_claims": "There are no proofs of theoretical claims that need to be checked.", "experimental_designs_or_analyses": "The experimental design is sound, but a few aspects could be improved. For example, only 15 compounds are generated and evaluated in Tables 1 and 2 for all but two best models. I believe all methods should be assessed based on 40 compounds. It is unclear whether the number of active scaffolds and the results of the top compounds are computed from all 40 compounds or just 15. Furthermore, the initially generated compounds prior to filtering could be assessed in terms of validity, synthetic accessibility, and drug-likeness.", "relation_to_broader_scientific_literature": "This paper presents an intriguing proposition for effectively training generative models to produce increasingly useful molecule candidates. A hierarchical approach with multiple latent spaces is proposed to capture representations for each fidelity separately. Stochastic variational Gaussian processes are used as surrogate functions trained on the obtained calculations of binding affinity, making these functions easy to train even for big datasets. MF-LAL can be useful in early drug discovery stages to propose novel hit candidates.", "essential_references_not_discussed": "The key references have been described in the paper.", "other_strengths_and_weaknesses": "All of my comments are described in the other sections.", "other_comments_or_suggestions": "In Algorithm 1, there is probably a typo in line 7. It should be $\\Sigma_{\\lambda_k}(z_k)<\\gamma_k$.", "questions_for_authors": "1. How were thresholds -8.2 and -6.8 kcal/mol chosen for the two tested targets? Was it based on reference compounds or balance of the activity classes in training regression model for the lowest fidelity?\n2. The choice of the decoder architecture seems nonstandard. Text representations such as SMILES and SELFIES are usually generated in the autoregressive fashion. Have you tried using RNNs? Was the transformer trained also to predict all characters at the same time, or autoregressively?", "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": "", "extra_scores": {}}, {"review_id": "7hXZzNa7Ic", "reviewer": "Reviewer_kXA7", "summary": "This paper introduces Multi-Fidelity Latent space Active Learning(MF-LAL), an framework that  integrates a set of different oracle functions to guide the generation of molecules to get higher predicted activity. It combines the generative model and surrogate model into a single framework, and the computational cost is reduced with active learning method. MF-LAL is able to achieve around 50% improvement in binding free energy score for the molecules generated compared to baseline methods, especially for two disease-relevant proteins (BRD4(2) and c-MET).", "questions": "", "limitations": "", "rating": 3, "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": "We thank the reviewer for their helpful feedback and positive comments about the work.\n\n> **Q1:** In table 1, POCKET2MOL and MF-LAL generated 40 molecules while other baseline methods generated 15 molecules. It seems that this is unfair as generating more molecules would definitely result in better ABFE scores for the top-3 molecules and more active scaffolds. But the increase in mean value is solid, so I think the author should show the separated results mean value for 40 molecules ; number of active scaffolds and top-3 values for 15 molecules \n\n> when comparing the top-3 values, it should also generating 15 molecules as for other methods for fair comparasion\n\n**A1:** Based on this and other comments from reviewers, we will make two separate tables in the updated draft reporting results on both 15 (for all methods) and 40 compounds (for the methods that have them). See the response to Reviewer QauA for the MF-LAL and baseline results on only 15 compounds, including the top compound scores and the number of active scaffolds, which remain consistent with our conclusions about the strong performance of MF-LAL.\n\n> **Q2:** Another concern is that authors use Pocket2Mol and DecompDiff as baseline model. But they are 3D pocket-based molecule generation models instead of optimization models. There are some 3D optimization models, like, DecompOpt[1] and TagMol[2]. Also RGA[3] can be included\n\n**A2:** Thank you for the references, we will cite them in the updated draft. We agree that comparing MF-LAL to a 3D optimization model would be valuable, so we are currently running TAGMol as a baseline. While the results are not yet finished due to computational cost, we will post them when they are finished during the author-reviewer discussion period. Following the reviewer’s suggestion, we have also run RGA. We ran RGA using a single fidelity (docking) as the oracle, similar to how we implemented the SF-VAE (only docking) and REINVENT (only docking) baselines in our paper. We chose to use docking, instead of ABFE, as the single fidelity oracle due to computational cost and the presumed inability of a genetic algorithm to make use of a very small number of ABFE oracle calls. We used the default parameters of RGA, with random ZINC250k compounds as the starting population for the genetic algorithm. The results from RGA are as follows:\n\n| | BRD4(2) ABFE | | | | | | c-MET ABFE | | | | | |\n| --- | --- | ---| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Method | Mean $\\pm$ std | # active scafs | Count | 1st | 2nd | 3rd | Mean $\\pm$ std | # active scafs | Count | 1st | 2nd | 3rd |\n| RGA (only docking) | -3.1 $\\pm$ 3.9 | 0 | 15 | -7.8 | -7.0 | -6.8 | -2.1 $\\pm$ 3.0 | 0 | 15 | -6.0 | -5.5 | -5.4 |\n| MF-LAL | **-6.3** $\\pm$ 3.7 | **8** | 40 | **-12.0** | **-11.3** | **-10.2** | **-7.1** $\\pm$ 3.0 | **6** | 40 | **-13.9** | **-12.9** | **-7.9** |\n\nThe results from MF-LAL are also shown for comparison. MF-LAL significantly outperforms RGA, with the latter having performance similar to that of the REINVENT baseline. We will include these results in the updated draft. \n\nFinally, we do not think DecompOpt is a good baseline to compare with because it requires knowledge of existing binders for generation (to compute the “reference arms”). Since MF-LAL and our other baselines are de novo generation methods that do not use knowledge from existing binders, we do not think a comparison with DecompOpt would be fair.\n\n> **Q3:** tested targets are limited\n\n**A3:** The number of targets we tested is limited by the high cost of ABFE calculations. In addition, the ABFE framework we use is only validated and configured for a few targets, and BRD4(2) and c-MET are the only of those targets that are of interest from a biological/drug discovery perspective.\n\n> **Q4:** From the ablation it seems that even the Linear regression fidelity contributes to the performance. Removing it would results in significant decrease of number of active scaffolds from 4 to 0. The ABFE scores for top 3 molecule also significantly decreased. Can you explain more on why this happens? My understanding is that it should have some kind of influence but should not be that obvious, as ABFE is much accurate than a linear regression model.\n\n**A4:** The lowest fidelity oracle is critical for performance because it provides the majority of the data for the multi-fidelity model. As stated in Appendix B, we provide the model with an initial dataset of 200,000 ZINC250k compounds and associated oracle outputs at the first fidelity level (linear regression). Thus, removing this fidelity greatly reduces the total data available to the model. Even if this data is significantly less accurate than ABFE, the quantity of data is still important for model performance, and so it is expected that removing this data significantly reduces performance.", "claims_and_evidence": "The main claim of this paper is the effectiveness of the proposed MF-LAL framework, which surpass other baseline methods in molecule binding free energy optimization task. Here are some concerns:\n\n1. In table 1, POCKET2MOL and MF-LAL generated 40 molecules while other baseline methods generated 15 molecules. It seems that this is unfair as generating more molecules would definitely result in better ABFE scores for the top-3 molecules and more active scaffolds. But the increase in mean value is solid, so I think the author should show the separated results mean value for 40 molecules ; number of active scaffolds and top-3 values for 15 molecules.\n\n2. Another concern is that authors use Pocket2Mol and DecompDiff as baseline model. But they are 3D pocket-based molecule generation models instead of optimization models. There are some 3D optimization models, like, DecompOpt[1] and TagMol[2]. Also RGA[3] can be included\n\n\n3. The case shown in Figure 2 are not very good. There are some uncommon or weird structures in the generated molecules.\n\n\n\n\n\n[1] Zhou, Xiangxin, et al. \"DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization.\" The Twelfth International Conference on Learning Representations.\n\n[2] Dorna, Vineeth, et al. \"TAGMol: Target-Aware Gradient-guided Molecule Generation.\" ICML'24 Workshop ML for Life and Material Science: From Theory to Industry Applications.\n\n[3] Fu, Tianfan, et al. \"Reinforced genetic algorithm for structure-based drug design.\" Advances in Neural Information Processing Systems 35 (2022): 12325-12338.", "methods_and_evaluation_criteria": "## Method\n\nThe method proposed is interesting. It is tring to integrate multi-fidelity surrogate functions to guide the molecule generation. It introduces a Hierarchical Latent Space Representation to optimize the latent space at each fidelity and decode the molecule at highest fidelity. It also includes an active learning step. Overall I think the method is simple but effective and makes sense for the problem.\n\n## Evaluation\n\nThe evaluation is done on two targets. The concern is that the number of targets is too limited, but it is understandable as ABEF is very time-consuming and expensive.", "theoretical_claims": "There is no theoretical claims in this paper.", "experimental_designs_or_analyses": "The experimental design is reasonable. It is done on two cancer-relevant proteins, BRD4(2) and c-MET. Also, ABFE  are well-validated on those targets and have good agreement with experimental data. \n\nAs previously discussed, the issues are the limited number of targets, and the unmatched number", "relation_to_broader_scientific_literature": "I think the scope of this paper is molecule optimization for better binding energy. It does not relate to the broader scientific literature.", "essential_references_not_discussed": "As previously stated, 3D optimization models, like RGA[1], DecompOpt[2] and TagMol[3] should be referenced and add to baselines.\n\n\n[1] Fu, Tianfan, et al. \"Reinforced genetic algorithm for structure-based drug design.\" Advances in Neural Information Processing Systems 35 (2022): 12325-12338.\n\n[2] Zhou, Xiangxin, et al. \"DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization.\" The Twelfth International Conference on Learning Representations.\n\n[3] Dorna, Vineeth, et al. \"TAGMol: Target-Aware Gradient-guided Molecule Generation.\" ICML'24 Workshop ML for Life and Material Science: From Theory to Industry Applications.", "other_strengths_and_weaknesses": "## Other Strengths\n\n1. The paper is well written, with clear description of methods and experiment results.\n\n2. The method is simple but effective\n\n\n## Other Weaknesses\n\n1.  some 3d based optimization models are not included in the baseline\n\n2.  tested targets are limited\n\n3. when comparing the top-3 values, it should also generating 15 molecules as for other methods for fair comparasion", "other_comments_or_suggestions": "1. If possible, it would be benificial to have figure 3 shown in the main text as it gives a more clear illustration of the framework.", "questions_for_authors": "1. From the ablation it seems that even the Linear regression fidelity contributes to the performance. Removing it would results in significant decrease of number of active scaffolds from 4 to 0. The ABFE scores for top 3 molecule also significantly decreased. Can you explain more on why this happens? My understanding is that it should have some kind of influence but should not be that obvious, as ABFE is much accurate than a linear regression model.", "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": "", "extra_scores": {}}, {"review_id": "uoZ0OrNbRy", "reviewer": "Reviewer_QauA", "summary": "The paper introduces a novel framework for multi-fidelity active learning that is based on learning of hierarchical latent representations. The authors evaluate the approach in a multi-fidelity setting culminating in ABFE evaluation on two different protein targets.", "questions": "", "limitations": "", "rating": 3, "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": "We thank the reviewer for their helpful feedback and positive comments about the work.\n\n> **Q1:** Because the authors opt to use a setting close to real-life, with MD as the highest-fidelity oracle, they are limited to sampling very few samples in the end (15 per method). This is somehow understandable given high computational cost, but limits the reliability of the results.\n\n**A1:** We would like to emphasize the statistical tests in Section 4.3 and Appendix B.3, where we show that the ABFE scores of MF-LAL compounds are significantly better than those from baselines in terms of both mean and top scores for both targets. So while we do have a relatively small number of samples, we show that MF-LAL makes statistically significant and reliable improvements over baselines.\n\n> **Q2:** I wonder if it would be possible to instead do a simulated multi-fidelity setup, as in some earlier papers; or perhaps to pick a lower-cost highest-fidelity oracle.\n\n**A2:** While many previous works have indeed focused on a simulated multi-fidelity setup, we do not think that such a setup is a very good proxy for real-world simulators. This is because the method of ABFE calculation is fundamentally different from docking or other activity prediction techniques, and so it is difficult to substitute it with other cheaper techniques and still reach useful conclusions. If it is possible to reach statistically significant conclusions using the real-world MD simulator, which we believe to have done in this paper, then we think it is most valuable to use the real simulator instead of an artificial setup.\n\n> **Q3:** ...for the scaffolds, the authors perform statistical analysis only for two best methods (the information about which is hidden away in the appendix), which might be misleading. I would strongly suggest limiting the results in this table to the same budget of oracle calls (15 each), and perhaps having a separate table / figure for 40 compound setting.\n\n**A3:** We agree that making two separate tables for 15 and 40 compounds would increase the clarity of the results. In the updated draft, we will include these two tables, as well as statistical tests comparing MF-LAL to all applicable baselines in both settings. As noted in Appendix B.3, statistical tests comparing MF-LAL to all baselines where all methods were limited to 15 compounds still showed statistically significant results in favor of MF-LAL (except for the binomial test for the number of active scaffolds between MF-LAL, which generated 4 scaffolds, and REINVENT, MF-AL-PPO, and DecompDiff which generated 1 scaffold, where p=0.07). The results for MF-LAL and the top baseline for each target using only 15 compounds are shown below, because they were not included in the original draft. These results remain consistent with our conclusions about the strong performance of MF-LAL.\n\n| | BRD4(2) ABFE | | | | | | c-MET ABFE | | | | | |\n| --- | --- | ---| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Method | Mean $\\pm$ std | # active scafs | Count | 1st | 2nd | 3rd | Mean $\\pm$ std | # active scafs | Count | 1st | 2nd | 3rd |\n| MF-AL-PPO | | | | | | | -4.2 $\\pm$ 2.8 | 0 | 15 | -6.6 | -5.8 | -5.5 |\n| Pocket2Mol | -4.3 $\\pm$ 3.8 | 1 | 15 | -9.8 | -8.7 | -8.0 | | | | | | |\n| MF-LAL | **-6.2** $\\pm$ 3.9 | **6** | 15 | **-12.0** | **-10.2** | **-9.8** | **-6.7** $\\pm$ 3.1 | **4** | 15 | **-12.9** | **-7.9** | **-7.7** |\n\n\n\n> **Q4:** I’d be curious to see some citation backing up this claim [about query synthesis] (that’s also more recent).\n\n**A4:** [1, 2, 3, 4] are recent papers that explore query synthesis approaches, and many of them find that query synthesis outperforms traditional pool-based methods in active learning. We will include these citations in the updated draft.\n\n[1] Morand et al. “Efficient Exploration of Microstructure-Property Spaces via Active Learning.” Frontiers in Materials 2022.\n\n[2] Schumann and Rehbein. “Active Learning via Membership Query Synthesis for Semi-Supervised Sentence Classification.” CoNLL 2019.\n\n[3] Guo et al. “Dual generative adversarial active learning.” Applied Intelligence 2021.\n\n[4] Zhu and Bento. “Generative Adversarial Active Learning.” arXiv 2017.\n\n> **Q5:** “Ensembled AutoDock4 (cost: 44s, ROC-AUC BRD4(2): 0.80, c-MET: 0.80)” - one cost is provided for both targets, while c-MET seems to use 5 crystal structures, whereas the other uses 8; could authors explicitly confirm that the cost is supposed to be the same in both cases?\n\n**A5:** Thank you for pointing out this omission, the shown cost is indeed only for BRD4(2). The correct cost for c-MET is 68s, which we will include in the updated draft.\n\n> **Q6:** “Additionally, the pairwise Tanimoto similarity among the 40 compounds generated by MF-LAL is less than 0.2” - does this refer to mean pairwise similarity?\n\n**A6:** Yes, mean pairwise similarity. We will update the draft to clarify.", "claims_and_evidence": "The claims are supported by evidence, with some questions regarding the experimental evaluation and presentation of the results (below).", "methods_and_evaluation_criteria": "Used multi-fidelity setting, in particular the choice of oracles, is convincing, and the method is evaluated in two different protein targets, which further strengthens the results. The main issue lies in the number of tested molecules (discussed in more detail below).", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "Discussed below.", "relation_to_broader_scientific_literature": "The paper builds on earlier work on multi-fidelity generative models, including MF-GFN, and expends on some of its perceived limitations.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "The problem setting is of (in my opinion) high significance, and the authors thoroughly evaluate their proposed method, including some ablations and comparison with reasonable baselines. The setup of oracles also reflects real-life setting, which is another strength of the paper.\n\nThe biggest weakness, in my opinion, is however also related to this. Because the authors opt to use a setting close to real-life, with MD as the highest-fidelity oracle, they are limited to sampling very few samples in the end (15 per method). This is somehow understandable given high computational cost, but limits the reliability of the results. I wonder if it would be possible to instead do a simulated multi-fidelity setup, as in some earlier papers; or perhaps to pick a lower-cost highest-fidelity oracle. I do not expect the authors to necessarily address this in any way, since it would require a substantial rework of the experiments, but raising my concern about the reliability of the presented results.\n\nAbout actionable weaknesses, I do have the following comment:\n\n“For MF-LAL and the most competitive baseline for each target, we ran an additional 25 compounds” - this seems to me to be a bizarre design decision, since the authors compare, among other things, the number of discovered modes (“scaffolds”). This obfuscates the results, in particular since for the scaffolds, the authors perform statistical analysis only for two best methods (the information about which is hidden away in the appendix), which might be misleading. I would strongly suggest limiting the results in this table to the same budget of oracle calls (15 each), and perhaps having a separate table / figure for 40 compound setting.", "other_comments_or_suggestions": "- “We will focus on “query synthesis” approaches (Angluin, 1988), where the model generates its own queries to send to the oracles, speeding up learning compared to approaches that query oracles with samples from a fixed candidate set.” - I’d be curious to see some citation backing up this claim (that’s also more recent).\n- “Ensembled AutoDock4 (cost: 44s, ROC-AUC BRD4(2): 0.80, c-MET: 0.80)” - one cost is provided for both targets, while c-MET seems to use 5 crystal structures, whereas the other uses 8; could authors explicitly confirm that the cost is supposed to be the same in both cases?\n- “Additionally, the pairwise Tanimoto similarity among the 40 compounds generated by MF-LAL is less than 0.2” - does this refer to mean pairwise similarity?", "questions_for_authors": "N/A", "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": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This is a nice paper, and all reviewers generally had positive comments about the novelty, appropriateness, and applicability of the proposed multi-fidelity approach. All reviewers agreed the problem setting is important and the methodology is sound. All reviewers had various more minor concerns, mostly regarding evaluation or baselines. The authors provided detailed rebuttals for most issues; the consensus across all reviewers was a "weak accept", and I think based on its merits the paper would be a good contribution to ICML.
Decision: Accept (poster)