Learning Molecular Representation in a Cell

## Abstract

Abstract Predicting drug efficacy and safety in vivo requires information on biological responses (e.g., cell morphology and gene expression) to small molecule perturbations. However, current molecular representation learning methods do not provide a comprehensive view of cell states under these perturbations and struggle to remove noise, hindering model generalization.
We introduce the Info rmation Align ment (InfoAlign) approach to learn molecular representations through the information bottleneck method in cells. We integrate molecules and cellular response data as nodes into a context graph, connecting them with weighted edges based on chemical, biological, and computational criteria.
For each molecule in a training batch, InfoAlign optimizes the encoder’s latent representation with a minimality objective to discard redundant structural information.
A sufficiency objective decodes the representation to align with different feature spaces from the molecule’s neighborhood in the context graph.
We demonstrate that the proposed sufficiency objective for alignment is tighter than existing encoder-based contrastive methods.
Empirically, we validate representations from InfoAlign in two downstream applications: molecular property prediction against up to 27 baseline methods across four datasets, plus zero-shot molecule-morphology matching.

## 1 Introduction

Drug properties, e.g., toxicity and adverse effects [], are induced by molecular initiating events—interactions between a molecule and a biological system—that first impact the cellular level and ultimately influence tissue or organ functions [].
However, a chemical molecule’s structure alone is insufficient information to predict its impact on cells: each chemical interacts with multiple cells and genes and induces complex changes in gene expression and cell morphology, making predictions of downstream responses challenging [, ].
Hence, molecular representation learning should make use of information about cellular response, enhancing the representation of the mode of action and thereby improving predictions for downstream bioactivity tasks [, ].

There is a lack of exploration for holistic molecular representations from molecular structure, cell morphology, and gene expression [, , , , ]. For example, graph self-supervised methods only manipulate molecular structures to perturb or mask molecular graphs using contrastive or predictive losses [, , ]. Moshkov et al. [] explored the ability of different data modalities, taken independently, to predict molecules’ assay activity in a diverse set of assays (tasks). They found (from []’s Fig.2) that molecular structure supports highly accurate prediction (AUC > 90%) in 31% (16/52) of tasks, gene expression in 37% (19/52) and cell morphology in 54% (28/52).
Similarly, in our experiments (Figure 3), we observe that molecular structure is not a one-size-fits-all solution.

Figure: Figure 1: Comparison of Representation Learning Methods: (a) Existing contrastive methods use two encoders—one for molecules and another for cell morphology or gene expression features—without sharing the molecule encoders for different alignment targets. (b) InfoAlign remove redundant information from molecules, cell morphology, and gene expressions based on the information bottleneck, resulting in more concise yet predictive molecular representations [].
Refer to caption: x1.png

Cells can be perturbed by treating them with chemicals or genetic reagents that disrupt a particular gene or pathway.
These chemical and genetic perturbations in vitro naturally bridge molecules with cell morphology and gene expression, as illustrated in Figure 1 (b).
However, multi-modal contrastive methods such as CLOOME [] and InfoCORE [], depicted in Figure 1 (a), focus primarily on aligning molecular representations with cell morphology [, ] or gene expression [].
These approaches fall short in two ways.
(1) They do not remove redundant information, grey-colored area in Figure 1 (b), that may harm representation generalization.
The presence of redundant information [] may induce spurious correlations, adversely affecting the generalization of molecular representations.
For example, in small molecule perturbations [, ], batch identifiers can signify confounding technical factors, creating misleading associations between molecular structures and cell morphology [].
(2) They treat molecules as the sole connectors between gene expression and cell morphology, ignoring the potential for genetic perturbations [] to directly establish connections between these modalities.
Genetic perturbations [] not only enrich the feature space of gene expression and cell morphology but also enhance the navigation of molecular representation learning towards the overlapped (bottleneck) area in Figure 1 (b).

To address the aforementioned challenges, we conceptualize the cellular response processes as a context graph, capturing a more complete set of interactions among molecules, gene expression, and cell morphology.
We identify the neighborhood of the molecule on the context graph and apply the information bottleneck [] to optimize molecular representations, which aligns them with neighboring biological variables to remove redundant information and improve generalization.

We propose the Information Alignment (InfoAlign) approach, as presented in Figure 1 (b). InfoAlign uses one encoder and multiple decoders with information bottleneck for minimal sufficient statistics in representation learning.
The minimality objective optimizes the encoder to learn the minimal informative representation from molecular structures by discarding redundant information.
The sufficiency objective ensures the encoder retains sufficient information, allowing decoders to reconstruct features for biological variables in neighborhood areas of the context graph.
We construct the context graph based on molecule and genetic perturbations [, , ] and introduce more biological (gene-gene interaction []) and computational (cosine similarity) criteria to increase edge connectivity.
We conduct random walks on the context graph, beginning with the molecule in the training batch, to identify its neighborhood. Cumulative edge weights indicate similarity between the molecule and variables along the path.
The molecule is encoded, and its latent representation is decoded to align with features identified in the random walk.
Encoders and decoders are jointly optimized using an upper bound for the minimality objective and a lower bound for the sufficiency objective.

The sufficiency objective introduces a decoder-based bound for multi-modal alignment. We show its theoretical advantages by demonstrating that it provides a tighter bound than the encoder-based approaches used in previous contrastive methods [, ], as discussed in Section 4.3. In experiments, InfoAlign outperforms up to 27 baselines across three classification and one regression dataset, covering 685 tasks, with average improvements of up to 6.4%. InfoAlign also demonstrates strong zero-shot multi-modal matching on two molecule-morphology datasets.

## 2 Related Work

Representation Learning on Molecular Structure:
Representation learning approaches for molecules can be categorized into sequential-based [, ] or graph-based models [, , , ].
Sequential models, utilizing string formats of molecules like SMILES and SELFIES [], have evolved from Recurrent Neural Networks (RNNs) to Transformers [, ]. These models typically follow specific pretraining strategies similar to language models such as BERT [], RoBERTa [, ] and GPT []. The pretraining targets are thus often the next token predictions or mask language modeling [, ] on SMILES or SELFIES sequences [].
Graph Neural Networks (GNNs) are the architectures for graph-based approaches [, , , ], where methods to pretrain GNNs often perturb or mask the atoms, edges, or substructures of molecular graphs with contrastive [, ] and predictive losses [, ].
Recent evidence highlights the challenges of developing universal molecular representations based solely on molecular structures without integrating domain knowledge [, , , , ]. Although using motifs is a common method to incorporate such knowledge [, ], the incorporation of information about molecules’ biological impacts is much less explored. We aim to enhance molecular representation learning by incorporating domain knowledge from cellular response data.

Representation Learning with Different Modalities:
Existing methods on multimodal alignment, such as CLIP [], primarily address pairwise relationships between texts and images and use methods like InfoNCE [, , ]. These approaches use separate encoders for different modalities to compute contrastive loss, which is upper bounded by the number of negative examples []. Subsequent research on molecules similarly focuses on pairwise alignment between molecules and cell images [, ], molecules and protein sequences [], and molecules and text [, ]. Although BioBridge [] handles multiple modalities, it leverages a knowledge graph for transforming representations between modalities rather than optimizing molecular representations.

Representation Learning with Cellular Response Data:
A primary goal of molecular representation learning is to predict molecular bioactivity. Likewise, emerging gene expression [] and morphological profiling approaches [, ] that describe perturbed genetic or cellular states in cell cultures can also be used to predict bioactivity. In some datasets, molecules are the perturbations, and the perturbed cell states measured are gene expression values for a thousand or more genes [] and/or microscopy Cell Painting images, which can be represented as a thousand or more morphology features [].
Recently created large-scale perturbation datasets [, , ] could enrich molecular representation learning approaches. CLOOME [] and MoCoP [] contrast cellular images with molecules and InfoCORE [] contrasts molecule with either morphological profiling [] or gene expression []. InfoCORE [] aims to mitigate confounding batch identifiers, but its effectiveness depends on a batch classifier, which is impractical without batch identifiers.
We integrate cellular response data and molecules into a context graph to capture cellular response patterns, focusing on learning molecular representations to remove nuisances [].

## 3 Problem Definition

We denote $x\in\mathcal{X}$ as the molecule from the space $\mathcal{X}$. An encoder with parameters $p_{\theta}(\mathbf{z}\mid x)$ maps $x$ to a $D$-dimensional latent representation $\mathbf{z}\in\mathbb{R}^{D}$. One may implement a Graph Neural Network (GNN) [] as the encoder. The GNN first updates node representations and then performs a readout operation (e.g., summation) over the nodes to obtain the latent representation.

Existing research has extensively used structural features to pretrain the GNN encoder [, ]. However, incorporating more expressive features from the cellular context, such as cell morphology and gene expression, remains largely unexplored for improving molecular representations. In this work, we use these features as targets to optimize molecular representations.

## 4 Multi-modal Alignment with InfoAlign

Figure: Figure 2: Molecular Representation Learning Using the Context Graph: (a) In Section 4.1, we construct the graph with various interaction, perturbation, and cosine similarities among molecules $x$, cell morphology profiles $c$, and genes $e$. Given a training batch of molecules, including $x_{1}$ and $x_{4}$, random walk extracts paths, for instance, of length four. (b) In Section 4.2, we aim to learn molecular representations based on the information bottleneck, preserving minimal information from the input molecule while ensuring sufficient information for decoding the target along the walk path $\mathcal{P}_{x}$.
Refer to caption: x2.png

We present the overall representation learning framework in Figure 2. In Section 4.1, we construct the context graph for cellular response data.
In Section 4.2, we introduce representation learning methods based on the principle of minimal sufficiency for molecules and their related modalities. In Section 4.3, we demonstrate the theoretical advantages of the proposed method.

### 4.1 Random Walks on Cellular Context Graph

Node Construction:
We model the interactions of the molecule $x$ with other molecules, the cell $c$, and genes $e$ using the context graph. They are nodes with different features $y$.
Molecular features are vectors obtained using fingerprint []. Cell morphology features are vectors derived from CellProfiler [] applied to Cell Painting microscopy images. Gene expression features are scalars using L1000 [] methods. We further rescale the feature spaces to a range between 0 and 1.

Edge Construction:
We link nodes using various chemical, biological, and computational criteria. For example, molecules can perturb cultured human cells, inducing changes in cell morphology [] and gene expression [], thus linking them to cell morphology and gene expression nodes. Genes could also perturb cells, inducing links between genes and cell morphology [].
Additionally, we calculate cosine similarity within the same feature space and use biological criteria such as gene-gene interactions [] to enrich the edge space. Each edge is assigned a weight $w$ with a value between 0 and 1. We construct the context graph with details Section 5. An example is provided in Figure 2 (a).

Random Walk Path Extraction:
The context graph identifies related cellular response patterns for input molecules in representation learning. Given an input molecule $x$, we extract its neighborhood through random walks starting from $x$. Specifically, we employ degree-based transition probabilities [] and denote the walking path as $\mathcal{P}_{x}:x\xrightarrow[]{w_{1}}v_{2}\xrightarrow[]{w_{2}}\dots
\xrightarrow[]{w_{L}}v_{L}$, where $v_{2}$ is a direct neighbor of $x$. To quantify the similarity between $x$ and node $v_{i}$ ($2\leq i\leq L$) on $\mathcal{P}_{x}$, we compute the cumulative product of edge weights as $\alpha(v_{i}\mid\mathcal{P}_{x})=\prod_{j=1}^{i-1}w_{j}$.

### 4.2 Optimization for Representation with Information Bottleneck

The information bottleneck (IB) [, ] is an appealing method for defining concise representations with strong predictive power. For molecular representation, we extract minimal sufficient information from the random variable $X$ of molecules. This is achieved by aligning the molecular representations $Z$ with the targets $Y$, derived from node features along the walk path $\mathcal{P}$. The IB has two principles based on mutual information (MI): (1) the minimality principle, which minimizes MI between molecules and their latent representations as $I(X;Z)$, and (2) the sufficiency principle, which decodes latent representations to maximally reconstruct feature spaces for variables along the walk path $I\left(Z;Y\right)$. Together, these form the optimization objectives:

$$ $\min_{p(\mathbf{z}\mid x)}\left[-I\left(Z;Y\right)+\beta I(X;Z)\right],$ (1) $$

where $\beta$ controls the trade-off between minimality and sufficiency. The exact computation of $I(Z;Y)$ and $I(X;Z)$ is intractable due to the unknown conditional distribution $p(y|\mathbf{z})$ and the marginal $p(\mathbf{z})$. We introduce the variational approximations $q(y|\mathbf{z})$ and $q(\mathbf{z})$ for them, respectively. This results in a lower bound estimation for the first decoding term $I_{DLB}$ and an upper bound for the second encoding term $I_{EUB}$ [].

$$ $\displaystyle I(Z;Y)$ $\displaystyle\geq\mathbb{E}_{p(\mathbf{z},y)}\left[\log q(y\mid\mathbf{z}) \right]+H(Y)\triangleq I_{DLB}$ (2) $\displaystyle I(X;Z)$ $\displaystyle\leq\mathbb{E}_{p(x)}\left[\operatorname{KL}\left(p(\mathbf{z} \mid x)\|q(\mathbf{z})\right)\right]\triangleq I_{EUB}$ $$

$H(Y)$ is the differential entropy. Proofs are in Section A.1. Together, $I_{DLB}$ and $I_{EUB}$ upper bound Eq. 1, forming a tractable objective $-I_{DLB}+I_{EUB}$ to optimize the encoder.
For the target $Y$, the $I_{DLB}$ objective requires decoders rather than encoders, as typically used in prior work []. We use distinct decoders, denoted as $q_{\phi}$ with parameters $\phi$, for various targets, including molecular fingerprints, gene expressions, and cell morphology features.

After ignoring the constant terms, one could formulate the loss function according to Eq. 2 for the molecule sample $x$, its latent representation $\mathbf{z}$, and the targets $y_{v}$ from $\mathcal{P}_{x}$:

$$ $\mathcal{L}=\frac{1}{L}\sum_{v\in\mathcal{P}_{x}}\alpha(v|\mathcal{P}_{x}) \left[-\log\left(q_{\phi}(y_{v}\mid\mathbf{z}\right)\right]+\beta\operatorname {KL}\left(p_{\theta}(\mathbf{z}\mid x)\mid\mathcal{N}(0,I)\right),$ (3) $$

where the first term aligns the representation with other features, and $\operatorname{KL}$ is the Kullback–Leibler divergence used for regularization. $\mathcal{N}(0,I)$ is the The Gaussian prior. In this formulation, the encoder models a distribution instead of a single representation $\mathbf{z}$, learning the mean and variance $\boldsymbol{\mu},\boldsymbol{\sigma}\in\mathbb{R}^{D}$. One may use parameterization tricks to sample $\mathbf{z}$ from the distribution []. The decoder then reconstructs $y_{v}$, the features of the neighboring node $v$ on the context graph.

InfoAlign uses multiple decoders for $q_{\phi}$ to align multi-modal features, while prior work relies on encoders with CLIP-like losses to align the latent space [, , , ]. Next, we provide the theoretical benefits of decoder-based alignment alongside the empirical advantages in Section 6.

### 4.3 Theoretical Motivation for Decoder-based Alignment

InfoNCE [] is the contrastive loss used for most CLIP-like methods [, ]. In this work, we show that the MI lower bound based on InfoAlign is tighter than that based on InfoNCE.

###### Proposition 4.1 .

For the molecular representation $Z$ and target $Y$ (from cell morphology, gene expressions, or molecular fingerprints), the encoder-based MI lower bound $I_{ELB}$ for InfoNCE can be derived by incorporating $K-1$ additional samples, denoted as $y_{2:K}$, to build the Monte Carlo estimate $m(\cdot)$ of the partition function [, ]:

$$ $I_{ELB}=1+\mathbb{E}_{p(z,y)p(y_{2:K})}\left[\log\frac{e^{h(z,y)}}{m(z;y,y_{2: K})}\right]-\mathbb{E}_{p(z)p(y_{2:K})p(y)}\left[\frac{e^{h(z,y)}}{m(z;y,y_{2: K})}\right],$ (4) $$

where $h(z,y)$ is the neural network parameterized critic for density approximation with the energy-based variational family. The decoder-based lower bound $I_{DLB}$ is defined in Eq. 2, then we have that $I_{DLB}$ is tighter than $I_{ELB}$, i.e., $I(Z;Y)\geq I_{DLB}(Z;Y)\geq I_{ELB}(Z;Y)$.

Proofs are in Section A.2. The result aligns with empirical observations in previous studies such as DALL-E 2 [], where a prior model was introduced to improve representations from CLIP [] before decoding to another modality. In this work, we learn decodable latent representations from molecules to align with different biological features.

###### Proposition 4.1 .

## 5 Implementation of Context Graph and Pretraining Setting

Data Source of Context Graph:
We create the context graph based on (1) two Cell Painting datasets [, ], containing around 140K molecule perturbations (molecule and cell morphology pairs) and 15K genetic perturbations (gene and cell morphology pairs) across 1.6 billion human cells; (2) Hetionet [], which captures gene-gene and gene-molecule relationships from millions of biomedical studies; and (3) a dataset reporting differential gene expression values for 978 landmark genes [] for chemical perturbations (molecule and gene expression pairs) [].

Node Features:
Different profiling methods provide node features in different ways. Morgan fingerprints [] are feature vectors extracted from each molecule’s structure, CellProfiler features [] are computed from the image of each cell and represent cell morphology, and L1000 profiles [] capture gene expression values on 978 landmark genes from cells treated with a chemical perturbation. Here are two practical considerations for the context graphs:
(1)  Chandrasekaran et al. [] provided one dataset that measured the cell morphology impacts of perturbing individual genes. The 15K genetic perturbations [] provide gene-cell morphology pairs but lack corresponding gene expression profiles. Still, we keep the gene nodes from this dataset to account for potential gene-gene interactions and incorporate cell morphology features into them.
(2) All 978 landmark genes have expression values linked to the molecules used in []. We update new gene expression nodes with 978-dimensional feature vectors. These vectors summarize all molecule-gene expression connections for a small molecule perturbation. This approach efficiently reduces dense connections between landmark genes and molecules. We select the top 1% of gene-molecule expression values as new edges to enrich the context graph’s connectivity.
We scale cell morphology and gene expression features to a range of 0 to 1 using the Min-Max scaler along each dimension.

Edge Weights:
For edges based on chemical perturbations [, ], we assign the edge weight of 1.
We also compute cosine similarity for nodes if they are in the same feature space (such as two cell morphology/gene expression profiles, or Morgan fingerprints). To avoid noisy edges from computations, we apply a 0.8 threshold for cosine similarity, and additionally explicitly enforce 99.5% sparsity by selecting top similar edges.

All together, this results in a context graph of 276,855 nodes (129,592 molecules, 4533 genes + 13,795 gene expressions, and 128,935 cell morphology) and 366,384 edges.

Encoder and Decoder:
We use the Graph Isomorphism Model (GIN) [] as the molecule encoder. All molecules on the context graph are used to pretrain the encoder.
Because we extract feature vectors as the decoding targets in different modalities, we could efficiently use Multi-Layer Perception (MLP) as modality decoders.
In each training batch, random walks start from the molecule node to extract the walk path. Then, decoders are pretrained to reconstruct corresponding node features from nodes over the path.
More details are in appendix B.

## 6 Experiments

Table: Table 1: Datasets and task information. Classf. denotes classification and Regr. denotes regression.

We focus on three research questions (RQs) regarding InfoAlign’s representation for molecular property prediction, molecule-morphology matching, and performance analysis.

Table: Table 2: Results on ChEMBL2K and Broad6K. We report average AUC (Avg.), as well as the percentage of tasks achieving AUC above 80%, 85%, and 90%. We highlight the best and second best mean. We also highlight the row of the best method in each category.

### 6.1 RQ1: Molecular Property Prediction

#### 6.1.1 Experimental Setting

Dataset and Evaluation:
We select datasets for important tasks including activity classification for various assays in ChEMBL2K [] and Broad6K [], drug toxicity classification using ToxCast [], and absorption, distribution, metabolism, and excretion (ADME) regression using Biogen3K []. The dataset statistics are in Table 1, covering 685 tasks. We apply scaffold-splitting for all datasets. We follow [] for the ToxCast dataset, and a 0.6:0.15:0.25 ratio for training, validation, and test sets for other datasets.
We use the Area under the curve (AUC) for classification and mean absolute error (MAE) for regression.
Mean and standard deviations are reported from ten runs.

Baseline:
We include 27 baselines across six categories: (1) three molecular fingerprint (FP)-based methods []; (2) eleven pretrained GNNs; (3) four pretrained chemical language models; (4,5) six methods based on cell morphology and gene expression values from cells treated with each molecule; (6) CLOOME [] and InfoCORE [] for multi-modal alignment using structure, morphology, and gene expression data. We use MLPs, Random Forests (RF), and Gaussian Processes (GP) for methods in categories (1,4,5). We fine-tune MLPs on various representation learning approaches for predicting molecular properties. Setting details and all results are in Sections C.1 and C.3.

Table: Table 3: Results on ToxCast and Biogen3K. We report the average AUC and the percentage of AUC above 80% on ToxCast, and regression MAE (scaled by × 100) for Biogen3K. We highlight the best and second best mean. We also highlight the row of the best method in each category.

#### 6.1.2 Results and Analysis

We present results across various assays in Tables 2 and 3 and Figure 3. Key observations include:

(1) Molecular structures are superior compared to cell morphology and gene expression features for predicting various molecular assays. This is likely because the datasets and tasks we selected fundamentally involve predicting the binding affinity of a molecule to a protein []; furthermore, in these datasets, molecules with activity in a given assay tend to have highly related structures, rather than representing two or more structurally distinct classes of molecules with activity; together this implies that molecular structure alone will tend to yield strong results. When comparing the three popular structure-based representation approaches, no single method outperforms the others across all four datasets. Pretrained GNNs generally perform better than fingerprint-based methods and pretrained chemical language models, thanks to recent advancements. However, continued efforts in universal structural representation are still necessary.

(2) Cell morphology and gene expression features may complement molecular structures, yielding more generalizable representations.
As shown in Figure 3, cell morphology and gene expression outperform molecular structure in approximately 20% and 10% of tasks on the ChEMBL2K and Broad6K datasets, respectively. This suggests that incorporating cell context into representation learning would be beneficial. That said, existing multi-modal baselines (InfoCORE, CLOOME) only outperform molecular structure-based approaches on ChEMBL2K and ToxCast, as they do not construct molecular representations holistically by using all cell-related modalities.

(3) InfoAlign achieves the best average performance on all tasks compared to 27 baselines. The improvements from InfoAlign range from 2.5% to 6.4% on average across four datasets compared to the second-best method. These gains are more significant when using the 80% AUC threshold on classification datasets. While InfoCORE (GE) performs best among baselines on the ChEMBL2K and ToxCast datasets, it struggles to align molecular representations with more than two modalities and sometimes leads to negative transfer, as seen in Broad6K and Biogen3K.

Figure: (a) ChEMBL2K with 41 Tasks.
Refer to caption: x3.png

### 6.2 RQ2: Molecule-Morphology Cross-Modal Matching

Table: Table 4: Retrieval results on ChEMBL2K (top) and Broad6K (bottom): Left tables display ranking metrics for top candidates. Right figures visualize the distribution of rankings for the correct matching.

#### 6.2.1 Experimental Setting

We evaluated zero-shot matching performance of various methods for predicting cell morphology from query molecules, including baselines CLOOME and InfoCORE (CP) with pretrained encoders. For retrieval, we calculate the cosine similarity between the molecular representation and all cell morphology candidates, rank these candidates, and compute Normalized Discounted Cumulative Gain (NDCG) and HIT scores for the top-1 and top-10 candidates as metrics. To ensure a fair evaluation of zero-shot matching, we exclude the cell morphology data for molecules that were used to train the baseline encoders. Consequently, we have 80 molecule-cell morphology pairs from ChEMBL2K and 196 pairs from Broad6K. All the morphology data are used as candidates for matching.

For InfoAlign, we use the pretrained decoder from Section 5 to extract the morphology features of the encoded molecule and then calculate the likelihood of these decoded features against the candidate morphology data. We then rank the candidates in the decoding space based on their likelihood scores.

#### 6.2.2 Results and Analysis

Cross-modal matching results are in Table 4. InfoAlign outperforms InfoCORE on ChEMBL2K and is comparable to InfoCORE on Broad6K, with both surpassing CLOOME. Additionally, we visualized the distribution of ranking positions for correct matching pairs to compare overall retrieval performance. The results show that InfoAlign and InfoCORE perform similarly, while CLOOME consistently ranks correct pairs lower.

### 6.3 RQ3: Performance Analysis

#### 6.3.1 Ablation Studies

Table: Table 5: Ablation studies on the pretraining loss. Different node features are removed from the context graph to assess their impact on downstream tasks. Avg. AUC is reported.

We perform ablation studies on Eq. 3 by pretraining encoders with different targets removed: (1) molecule-related, (2) cell morphology-related, and (3) gene expression-related features.
The results in Table 5 cover all datasets. We observe that both cell morphology and gene expression features are crucial for achieving the best performance. Different biological targets have varying impacts across datasets: molecular structure has more influence on Broad6K and Biogen3K, while gene expression is more important for ChEMBL2K and ToxCast.

Figure: (a) Losses and AUC on varying $\beta$ (Default: 1e-9).
Refer to caption: x7.png

#### 6.3.2 Hyperparameter Analysis

Lastly, we perform analysis for the hyperparameters: the strength of the regularization to the prior Gaussian distribution $\beta$ and the length of the random walk paths $L$. Results are presented in Figure 4. We observe a trade-off between the principles of minimality and sufficiency in Figure 4(a): a too-high $\beta$ value (minimal information) makes it challenging for the representation to be sufficiently expressive for molecular, gene expression, and cell morphology features, potentially degrading downstream performance. Conversely, a too-low $\beta$ value weakens minimality and may impair generalization. The convergence of the pretraining loss could serve as a good indicator to balance these aspects. For the hyperparameter $L$, we observe in Figure 4(b) that downstream performance on ChEMBL2K is relatively robust across a wide range of walk lengths.

## 7 Conclusion

In this work, we proposed learning molecular representations in a cell context with three modalities: molecular structure, gene expression, and cell morphology. We introduced the information bottleneck approach, InfoAlign, using a molecular graph encoder and multiple MLP decoders. InfoAlign learned minimal sufficient molecular representations extracted by reconstructing features in the random walk path on a cellular context graph. This context graph incorporated molecules, cell morphology, and gene expression information defined in scalar or vector spaces to construct nodes, and used various chemical, biological, and computational criteria to define their weighted edges. We demonstrated the theoretical and empirical advantages of the proposed method. InfoAlign outperformed other representation learning methods in various molecular property prediction and zero-shot molecule-morphology matching tasks.

#### Acknowledgments

This study was supported by National Institutes of Health (R35 GM122547 to AEC) and an internship funded by the Massachusetts Life Sciences Center (to GL).

## Appendix A Proof Details

### A.1 Proof of Eq. 2

For the input, latent, and target variables $X$, $Z$, and $Y$, the exact computation of the mutual information (MI) $I(Z;Y)$ and $I(X;Z)$ is intractable. For the molecule $x$, its latent representation $z$, and any biological target from cellular responses $y$, we introduce variational approximations $q(y|z)$ to obtain a lower bound on $I(Z;Y)$:

$$ $\displaystyle I(Z;Y)$ $\displaystyle=\mathbb{E}_{p(z,y)}\left[\log\frac{p(z,y)q(y|z)}{p(y)p(z)q(y|z)} \right],$ (5) $\displaystyle=\mathbb{E}_{p(z,y)}\left[\log\frac{q(y|z)}{p(y)}\right]+\mathbb{ E}_{p(z)}\left[\operatorname{KL}\left(p(y|z)\|q(y|z)\right)\right],$ $\displaystyle\geq\mathbb{E}_{p(z,y)}\left[\log q(y|z)\right]+H(Y)\triangleq I_ {DLB}$ $$

This is because that $\operatorname{KL}\left(p(y|z)\|q(y|z)\right)\geq 0$.
We introduce the variational approximations $q(z)$ for a upper bound on $I(X;Z)$:

$$ $\displaystyle I(X;Z)$ $\displaystyle=\mathbb{E}_{p(x,z)}\left[\log\frac{p(x,z)q(z)}{p(x)p(z)q(z)} \right],$ (6) $\displaystyle=\mathbb{E}_{p(x,z)}\left[\log\frac{p(z|x)}{q(z)}\right]-\mathbb{ E}_{p(z)}\left[(p(z)\|q(z)\right],$ $\displaystyle\leq\mathbb{E}_{p(x)}\left[\operatorname{KL}\left(p(z|x)\|q(z) \right)\right]\triangleq I_{EUB}$ $$

### A.2 Proof of proposition 4.1

For the molecule $x$, its latent representation $z$, and any biological target from cellular responses $y$, we use the neural network parameterized critic $h(z,y)$ with the energy-based variational family for density approximation []:

$$ $q(y|z)=\frac{p(y)}{\mathbb{E}_{p(y)}\left[e^{h(z,y)}\right]}e^{h(z,y)}.$ $$

Thus, we can rewrite $I_{DLB}$ based on the unnormalized distribution of $q(y|z)$:

$$ $\displaystyle I_{DLB}$ $\displaystyle=\mathbb{E}_{p(z,y)}\left[\log q(y|z)\right]+H(Y)$ (7) $\displaystyle=\mathbb{E}_{p(z,y)}\left[\log\left(\frac{p(y)}{\mathbb{E}_{p(y)} \left[e^{h(z,y)}\right]}e^{h(z,y)}\right)\right]-\mathbb{E}_{p(y)}\left[\log p (y)\right],$ $\displaystyle=\mathbb{E}_{p(z,y)}\left[h(z,y)\right]-\mathbb{E}_{p(z,y)}\left[ \mathbb{E}_{p(y)}[e^{h(z,y)}]\right],$ $\displaystyle=\mathbb{E}_{p(z,y)}\left[h(z,y)\right]-\mathbb{E}_{p(z)}(\log \tilde{Z}(z)),$ $$

where $\tilde{Z}(z)=\mathbb{E}_{p(y)}[e^{h(z,y)}]$ is the partition function.

Note that the log partition function is intractable. Poole et al. [] introduced a new variational parameter $a(\cdot)$ to upper bound $\tilde{Z}(z)$, deriving a tractable lower bound for $I_{DLB}$:

$$ $\displaystyle I_{DLB}\geq\mathbb{E}_{p(z,y)}[h(z,y)]-\mathbb{E}_{p(z)}\Bigg{[} \frac{\mathbb{E}_{p(y)}[e^{h(z,y)}]}{a(z)}\quad+\log(a(z))-1\Bigg{]}.$ (8) $$

This is because $\forall x,a>0$, the inequality $\log(x)\leq\frac{x}{a}+\log(a)-1$ holds, which can be applied to the second term of Eq. 7. The $I_{NWJ}$ bound [] is a special case where $a(z)=e$.

$$ $\displaystyle I_{NWJ}$ $\displaystyle\triangleq\mathbb{E}_{p(z,y)}[h(z,y)]-\mathbb{E}_{p(z)}\Bigg{[} \frac{\mathbb{E}_{p(y)}[e^{h(z,y)}]}{e}\quad+\log(e)-1\Bigg{]}$ (9) $\displaystyle=\mathbb{E}_{p(z,y)}[h(z,y)]-e^{-1}\mathbb{E}_{p(z)}[\tilde{Z}(z)].$ $$

$I_{NWJ}$ has high variance due to the estimation of the upper bound on the log partition function. Based on $I_{NWJ}$ and multiple examples, one can derive the encoder-based lower bound $I_{ELB}$ for InfoNCE.

Suppose there are $K-1$ additional examples independently and identically sampled and denoted as $y_{2:K}$, and the critic is configured with parameters $a(\cdot)$ as $1+\log\frac{e^{h(z,y)}}{a(z;y,y_{2:K})}$. Then, we can rewrite $I_{NWJ}$ for its multi-sample version:

$$ $\displaystyle I_{NWJ}$ $\displaystyle=\mathbb{E}_{p(z,y)p(y_{2:K})}\left[1+\log\frac{e^{h(z,y)}}{a(z;y ,y_{2:K})}\right]-e^{-1}\mathbb{E}_{p(y)p(z)p(y_{2:K})}\left[e^{1+\log\frac{e^ {h(z,y)}}{a(z;y,y_{2:K})}}\right],$ (10) $\displaystyle=1+\mathbb{E}_{p(z,y)p(y_{2:K})}\left[\log\frac{e^{h(z,y)}}{a(z;y ,y_{2:K})}\right]-\mathbb{E}_{p(y)p(y_{2:K})p(z)}\left[\frac{e^{h(z,y)}}{a(z;y ,y_{2:K})}\right].$ $$

Multiple samples can be utilized for the Monte Carlo method $m(z;y,y_{2:K})$ to estimate the upper bound on the partition function $a(z;y,y_{2:K})$:

$$ $a(z;y,y_{2:K})=m(z;y,y_{2:K})=\frac{1}{K}\left(e^{h(z,y)}+\sum_{i=2}^{K}e^{h(z ,y_{i})}\right),$ $$

where $K-1$ independent samples are drawn from $\prod_{i}p({y_{i}})$ and one sample from $p(z,y)$ for the term $\mathbb{E}_{p(z,y)p(y_{2:K})}[\cdot]$ or $K$ samples from $\prod_{i=1}^{K}p(y_{i})$ (we set $y_{1}=y$) for a $p(z)$ sample in the $\mathbb{E}_{p(y)p(y_{2:K})}[\cdot]$ term.
Therefore, we can derive $I_{ELB}\triangleq I_{NCE}$:

$$ $\displaystyle I_{ELB}\triangleq I_{NCE}$ $\displaystyle=1+\mathbb{E}_{p(z,y)p(y_{2:K})}\left[\log\frac{e^{h(z,y)}}{m(z;y ,y_{2:K})}\right]-\mathbb{E}_{p(y)p(y_{2:K})p(z)}\left[\frac{e^{h(z,y)}}{m(z;y ,y_{2:K})}\right],$ (11) $\displaystyle=1+\mathbb{E}_{p(Y|Z)p(z)p(y_{2:K})}\left[\log\frac{e^{h(z,y)}}{ \frac{1}{K}\sum_{i=1}^{K}e^{h(z,y_{i})}}\right]$ $\displaystyle\quad\quad-\mathbb{E}_{p(y)p(y_{2:K})p(z)}\left[\frac{e^{h(z,y)}} {\frac{1}{K}\sum_{i=1}^{K}e^{h(z,y_{i})}}\right],$ $\displaystyle=\mathbb{E}_{p(z,y)}\left[h(z,y)\right]-\mathbb{E}_{p(z)}\left[ \log\frac{1}{K}\sum_{i=1}^{K}e^{h(z,y_{i})}\right].$ $$

Note that for $\mathbb{E}_{p(y)p(y_{2:K})p(z)}[\cdot]$, we average the bound over $K$ replicates as well to ensure that the last term in Eq. 10 is the constant 1. Now, $I_{ELB}$ or $I_{NCE}$ is upper bounded by $\log K$, rather than $a(\cdot)$.
Hence, the difference between $I_{DLB}$ and $I_{ELB}$ is

$$ $\displaystyle I_{DLB}-I_{ELB}$ $\displaystyle=\mathbb{E}_{p(z)}\left[\log\frac{1}{K}\sum_{i=1}^{K}e^{h(z,y_{i} )}\right]-\mathbb{E}_{p(z)}(\log\tilde{Z}(z))\geq 0.$ (12) $$

When $K$ is sufficiently large to estimate the partition function, we have $\mathbb{E}_{p(z)}\left[\log\left(\mathbb{E}_{p(y)}\left[e^{h(z,y)}\right]
\right)\right]$ for the left term, indicating that $I_{DLB}-I_{ELB}=0$. Since $I_{NCE}$ is upper bounded by $\log K$ [], smaller values of $K$ may result in a less tight $I_{ELB}$, causing $I_{DLB}-I_{ELB}\geq 0$ to always hold. In particular, $I(Z;Y)>\log K$ implies that the bound $I_{ELB}$ will be loose.

## Appendix B Context Graph Details

Figure: Figure 5: From the initial idea in Section 4 to the practical implementation of the context graph, we first display relations between molecules and all the landmark genes from [] for the $X_{1}-E_{3}$ and $X_{3}-E_{2}$ relationships. $E_{3}$ and $E_{2}$ are landmark genes involved in small molecule perturbations and cell morphology perturbation; we display them separately for clarity. Next, we merge all landmark genes into new gene expression nodes and integrate genes from genetic perturbations in the JUMP dataset [] with cell morphology features. Practical considerations are detailed in Sections 5 and B.
Refer to caption: x9.png

### B.1 Edge Construction

Edges represent similarity relationships between molecules, genes and cells. According to the chemical or biological criteria, we have following types of edges:

- 1.
Molecule-Cell Morphology Edges: These edges are introduced through molecule perturbation experiments from cell painting datasets created by [] and the JUMP dataset []. It links molecule nodes with cell morphology nodes. We use the edge weight $1$ for all these edges.
- 2.
Edge-Cell Morphology Edges: These edges should be introduced by genetic perturbation from the JUMP dataset []. The perturbations are either based on gene overexpression (ORF) or gene knockout techniques (CRISPR). They link the gene nodes and the cell morphology nodes. However, the genes introduced by the genetic perturbations lack gene expression profiling from [] as node features. We did not implement gene-cell morphology edges from [] due to the absence of differential gene expression profiling values []. Instead, we merged the gene nodes from [] with their linked cell morphology nodes, creating single nodes. This approach enables a more efficient context graph, incorporating some gene nodes with cell morphology features.
- 3.
Molecule-Gene Edges: These edges could represent molecule-gene binding and regulation relationships, linking molecules to genes []. Some links can be sourced from [], and we also retrieve gene-molecule links from [] by selecting the top 5% absolute differential expression values.
- 4.
Gene-Gene Edges: These edges denote the relationships of gene-gene covariance and interaction and we use the links from [].

We enrich the edges in the context graph by incorporating computational similarity edges, where cosine similarity is computed among within nodes having the same type and feature vectors. We note that the cell morphology features from [] and [] have different dimensions since the latter has applied batch correction techniques [] on the CellProfiler features []. Thus, we cannot compute the similarity between these two subsets of cell morphology nodes.
We use (1) a 0.8 similarity threshold and (2) a minimal sparsity of 99.5% by selecting top 0.5% similar edges to avoid excessive noise in computational similar edges.

### B.2 Dataset Sources of Nodes

Here are the datasets we used to create different types of nodes on the context graph:

- •
Molecule nodes: Molecular nodes are sourced from two cell painting datasets: one by Bray et al. [] and the other from the recently released JUMP dataset [], and the third source from Wang et al. [], which are used to study adverse drug reactions.
- •
Gene nodes: Gene nodes are from the landmark genes used by Wang et al. [] in creating the LINCS L1000 profiling of drugs. Other gene nodes come from genetic perturbations in the JUMP dataset []. The gene nodes from [] have cell morphology features as described in Section B.1. The landmark gene nodes from [] have scalar gene expression profiles, but these values are updated in the new gene expression nodes.
- •
Cell morphology nodes: Cell nodes are sourced from the two cell painting datasets [, ].
- •
Gene expression nodes: Based on landmark genes from [], each gene expression node summarizes all gene expression profiles into vectors from a small molecule perturbation. Since Wang et al. [] measured the same landmark genes for a set of molecules, we update new gene expression nodes with feature vectors for all these landmark genes. This approach efficiently constructs decoding targets from molecules to gene expression profiles and prevents redundant gene-molecule connections.

We present an example of the cellular context graph in Figure 5.

## Appendix C Experiment Details

Figure: Figure 6: An overview of the representation’s predictive performance on all 41 bioactivity prediction tasks in ChEMBL2K. Results for molecular structure are obtained from the best method ContextPred. Results for cell morphology and gene expression come from the best method based on MLPs.
Refer to caption: x10.png

Figure: Figure 7: An overview of the representation’s predictive performance across five major task categories on Broad6K. Results for molecular structure are obtained from the best method based on JOAO. Results for cell morphology come from the best method based on RF. Results for gene expression are derived from the best method based on MLP.
Refer to caption: x11.png

### C.1 Prediction Datasets

All experiments were run on a single 32G V100.
Prediction dataset statistics are in Table 1:

- •
ChEMBL2K []: The dataset is a subset of the ChEMBL dataset [], overlapping with the JUMP CP [] datasets. We determined activity using the “activity_comment” provided by ChEMBL. If not, we applied a threshold of 6.5, labeling compounds with pChEMBL > 6.5 as active. We exclude all molecules in the dataset from the pretraining set to avoid data leakage. There are a total of 41 tasks related to protein binding affinity, which are converted to binary activity values. We filter the dataset to ensure that each task has at least one positive and five negative examples.
- •
Broad6K []: The original version provided by Moshkov et al. [] is a collection of 16,170 molecules tested in 270 assays, resulting in a total of 585,439 readouts. However, there are a large number of missing values, with 153 assays having a missing value percentage above 99%. To mitigate bias in the conclusions, we extract subsets where the percentage is less than 50%.
- •
ToxCast []: The toxicology data is collected from the “Toxicology in the 21st Century” initiative, widely utilized in many graph machine learning models []. The dataset comprises 8,576 molecules and 617 binary classification tasks.
- •
Biogen3K []: The dataset includes properties that describe the disposition of a drug in the body, including absorption, distribution, metabolism, and excretion (ADME). It is collected from 120 Biogen datasets across six ADME in vitro endpoints over 20 time points spanning about 2 years. The endpoints include human liver microsomal (HLM) stability reported as intrinsic clearance (Clint, mL/min/kg), MDR1-MDCK efflux ratio (ER), Solubility at pH 6.8 (µg/mL), rat liver microsomal (RLM) stability reported as intrinsic clearance (Clint, mL/min/kg), human plasma protein binding (hPPB) percent unbound, and rat plasma protein binding (rPPB) percent unbound.

We utilize scaffold-splitting with a ratio of 0.6:0.15:0.25 and follow [] for the ToxCast dataset.
We use the Area under the curve (AUC) score for classification and mean absolute error (MAE) for regression.
We report the mean and standard deviations from ten runs.

### C.2 Implementation and Baseline

We consider baselines from three representation sources: molecular structures, cell morphology, and gene expressions. Moreover, we have three different ways to represent molecular structures, including fingerprints based on domain knowledge, GNNs based on the graph structure of molecules, and chemical language models (ChemLM) based on SMILES-sequence structure of molecules.

- 1.
Molecular descriptors/fingerprints [] (Structure only): We train MLPs, Random Forests (RF), and Gaussian Processes (GP) on these representations.
- 2.
Pretrained GNN representations [] (Structure only): We consider AttrMask, ContextPred, and EdgePred with supervised pretraining []. We also include GraphCL [], GROVER [], JOAO [], MGSSL [], GraphLoG [], GraphMAE [], DSLA [], and UniMol []. We implement GraphCL, GROVER, and JOAO based on []. Fine-tuned MLPs are applied on top of the pretrained representations.
- 3.
Pretrained ChemLM representations [] (Structure only): We consider pretrained models such as 102M Roberta and 87M GPT2 implemented by []. We also include MolT5 [] and 19M ChemGPT []. We apply fine-tuned MLPs on top of these pretrained representations.
- 4.
Cell Morphology [] (Cell or Structure only): Cell morphology features are available in for part of molecules in the ChEMBL2K and Broad6K datasets. We train MLPs, RF, and GP on these representations. Note that not all molecules have corresponding cell morphology feature vectors; in such cases, we replace the predictions on the missing feature with ML predictions on the structure.
- 5.
Gene Expression [] (Gene or Structure only): Differential gene expression values are available for part of molecules in the ChEMBL2K and Broad6K datasets. We train MLPs, RF, and GP on these representations. Note that not all molecules have corresponding gene expression vectors over landmark genes; in such cases, we replace the predictions on the missing feature with ML predictions on the structure.
- 6.
CLOOME [] and InfoCORE [] (Structure-Cell or Structure-Gene aligned): CLOOME utilizes ResNet [] and descriptor-based MLP to align representation from cell morphology images with the molecular structure representation. We use their pretrained MLP to obtain molecular representations and fine-tune another MLP on top of these representations. InfoCORE has two versions, InfoCORE-CP and InfoCORE-GE, which align the molecular graph representation with cell morphology features or differential gene expression features, respectively. We use both versions as baselines and fine-tune another MLP on top of these representations.

### C.3 More Results for Molecular Property Prediction

We present additional comparisons on the ChEMBL2K dataset between basic representation approaches and InfoAlign across all task dimensions in Figure 6. Similarly, results for the Broad6K dataset, comparing basic representations across five major task dimensions (Cell, Yeast, Viral, Biochem, and Bacterial-related targets), are shown in Figure 7. Combined with Tables 2 and 3, these detailed results lead to further observations:

(1) Different structure-based molecular representations vary in sensitivity to model architecture. Dramatic performance drops occur with Morgan FP when replacing the MLP architecture with RF or GP in the ChEMBL2K and Broad6K datasets. Conversely, in the Biogen3K dataset, RF and GP significantly outperform MLP. In contrast, pretrained GNN and ChemLM representations maintain more consistent performance across various datasets.

(2) Learning universal molecular representations solely from molecular structures remains challenging, even within the representation category. For pretrained GNN representations, ContextPred outperforms others on the ChEMBL2K dataset. JOAO excels on the Broad6K dataset. UniMol and GraphMAE are the best pretrained GNN representations on ToxCast and Biogen3K datasets, respectively. For ChemLM representations, MolT5 excels over other sequential-based models in the ToxCast and Biogen3K datasets, but this is not the case with the ChEMBL2K and Broad6K datasets. Different datasets may emphasize varied aspects of bioactivity classification or regression and pose generalization challenges for molecular representation learning.

(3) InfoAlign shows strong generalization for the targets of non-human cells, as shown in Figure 7.
Although the context graph primarily uses data from small molecule and genetic perturbation datasets [, ] focused on human cell cultures, InfoAlign also exhibits robust generalization to bacterial and viral targets compared to basic representation approaches.

## Peer Reviews

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: - What are the minimum data requirements for cell morphology and gene expression to effectively apply InfoAlign? How does the method perform when these data are sparse or incomplete?
- Given the promising performance of structure-based pretrained GNNs, have the authors considered using representations from these pretrained models instead of Morgan fingerprints as molecular features? This might leverage the strengths of both approaches.
- How does the computational complexity of InfoAlign compare to existing methods, and what are the practical limitations in terms of dataset size and computational resources?
soundness: 3
strengths: - The approach is well-motivated. Applying information bottleneck to this problem for learning minimal yet sufficient molecular representations seems a valid match of theory and real-world problem.
- The approach is comprehensively evaluated by comparisons across different methods and even paradigms. InfoAlign demonstrates improved accuracy over up to 27 baseline models across four datasets.
- The paper is well-organized and clearly presented.
- In addition to empirical evidence, the paper provides theoretical proofs to support the advantages of the proposed method.
- The provided supplementary material contains code, dataset and checkpoints. This suggests good reproducibility of the results in the paper.
summary: The paper introduces a novel approach called Information Alignment (InfoAlign) for learning molecular representations by integrating molecular structure, cell morphology, and gene expression data. The method leverages the information bottleneck principle to optimize a molecular graph encoder and multiple MLP decoders, aiming to achieve minimal yet sufficient molecular representations.

The authors demonstrate the effectiveness of InfoAlign through extensive experiments on molecular property prediction and zero-shot molecule-morphology matching, showing superior performance compared to 27 baseline methods across four datasets.

I find the paper of good quality in general. Besides, the problem it is tackling is meaningful but less explored. I suggest an acceptance to advocate this direction.
weaknesses: - As I mentioned in the summary, the problem is meaningful yet less tackled in the AI community. To my eyes, it is mostly due to the missing prerequisites of biological knowledge. The paper provides some explanation of the problem in the introduction, but it would be much more helpful if more context could be provided (maybe in the appendix).
- Line 215: The motivation for computing edge weights on random walk paths is unclear, and no empirical evidence is provided to support it. Since the context graph incorporates data from three modalities, the edges likely exhibit strong heterogeneity. Is there evidence suggesting that a cumulative product of edge weights effectively captures dependency or similarity between nodes?
- Line 303: The approach for avoiding noisy edges in computations lacks motivation and an ablation study. Providing more detail here would offer valuable insights for researchers interested in extending InfoAlign to new contexts.

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 4
questions: - Are the authors surprised by the relatively minor drop in ROC AUC values when omitting individual modalities?
- Some additional relevant literature that could enhance the discussion includes:
    [0] Cross-Modal Graph Contrastive Learning with Cellular Images
    [1] How Molecules Impact Cells: Unlocking Contrastive PhenoMolecular Retrieval (a work evaluating zero-shot classification)
    [2] Approximating Mutual Information of High-Dimensional Variables Using Learned Representations (proposes a scalable approach for approximating mutual information of high-dimensional objects)
- One of the conclusions from the work is emphasizing the importance of molecular features. Dot he authors have an explanation for why the absence of molecular features in the ablation results in a ToxCast AUC that overlaps the non-ablated model performance? Without seeing the results I would expect the performance in the absence of an ablated molecular feature reconstruction loss to be a lot worse.
soundness: 3
strengths: - The authors perform a comprehensive evaluation against baseline models across a variety of datasets.
- They convincingly demonstrate that including additional modalities improves performance, as evidenced by thorough evaluations and ablation studies.
- The incorporation of a graph is an interesting way to introduce prior knowledge into the learning representations for a particular molecule.
summary: The authors propose a method called InfoAlign for predicting molecular properties by integrating three different modalities: molecular structures, gene expression, and phenomics embeddings. To learn useful representations, they construct a weighted connected graph over cell morphology profiles, related molecules, and gene expression values. They train an encoder-decoder architecture where, for a molecule of interest, they encode its representation and decode both itself and all other nodes encountered during a random walk on a pre-specified graph. This approach results in mutual information maximization between the compound of interest $x_i$ and related entities discovered through the random walk on the pre-encoded graph. The authors test their method on a variety of chemical property prediction datasets, demonstrating that they outperform various baselines, including pre-trained Graph Neural Networks (GNNs), chemical language models, uni-modal models such as cell morphology or gene expression, and some multi-modal alignment models.
weaknesses: - The validity and robustness of the pre-specified graph are not thoroughly explored. It would be informative to assess how sensitive the method is to the quality of the graph. For example, one experiment could involve removing 50% of valid connections and replacing them with random pairs of nodes; another could involve using a completely random graph.
- The second gap identified by the authors is slightly misformulated: "They treat molecules as the sole connectors between gene expression and cell morphology, ignoring the potential for genetic perturbations."
    - Essentially, the authors are arguing that incorporating genetic perturbation data can further improve predictive capacity. However, there is no ablation study where this information is omitted to directly validate its impact on empirical performance.
- Regarding the ToxCast dataset, the authors report a performance of 0.72 ROC AUC using GROVER. Did the authors use a different partitioning of the dataset than previous works?
- The ablation loss is only regarding removal of the losses as far as I understand the data itself is still input into the training. Can the authors perform an ablation where a full data modality is not added as part of training?

---

confidence: 3
contribution: 2
initial_rating: 6
presentation: 3
questions: Questions / suggestions:
* I would ask for some more clarity on the results presented in table 1, specifically for the Broad6k results. Many columns have a +/- 0 error on a reoccurring 3.1 result. I suspect this means that there are a few tasks that are always identified with a high AUC, but given the lack of discussion of these results it’s hard to interpret. It might be worth using a different set of thresholds for the Broad6K to get more resolution? 
* It would also help in section 6 for each of the research questions to have a couple of sentences explaining what each question is and why we are asking them, otherwise the results feel disjointed to the uninitiated reader and hard to connect. 
* I found the explanation of the exact model architecture / parameters used to be lacking, and while pointed in the main text to the appendix I did not find enough information there on the size of/ structure of the MLPs / training regime to feel like the result could be replicated. This is of particular importance in Table 1 where comparing to other methods I can only guess at things like parameter efficiency etc. 

* In general I feel like the weighting of the paper is very theoretical, no bad thing I really like the inclusion of the mutual information, but I wonder if more details could be moved to the appendix to free up more space for the experimental method, the model construction, and discussion of the results. In the current format of the paper I find a really interesting set of ideas, that I find very hard to understand how to weight the importance of / a method that I could follow to replicate certain components. 


Specific formatting suggestions:
* Fig. 3. I don’t really understand what this graph is conveying? The top bar shows the proportion of single representation tasks, but the bottom splits along the model types? I either need more detailed explanation, or maybe consider a better type of graph to convert this information?
* Table 3. (right) (This should be a separate figure - I understand it might make formatting harder but it is hard to reference) I personally don’t like these KDE type plots as they imply smooth functions from what is usually limited data, and make it almost impossible to draw quantified conclusions from, I would be much happier with a histogram if this is important information to convey. Additionally x-axis labels. 
* Fig 4 (a) - this plot is almost unreadable with the overlapping lines / y-scale, and the meaning I think is being conveyed with the LR spans such a number of magnitudes in range that I would rather see both more granularity and perhaps these results presented in a table? 
* Fig 4 (b) - I can guess what the plot means but without a key / description detailing elements like the error band (? 1 std dev I assume, based on what variation is unclear though), the points are connected, but given the discrete data this is misleading, and the huge discrepancy at length 8 suggests to me either the error band is under-estimating the variance, or there are properties of a random walk length 8 that are not discussed. Again this is a really interesting result as it's looking at the way that different parts of the compute graph contribute to the final result, but I'm left asking more questions with this figure than it answers. 
    * While I thin this statement on line 521 is correct, “we observe in Figure 4b that downstream performance on ChEMBL2K is relatively robust across a wide range of walk lengths.” The inclusion of this plot raises questions that are not answered.  
* On a similar point to Fig 4b, I would be very interested to see a description / plot of what the typical construction of the random walk graphs contain. 



Thank you again for a really interesting read, I like the approach with InfoAlign, and appreciate the large quantity of effort put into this work. 
I'd request a slight look again at the weighting of different sections in this paper, as I found it slightly unbalanced, and think as a reader I would find benefit from more detail in the method so I could reproduce if I wanted, and more detail in the discussion of the results to understand how to place the results in better context. i.e. which parts of the method are the most important.
soundness: 3
strengths: * The novel construction of the problem mitigates a significant issue with current implementations using a standard contrastive learning approach, by combining the modalities into a single method there is no decoupling between the different representations, and the MI approach to filter the data seems an effective way to reduce the data required to train over, potentially increasing data quality and improving time to train. 
* The visual presentation is good, with tables are figures clearly designed to convey meaning. 
* The breadth of models evaluated against gives a really clear status against both several standard approaches one might take, and also against SOTA prior work. This comparison is really nice to see.
summary: Thank you for a really interesting read, I agree that the most important next step in molecular representation is combining different modalities and current methods leave much to be desired, and I really liked the novel way shown here to combine data in a constricted way. It is well mathematically motivated and the work done clearly extensive. 

Summary:
* The authors present a new multi-domain method to learn the representation between drugs, genes and cells. In contrast to typical contrastive training setups the InfoAlign method removes the redundant information through a bottleneck using a well formulated mutual information method. 
* They show a method to create walks over the cellular context  graph representing the interactions between the modalities, and use this to populate the compute graph for their representation learning. 
* This representation framework uses Morgan fingerprints as molecular node features, CellProfiler features for the cell node features, and L1000 features for the gene node features, and the connections are based on chemical perturbations and cosine similarities. 
* The authors show results across a range of benchmarks, demonstrating good performance, achieving top ranking scores in all but 2 / 15 of the key datasets/criteria evaluated in Tables 1 and 2.
weaknesses: * Model clarity - I found it hard reading this paper to extract exactly how the model was constructed to run these experiments. The method is clearly novel, and an interesting approach to the multi-domain problem, but after being strongly theoretically motivated the method / implementation details, or even a description of model size was lacking. If these details could be expanded on it would help place the model / method in the appropriate context. 
* Impact of the MI bottleneck - The mutual information bottleneck is well theoretically motivated, however I didn’t feel the power of the bottleneck was evaluated in the paper? A different approach would be just using all the data and relying on data size / model size to outweigh data quality. I like the idea with MI, but would have liked to see an ablation with this feature included / not as that would help me evaluate the importance of the bottleneck vs the joined training setup?
* Impact of context graph - Similarly the impact of the context graph and different ways of including the context felt under-explored. Fig 4(b) I think shows that the random walk length had little impact, but how this is impacted by composition of the random walk path (are the walks just reconstructing the most likely combinations that would form a triplet anyway?) and what happens if instead of walking the relevant combinations are just grouped together. This feels like an important baseline. 
* The presentation of the research questions felt more like a report than a paper, I would have liked to see some more motivation / explanation of each rather than assuming knowledge on the readers part.

---

confidence: 4
contribution: 3
initial_rating: 5
presentation: 2
questions: - **Methodology**
  - How is the neighboring node of $x$ defined in line 250? Is it the neighbor of $x$ on the context graph or all the $v_i$ on the sampled path?
  - As shown in Fig. 2, different decoders are used to reconstruct the features of different types of nodes. However, if there are multiple neighbors $v_1, v_2, \ldots, v_n$ of a certain molecule $x$ sharing the same type, how can the decoder decode various $y_{v_i}$ from the same encoded latent  $z$ of $x$ without any additional information about $v_i$ being provided?

- **Experiments**
  - The ChEMBL dataset provides information on whether a certain molecule exhibits activity against a specific target. In this manuscript, a task is defined as predicting whether a molecule can interact with a given target. However, it is unclear why the molecule would be characterized by **Cell Morphology** and **Gene Expression**. Such information should be related to the task (target) itself rather than the input molecule. Could the authors explain how **Gene Expression** and **Cell Morphology** data are generated for molecules?
  - To substantiate the claim that the proposed multimodal alignment method more effectively models molecular properties within a cellular context, the authors must include a baseline comparison using a simple concatenation approach for alignment. Specifically, the authors should employ a pretrained GNN, such as Uni-Mol[1], to extract molecular features and concatenate them with Cell Morphology and Gene Expression representations as inputs for prediction tasks on the ChEMBL2k and Broad6k datasets.
  - During the fine-tuning for downstream tasks, is the encoder frozen or is a full-fine-tune performed with the encoder also being trained?

**If the authors can address all my major concerns, I would be pleased to raise the score.**

[1] Zhou G, Gao Z, Ding Q, et al. Uni-mol: A universal 3d molecular representation learning framework[J]. 2023.
soundness: 3
strengths: - This article pioneeringly incorporates cellular modality information in molecular representation learning, which enables the learned molecular representations to achieve better results in biochemistry-related tasks.
- The article conducts sufficient experiments to validate the effectiveness of the model.
- The paper is well-motivated; adding cellular modality data to enhance the model's performance in biochemical aspects is very reasonable.
summary: This article proposes a pre-training method where the authors utilize genes, cells, and molecular information as nodes, and construct a context graph using the interactive or similar relationships between different components as edges. The authors then extract paths on the graph using random walks to construct training data, design training objectives from the perspective of mutual information, and integrate cellular and genetic information into molecular representations. After pre-training, the authors fine-tune the model on downstream tasks across four datasets to validate its performance.
weaknesses: - The writing requires improvement; the methodology is difficult to follow, and many variables are not clearly defined. See Questions for details.
- The description of the dataset and downstream tasks is not sufficiently detailed, with some parts being confusing. See Questions for details.

Meta-review: This paper proposes a new approach to learn molecular representations through incorporating the information of cellular responses. This is done by (1) constructing a context graph for cellular response data and (2) information bottleneck training on the extracted random walk. 

Overall, I find the paper to provide meaningful and solid contribution to the field via introducing a (relatively) new data modality. The experiments are convincing (despite some room for improvement). This paper is likely to promote some future works to consider learning molecular representation using cellular responses. 

There was a valid concern raised by the reviewers, that the main experiments are conducted without fine-tuning the model. I tend to agree with the concern and it would have been better for the authors to fully explore the performance of models after finetuning. Especially, the authors could have selected a subset of the considered baselines and compared with them after finetuning. However, I believe this concern is partially alleviated by the new experiments constructed by the authors during the rebuttal. I also believe that the old experiments still convincingly show the promise of the new idea. 

Overall, I recommend acceptance for this paper since it introduces a meaningful data modality to molecular representation learning with meaningful results. The highly encourage the authors to extend their evaluation to fine-tuning setting which better aligns with the practical scenarios.

Decision: Accept (Poster)