LICO: Large Language Models for In-Context Molecular Optimization

## Abstract

Abstract Optimizing black-box functions is a fundamental problem in science and engineering.
To solve this problem, many approaches learn a surrogate function that estimates the underlying objective from limited historical evaluations.
Large Language Models (LLMs), with their strong pattern-matching capabilities via pretraining on vast amounts of data, stand out as a potential candidate for surrogate modeling.
However, directly prompting a pretrained language model to produce predictions is not feasible in many scientific domains due to the scarcity of domain-specific data in the pretraining corpora and the challenges of articulating complex problems in natural language.
In this work, we introduce LICO, a general-purpose model that extends arbitrary base LLMs for black-box optimization, with a particular application to the molecular domain.
To achieve this, we equip the language model with a separate embedding layer and prediction layer, and train the model to perform in-context predictions on a diverse set of functions defined over the domain.
Once trained, LICO can generalize to unseen molecule properties simply via in-context prompting.
LICO achieves state-of-the-art performance on PMO, a challenging molecular optimization benchmark comprising over 20 20 20 20 objective functions.

## 1 Introduction

Black-box optimization (BBO) is the problem of optimizing an unknown, often complex objective function without direct access to its structure or derivatives. This problem is ubiquitous in many science and engineering fields, including material discovery [], protein engineering [, , ], molecular design [], mechanical design [, ], and neural architecture search []. Typically, BBO involves an iterative process where each step constructs a surrogate model to approximate the objective function. This model then guides the selection of promising candidates for subsequent evaluation. The main challenge of this approach lies in learning an effective surrogate function that can accurately estimate the objective from limited historical data.

In stark contrast, we have seen impressive generalization abilities of Large Language Models (LLMs) [, , , , , , , ] for language-driven reasoning over many kinds of domains. By pretraining on Internet-scale data, LLMs have demonstrated exceptional pattern-matching abilities and generalization from limited observations in both natural language [, , ] and other domains [, , ]. This positions LLMs as a promising solution for enhancing surrogate modeling for BBO.
Some recent works have indeed shown great potential for using LLMs for solving optimization problems [, , , ]. The main idea behind these methods is to frame the optimization problem in natural language, and prompt the language model using previously collected observations to make predictions for new data points [] or to propose better candidates [, , , , , , , , ]. However, this approach has several limitations. First, performing optimization in the text space requires the problem and solution to be expressed in natural language, thus limiting this approach to selected domains. Second, the scarcity of domain-relevant data in the text corpora used to train language models poses generalization challenges when using these models for general scientific domains such as molecular optimization. Therefore, existing works have only demonstrated the success of LLMs in neural architecture search [, , ], prompt optimization [], and code generation [, ], corresponding to domains that are well-represented in the training dataset for common language models [, , ]. Third, relying on verbose textual descriptions for both the problem and its solution imposes practical constraints by inflating the context length and thereby reducing the number of historical observations the model can effectively utilize.

In this work, we propose Large Language Models for In-Context Optimization (LICO), a general-purpose model that leverages LLMs for black-box optimization, with a particular application to the molecular domain. To generalize a language model to a new scientific domain unseen during pretraining, we equip the model with two embedding layers for embedding the previously collected molecules and their scores, and a prediction head to predict the score of unseen candidates. Intuitively, the embedding layers map the molecules and their scores to the same feature space already learned by the language model, allowing the model to perform in-context learning in this space instead of the raw text space.
Unlike previous methods, this approach is applicable to domains that may not be easily described in natural language such as molecular optimization. Moreover, avoiding verbose textual descriptions enables the model to condition on more historical observations, thus scaling better to harder problems that cannot be solved within a few steps.

We train the new layers together with the (frozen) LLM to perform in-context predictions on a family of functions. Specifically, for each function sampled from this family, we condition the model on a set of inputs and their corresponding evaluations, and task the model to predict the function value of the remaining data points. This task mimics surrogate modeling in BBO, where the surrogate model has to iteratively update its estimation of the underlying objective by conditioning on historical data.
An ideal function family to train the model should be close to the target objective functions we want to optimize, but also be diverse enough to encourage generalization. Therefore, we propose to combine intrinsic functions and synthetically generated functions for training LICO. Intrinsic functions are inherent properties of the input that are easy to evaluate. In molecular optimization, for example, intrinsic functions include molecular weight, the number of rings, or heavy atom count, which are obtained via simple computation on the molecule. These intrinsic functions are closely related to the actual objective functions we want to optimize such as bioactivities against a target disease. To facilitate generalization outside of the intrinsic functions, we additionally train LICO on synthetic functions defined over the same target domain that are generated by Gaussian Processes. Our empirical evidence shows the importance of learning from both intrinsic and synthetic functions to the performance of the model on downstream tasks. Figure 1 illustrates our approach.

After training, LICO is capable of optimizing a wide range of molecular properties purely via in-context prompting. While the methodology of LICO applies to general scientific domains, in this paper we focus on molecular optimization. This problem plays a pivotal role in advancing drug and material discovery. The complexity of molecular structures and the vastness of the chemical space present unique challenges to black-box optimization algorithms. Moreover, since molecule-relevant data is likely under-represented in the pretraining corpora of existing language models, molecular optimization is a good problem to test the performance and applicability of LICO. We evaluate LICO against the state-of-the-art methods on Practical Molecular Optimization (PMO) [], a challenging molecular optimization benchmark with over $20$ objective functions. The experiments show that LICO achieves the best performance and is the highest-ranked method in the benchmark.

Figure: Figure 1: Our proposed approach. We equip a pretrained LLM with an embedding layer for $x$, an embedding layer for $y$, and a prediction layer. We train the model on semi-synthetic data to predict $y$ given $x$ and previous $(x,y)$ pairs. We prepend each $x$ with a special token <x> and each $y$ with a special token <y> to guide in-context reasoning.

## 2 Problem Statement

Let $f:\mathcal{X}\rightarrow\mathbb{R}$ be a real-valued function that operates on a $d$-dimensional space $\mathcal{X}\subseteq\mathbb{R}^{d}$. In black-box optimization (BBO), the goal is to find the input $x^{\star}$ that maximizes $f$:

$$ $x^{\star}\in\operatorname*{arg\,max}_{x\in\mathcal{X}}f(x),$ (1) $$

where we do not have direct access to the structure or gradient information of $f$. In molecular optimization, $\mathcal{X}$ is the space of all possible molecules, and $f$ is a certain property of the molecule we want to optimize over, such as bioactivities against a disease. While $f$ is unknown, we often have access to an unlabeled dataset $\mathcal{D}_{\text{u}}$ that consists of molecules $x^{\prime}s$ without the corresponding function values $y^{\prime}s$. ZINC [] is such a dataset, which contains thousands to millions of unlabeled molecules.

To solve the optimization in (1), we can query $f$ with a limited budget, since evaluation often involves expensive physical experiments. To overcome this challenge, a common BBO approach learns a surrogate model $f_{\theta}$ that approximates the objective $f$ from past observations $\mathcal{D}_{\text{obs}}=\{(x_{i},y_{i})\}_{i=1}^{n}$, which starts empty and incrementally expands with new data points $(x,f(x))$ we query at each iteration.
Formally, a surrogate model represents a predictive distribution $p_{\theta}(y\mid x,\mathcal{D}_{\text{obs}})$ of the function value $y$ conditioned on the input $x$ and the evolving observed dataset $\mathcal{D}_{\text{obs}}$.
The prediction of this surrogate guides the selection of candidates to balance exploration and exploitation for subsequent function evaluation. The newly selected points are then added to $\mathcal{D}_{\text{obs}}$, and the process continues.

The success of this approach highly depends on the efficiency of the surrogate model $f_{\theta}$ in estimating $f$ from limited data in $\mathcal{D}_{\text{obs}}$ at each iteration.
This resembles few-shot prediction,
a setting that Large Language Models (LLMs) have proven to excel in. By pretraining on vast Internet-scale data, LLMs can learn generalizable patterns from limited data, and are capable of adapting to multiple functions at test time simply via in-context prompting [, , , ]. A recent line of works [, , , ] has exploited this ability of LLMs for optimization, but they relied on natural language as the interface, thus lacking generality to scientific domains. In this work, we propose a more general and efficient approach to leveraging LLMs for black-box optimization.

## 3 Related Work

LLMs for Optimization Recent works have explored the use of LLMs for optimization. The general idea behind these works is to prompt the model with the textual description of the optimization problem and historical evaluations for few-shot reasoning. Yang et al. [], Liu et al. [], Zhang et al. [], Ma et al. [] propose to prompt the language model to directly suggest better candidates to evaluate given the past inputs and their corresponding scores. Meyerson et al. [], Lehman et al. [], Bradley et al. [] integrate LLMs with evolutionary algorithms, and prompt the model to perform crossover and mutation operations based on the population at each optimization step. Anonymous [] study the use of LLMs to enhance several components in Bayesian optimization, including warmstarting, surrogate modeling, and candidate generation.

The common approach in existing works has several inherent limitations. First, for general scientific domains, the input $x$ may not be easily described by natural language. Second, even when there is a textual description of the input, for instance, molecules can be
represented by SMILES strings [], it is likely that molecule-relevant data is significantly under-represented in the text corpora used for training existing language models. This hinders the generalization of LLMs to new domains outside of their training distribution.
These challenges are why existing works only consider hyperparameter optimization, prompt optimization, and code generation, domains that are easy to describe in text, and are well-represented in the training data of LLMs. Furthermore, from an engineering perspective, naively prompting a language model with verbose textual descriptions of the input $x$ results in an excessively long context, thus reducing the number of examples the model can condition on.
For example, an LLM with a maximum context length of $4000$ can only utilize up to $100$ past observations, assuming the average length of each data point is $40$. This practically limits the scalability of this approach to harder problems that require more steps to solve.

LLMs for Non-language Tasks In addition to optimization, several works have studied the extension of pretrained LLMs to non-language domains with two main directions. The first direction considers problems that can be described in natural language, and prompts a pretrained LLM to solve the problem directly in the text space [, , ]. The second direction tackles more general problems, and does it by learning separate encoders for the new domain and aligning it with the embedding space of the pretrained LLM [, , , ]. Our work is closely related to the latter direction. However, as discussed in the following sections, while many of these works completely leave the word space, we find it beneficial to include language instruction while training the new modules.

## 4 Method

We introduce LICO, a methodology for extending arbitrary base LLMs for surrogate modeling in black-box optimization. While the method applies to broad scientific domains, we choose molecular optimization to demonstrate LICO in this paper.
We aim to develop a model capable of efficiently adapting to various objective functions after training.
To achieve this, we propose a simple extension to existing LLMs and an unsupervised objective using semi-synthetic data to facilitate generalization.

### 4.1 Model Architecture

In black-box optimization, a surrogate model $f_{\theta}$ estimates the distribution of the function value $y$ given the input $x$ and past observations $\mathcal{D}_{\text{obs}}=\{(x_{i},y_{i})\}_{i=1}^{n}$ the model has collected until the optimization iteration $t$:

$$ $p_{\theta}(y\mid x,x_{1},y_{1},x_{2},y_{2},\dots,x_{n},y_{n}),$ (2) $$

where $x_{i}$ and $y_{i}=f(x_{i})$ are drawn from an objective function $f$.
Our goal is to explore LLMs to model $p_{\theta}$. As discussed earlier, we make no assumptions on the domain $\mathcal{X}$ to be expressed with natural language.
To extend a pretrained language model to an arbitrary new domain, we equip the model with $3$ new layers – an embedding layer for the inputs $x^{\prime}s$, an embedding layer for the function values $y^{\prime}s$, and a prediction layer for predicting the unknown function value $y$. Learning separate embedding layers offers several benefits. First, the new embedding layers encode $x$ and $y$ to a shared hidden space obtained by the language model via pretraining, which enables the model to escape the raw text space and perform in-context reasoning in the hidden space instead. Moreover, by embedding each input $x$ to a single hidden vector instead of spanning it over several tokens, we effectively reduce the sequence length and thus allow the model to scale to more conditioning examples.

However, it is challenging for the model to perform this prediction task without any context information about the task. This is because, from the model point of view, embeddings of $x$ and $y$ do not mean anything more than some high-dimensional vectors.
In other words, the model does not know what task it should perform and what each token in the embedding sequence represents.
To address this issue, we prepend each sequence with a task prompt and prepend each input $x$ with a special token <x> and each function value $y$ with a special token <y>.
The task prompt instructs the model to perform the task, while the special tokens <x> and <y> inform the model of the position of each input $x$ and the corresponding function value $y$.
In other words, we use a language the model has mastered (natural language) to guide the learning of a new “foreign language” (e.g., molecule).
In practice, the task prompt is “Each x is a molecule and each y is the property of the corresponding molecule. Predict y given x.”, whereas <x> and <y> are two single characters “x” and “y”.
Finally, we apply the prediction layer on top of each token <y> to predict the function value given the tokens preceding it. Each prediction consists of a mean and a standard deviation value which will be used for the selection of candidates during optimization. Figure 1 illustrates the architecture of LICO.

It is worth noting that the combination of natural language and domain-specific embeddings is the main distinction between LICO and
previous works such as FPT [] which applies pretrained LLMs to sequence classification tasks in non-language modalities. FPT also learns new embedding layers for the new domain, but relies entirely on the pretrained self-attention layers to model these embeddings without any language instructions.
This distinction stems from the different nature of the tasks we aim to tackle. In sequence classification, the model produces a single prediction for the entire sequence, thus having a good representation of the sequence via self-attention is sufficient. For in-context learning, however, the model needs to associate each input $x$ with its corresponding value $y$ to infer the underlying function $f$ and make predictions for unknown $y$. A language instruction that specifies where $x$ is and where $y$ is helps the model identify this association and improve its in-context reasoning.
Our ablation study in 5.2.1 confirms this utility of retaining language tokens.

### 4.2 Semi-synthetic Training

Our goal is to train LICO on the unlabeled data $\mathcal{D}_{\text{u}}$ with an unsupervised objective to facilitate efficient generalization to an arbitrary objective function $f$ in the same domain $\mathcal{X}$ after training. Our key insight is, that if we train the model to perform the estimation in (2) for a wide range of functions, it should be able to adapt to any objective function after training. While the true function values are unknown before optimization, we can use the unlabeled data $x^{\prime}s$ to generate training data from other functions. Assume we have access to a family of functions $\tilde{\mathcal{F}}$ that operate on the same input domain $\mathcal{X}$. For each function $\tilde{f}$ drawn from $\tilde{\mathcal{F}}$, we sample a set of function evaluations $\{(x_{i},y_{i})\}_{i=1}^{n}$ and train the model to autoregressively predict $y$ given the input $x$ and preceding $(x,y)$ pairs:

$$ $\displaystyle\mathcal{L}(\theta)=\mathbb{E}\left[\sum_{i=1}^{n}\log p_{\theta} (y_{i}\mid x_{i},x_{<i},y_{<i})\right],$ (3) $$

in which the expectation is with respect to $\tilde{f}\sim\tilde{\mathcal{F}}$, $x_{1:n}\sim\mathcal{D}_{\text{u}}$, and $y_{1:n}=\tilde{f}(x_{1:n})$. After training, the estimation in (2) can be done purely via in-context prompting, where we condition the model on past observations to make predictions for new data points.

Ideally, the function family $\tilde{\mathcal{F}}$ should be close to the downstream objective $f$, but also be diverse enough to encourage broad generalization across functions. To achieve this, we propose to train LICO on a mix of intrinsic and synthetic functions, which we term semi-synthetic training. Intrinsic functions are functions that map each input molecule $x$ to an inherent property of $x$. For example, molecular weight, the number of rings, or heavy atom count are intrinsic properties of the molecule that are known from domain knowledge or can be easily computed using standard tools. These intrinsic properties are closely related to many downstream objective functions. For example, the biological activity of a drug molecule, such as its ability to inhibit a particular enzyme, is often closely related to the molecule’s shape or conformation. Therefore, training LICO from these functions encourages the model to learn useful representations of the input $x$ and obtain good prior knowledge about the optimization domain.

However, it is important to note that we are ultimately interested in optimizing other functions outside of the intrinsic function set. Training the model only on a limited set of intrinsic functions may result in overfitting and poor generalization to unseen functions. To diversify the training data, we additionally train the model on synthetically generated functions. A synthetic function family should be easy to sample from and be capable of producing diverse functions. Many such families exist, including Gaussian Processes (GPs), randomly constructed Gaussian Mixture Models, or randomly initialized neural networks. We choose to generate synthetic functions from Gaussian Processes with a Tanimoto kernel due to its simplicity and efficiency. Tanimoto kernel, also known as the Jaccard coefficient, measures the similarity between two vectors of binary values, a representation that is widely used for many scientific domains such as chemistry, drug discovery, or bioinformatics. Specifically, each synthetic function $\tilde{f}$ is sampled as follows,

$$ $\tilde{f}\sim\mathcal{G}\mathcal{P}(0,\mathcal{K}),\hskip 5.69046pt\mathcal{K} (x,x^{\prime})=\frac{x\cdot x^{\prime}}{||x||^{2}+||x^{\prime}||^{2}-x\cdot x^ {\prime}},$ (4) $$

where $\mathcal{K}(x,x^{\prime})$ is the Tanimoto kernel that measures the similarity between $x$ and $x^{\prime}$.

The final family of functions $\tilde{\mathcal{F}}$ used to train LICO is a mixture of intrinsic and synthetic functions with a certain ratio. This design choice is critical to the model’s performance. Intuitively, training on both types of functions ensures proximity to the downstream objectives and good coverage of the function space for efficient generalization.
The use of intrinsic functions is also the main difference between our work and ExPT [], a recent method that studies pure synthetic pretraining for optimization. We hypothesize that while synthetic data alone is sufficient for ExPT on a few simple tasks, for a more complex domain such as molecular optimization, synthetic training provides too little relevant signal for the model to generalize to downstream objectives. We empirically show the importance of both intrinsic and synthetic functions in the ablation study in section 5.2.2.

### 4.3 LICO for Black-box Optimization

After training, a single LICO model can be used for optimizing various objective functions within the domain $\mathcal{X}$. Optimization involves an iterative process. At each iteration $t$, we generate a set of candidates $\{x_{i}\}_{i=1}^{C}$ for which the model predicts the mean $\mu_{i}$ and standard deviation $\sigma_{i}$ conditioned on prior observations $\mathcal{D}_{\text{obs}}$, a dataset of $(x,y)$ pairs collected until $t$. An acquisition function $\alpha$ then calculates a utility score based on $\mu_{i}$ and $\sigma_{i}$ for each candidate, balancing between exploration (favoring high $\sigma$) and exploitation (favoring high $\mu$).
The top $k$ candidates determined by their utility scores are evaluated using the objective function $f$. These $k$ candidates and their corresponding evaluations are incorporated into the dataset $\mathcal{D}_{\text{obs}}$, and the cycle repeats. This process terminates once we exhaust the evaluation budget of $B$.
Algorithm 1 summarizes the optimization process.

## 5 Experiments

We evaluate LICO on molecular optimization, where the goal is to design new molecules with desired properties such as high chemical stability, low toxicity, or selective inhibition against a target disease. This problem plays a pivotal role in advancing drug and material discovery.

### 5.1 PMO Benchmark

Benchmark We evaluate LICO on Practical Molecular Optimization (PMO) [], a standard benchmark for molecular optimization with a focus on sample efficiency. We experiment on $21$ optimization objectives provided by PMO, including QED [], DRD2 [], and $19$ objective functions from Guacamol []. QED assesses a molecule’s drug-likeness by identifying certain "red flags". DRD2 is a machine learning model trained on experimental data to predict bioactivities for specific target diseases. Guacamol objectives emulate drug discovery goals through a multi-property objective (MPO) approach, considering factors like target molecule similarity, molecular weights, and CLogP. All objective values range from 0 0 to $1$, with $1$ indicating the best outcome.

Baselines We compare LICO against $3$ leading methods in PMO, namely REINVENT [], Graph GA [], and GP BO []. REINVENT is a reinforcement learning method that refines a pretrained RNN for generating SMILES strings. Graph GA, inspired by evolutionary processes, utilizes crossover operations derived from graph matching and mutation at atom and fragment levels to explore the molecule space. GP BO is a Bayesian optimization method that constructs a surrogate function using Gaussian Processes and employs an acquisition function that combines the surrogate’s predictions with uncertainty estimates to guide candidate selection. In addition to PMO baselines, we also compare LICO with TNP [], a state-of-the-art transformers model for few-shot learning. GP BO and TNP are similar to LICO, where the difference is we use an LLM for surrogate modeling instead of a GP or TNP.

LICO training We use ZINC 250K as the unlabeled dataset $\mathcal{D}_{\text{u}}$. ZINC 250K contains around $250000$ molecules sampled from the full ZINC database [] with moderate size and high pharmaceutical relevance and popularity. We adopt $2$-radius $2048$ bit molecular fingerprints as the input feature of the molecule. To generate training data, we use $47$ intrinsic properties of the molecule as the intrinsic functions, which we present in detail in Appendix A.1. We train LICO for $20000$ iterations with a batch size of $4$, where each data point is a sequence of $(x,y)$ pairs sampled from an intrinsic or synthetic function. The ratio of synthetic data is $0.1$. We use Llama-2-7b [] as the base LLM, and use LoRA [] for parameter-efficient finetuning.

Optimization details We limit the optimization budget of all methods to $1000$ function calls. We report the area under the curve (AUC) of the top-$10$ average objective value against the number of function calls as the performance metric. AUC metric favors methods that obtain high values with a smaller number of function calls, thus evaluating both optimization capability and sample efficiency. We min-max scale the AUC values to $[0,1]$. We aggregate the performance for each method across $5$ seeds for better reproducibility as suggested by PMO.

**Table 1: The performance of LICO and the baselines on $21$ optimization tasks in PMO. Higher score is better. We report the mean and stddev of scores averaged over $5$ random seeds. We use blue and violet to denote the best and second-best method for each task.**
| Task | GP BO | Graph GA | LICO | REINVENT | TNP |
| --- | --- | --- | --- | --- | --- |
| albuterol_similarity | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.636\pm 0.106}}$ | $0.583\pm 0.065$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.65<br>6\pm 0.125}}$ | $0.496\pm 0.020$ | $0.550\pm 0.034$ |
| amlodipine_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.519\pm 0.014}}$ | $0.501\pm 0.016$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.54<br>1\pm 0.026}}$ | $0.472\pm 0.008$ | $0.491\pm 0.014$ |
| celecoxib_rediscovery | $0.411\pm 0.046$ | $0.424\pm 0.049$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.44<br>7\pm 0.073}}$ | $0.370\pm 0.029$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.429\pm 0.048}}$ |
| deco_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.593\pm 0.013}}$ | $0.581\pm 0.006$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.59<br>6\pm 0.010}}$ | $0.572\pm 0.006$ | $0.586\pm 0.003$ |
| drd2 | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.857\pm 0.080}}$ | $0.833\pm 0.065$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.85<br>9\pm 0.066}}$ | $0.775\pm 0.086$ | $0.758\pm 0.066$ |
| fexofenadine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.70<br>7\pm 0.021}}$ | $0.666\pm 0.009$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.700\pm 0.023}}$ | $0.650\pm 0.007$ | $0.680\pm 0.015$ |
| isomers_c7h8n2o2 | $0.545\pm 0.158$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.735\pm 0.112}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.77<br>9\pm 0.099}}$ | $0.725\pm 0.064$ | $0.694\pm 0.123$ |
| isomers_c9h10n2o2pf2cl | $0.599\pm 0.059$ | $0.630\pm 0.086$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.67<br>2\pm 0.075}}$ | $0.630\pm 0.032$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.635\pm 0.071}}$ |
| median1 | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.213\pm 0.020}}$ | $0.208\pm 0.015$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.21<br>7\pm 0.019}}$ | $0.205\pm 0.012$ | $0.210\pm 0.012$ |
| median2 | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.20<br>3\pm 0.009}}$ | $0.181\pm 0.009$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.193\pm 0.009}}$ | $0.188\pm 0.010$ | $0.186\pm 0.013$ |
| mestranol_similarity | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.42<br>7\pm 0.025}}$ | $0.362\pm 0.017$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.423\pm 0.016}}$ | $0.379\pm 0.026$ | $0.368\pm 0.005$ |
| osimertinib_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.76<br>6\pm 0.006}}$ | $0.751\pm 0.005$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.759\pm 0.008}}$ | $0.737\pm 0.007$ | $0.752\pm 0.006$ |
| perindopril_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.458\pm 0.019}}$ | $0.435\pm 0.016$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.47<br>3\pm 0.009}}$ | $0.404\pm 0.009$ | $0.433\pm 0.010$ |
| qed | $0.912\pm 0.010$ | $0.914\pm 0.007$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.92<br>5\pm 0.005}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.921\pm 0.002}}$ | $0.917\pm 0.002$ |
| ranolazine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.70<br>1\pm 0.023}}$ | $0.620\pm 0.014$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.687\pm 0.029}}$ | $0.574\pm 0.044$ | $0.613\pm 0.033$ |
| scaffold_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.478\pm 0.009}}$ | $0.461\pm 0.008$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.48<br>0\pm 0.008}}$ | $0.447\pm 0.010$ | $0.469\pm 0.015$ |
| sitagliptin_mpo | $0.232\pm 0.083$ | $0.229\pm 0.053$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.31<br>5\pm 0.097}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.261\pm 0.026}}$ | $0.221\pm 0.034$ |
| thiothixene_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.35<br>1\pm 0.039}}$ | $0.322\pm 0.023$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.343\pm 0.035}}$ | $0.311\pm 0.021$ | $0.307\pm 0.034$ |
| troglitazone_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.31<br>3\pm 0.018}}$ | $0.267\pm 0.015$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.292\pm 0.028}}$ | $0.246\pm 0.009$ | $0.266\pm 0.009$ |
| valsartan_smarts | $0.000\pm 0.000$ | $0.000\pm 0.000$ | $0.000\pm 0.000$ | $0.000\pm 0.000$ | $0.000\pm 0.000$ |
| zaleplon_mpo | $0.392\pm 0.034$ | $0.374\pm 0.024$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.404\pm 0.022}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.40<br>6\pm 0.017}}$ | $0.377\pm 0.018$ |
| Sum of scores ($\uparrow$) | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>10.313}}$ | $10.076$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{10.7<br>60}}$ | $9.772$ | $9.944$ |
| Mean rank ($\downarrow$) | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>2.33}}$ | $3.62$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{1.48}}$ | $3.86$ | $3.65$ |

Results Table 1 summarizes the performance of the $5$ considered methods across $21$ optimization tasks. Overall, LICO is the leading method in this benchmark, achieving the highest aggregated score and the lowest mean rank. Specifically, LICO achieves the best performance in $12/21$ tasks and the second-best performance in the remaining $8/21$ tasks. It is important to note that LICO achieves this impressive result without being explicitly trained on data from downstream objectives. This shows the effectiveness of semi-synthetic training in enabling generalization to a broad range of functions via in-context prompting. TNP performs poorly in this benchmark, despite sharing a similar architecture with LICO. This performance gap highlights the importance of the pattern-matching capabilities LLMs acquire through extensive pretraining, which are crucial for adapting to new domains.

The second best-performing method in this benchmark is GP BO, a method very similar to LICO, where the only difference between the two is the surrogate model. This indicates the superiority of LICO compared to GP, a popular surrogate model for black-box optimization. To verify this, we compare the predictive performance of LICO and GP on several objective functions. We do this by first labeling the ZINC unlabeled dataset with the objective functions and randomly choosing a subset of the labeled data points for evaluation. For each task, we vary the number of examples given to each method from $32$ to $512$, and evaluate their performance on $128$ held-out data points. We use negative log-likelihood, mean squared error, and root mean squared calibration error as the evaluation metrics.
Figure 2 compares the predictive performance of LICO and GP in $3$ objective functions, median1, ranolazine_mpo, and troglitazone_rediscovery. The figure shows that the optimization performance of the method closely aligns with the predictive performance of the surrogate model. In median1 and ranolazine_mpo where LICO outperforms GP in terms of optimization score, the model also achieves lower negative log-likelihood, mean squared error, and calibration error. Similarly, LICO has worse predictive performance in troglitazone_rediscovery where it underperforms GP. This verifies our hypothesis and proves the effectiveness of LICO for surrogate modeling.

Figure: Figure 2: The predictive performance of LICO and GP on $3$ objective functions in PMO with different metrics and varying numbers of observations.
Refer to caption: x1.png

**Table 2: Performance of LICO on $5$ tasks with different language instructions.**
| Task | albuterol_similarity | amlodipine_mpo | celecoxib_rediscovery | deco_hop | drd2 | Sum ($\uparrow$) |
| --- | --- | --- | --- | --- | --- | --- |
| LICO w/o Language | $0.615\pm 0.104$ | $0.491\pm 0.018$ | $0.396\pm 0.051$ | $0.585\pm 0.010$ | $0.840\pm 0.063$ | $2.927$ |
| LICO w/o Task prompt | $0.641\pm 0.107$ | $0.523\pm 0.018$ | $\mathbf{0.457\pm 0.041}$ | $0.595\pm 0.006$ | $0.844\pm 0.105$ | $3.060$ |
| LICO | $\mathbf{0.656\pm 0.125}$ | $\mathbf{0.541\pm 0.026}$ | $0.447\pm 0.073$ | $\mathbf{0.596\pm 0.010}$ | $\mathbf{0.859\pm 0.066}$ | $\mathbf{3.099}$ |

**Table 3: Performance of LICO on $5$ tasks with different ratios of synthetic data.**
| Task | albuterol_similarity | amlodipine_mpo | celecoxib_rediscovery | deco_hop | drd2 | Sum ($\uparrow$) |
| --- | --- | --- | --- | --- | --- | --- |
| LICO Intrinsic | $0.598\pm 0.115$ | $0.524\pm 0.029$ | $0.412\pm 0.042$ | $0.585\pm 0.005$ | $0.891\pm 0.032$ | $3.010$ |
| LICO 0.1 Synthetic | $0.656\pm 0.125$ | $\mathbf{0.541\pm 0.026}$ | $\mathbf{0.447\pm 0.073}$ | $\mathbf{0.596\pm 0.010}$ | $0.859\pm 0.066$ | $\mathbf{3.099}$ |
| LICO 0.5 Synthetic | $\mathbf{0.663\pm 0.140}$ | $0.504\pm 0.016$ | $0.402\pm 0.016$ | $0.588\pm 0.006$ | $\mathbf{0.907\pm 0.020}$ | $3.063$ |
| LICO Synthetic | $0.547\pm 0.080$ | $0.498\pm 0.026$ | $0.404\pm 0.103$ | $0.585\pm 0.003$ | $0.902\pm 0.012$ | $2.936$ |

We also note that there is a discrepancy between Table 1 and the results reported in PMO. This is due to several reasons. First, we use a smaller optimization budget of $1000$ queries compared to $10000$ in PMO. We believe $1000$ is a more reasonable budget while still allowing optimization methods to achieve meaningful performances. Moreover, we found the GP BO implementation in PMO to be suboptimal, specifically in how it generated the candidate pool. The original implementation applied crossover and mutation to a mix of the best individuals and randomly selected individuals from the last iteration to generate the candidate pool for the current iteration. However, we found that only using the best individuals from the last iteration results in a much better performance. By implementing this change, GP BO becomes a much stronger baseline than Graph GA and REINVENT.

### 5.2 Ablation Analysis

We perform various ablation studies to understand the importance of different components and design choices in LICO. For the ablation experiments, we consider the first $5$ tasks in Table 1 only. We report the aggregated performance of different models using AUC Top-$10$ across $5$ random seeds.

#### 5.2.1 LICO without language instruction

First, we examine the importance of language instructions to the performance of LICO. We compare $3$ variants of LICO: 1) LICO without any language instruction, 2) LICO with special tokens <x> and <y> but without a task prompt, and 3) LICO with both special tokens and the task prompt. Table 2 compares the performance of the $3$ variants. LICO performs the best in $4/5$ tasks, followed by LICO without the task prompt. LICO without any language instruction performs the worst, often by a large margin. This result confirms the importance of guiding a pretrained LLM with language instruction when applying the model to in-context reasoning in a completely new domain.

#### 5.2.2 LICO with different synthetic ratios

We investigate the importance of training LICO on both intrinsic and synthetic data. To do this, we gradually increase the ratio of synthetic functions in the training data from 0 0 (intrinsic-only) to $1$ (synthetic-only), and compare the performance of LICO across different ratios. Table 3 shows that LICO with semi-synthetic training performs the best, outperforming both intrinsic-only and synthetic-only data. Training with synthetic data only performs the worst, which is expected when synthetic functions generated by a GP do not include any domain knowledge that is encoded by the intrinsic functions. In other words, synthetic data alone provides too little relevant signal for the model to generalize to unseen downstream objectives. Training with intrinsic functions only, on the other hand, results in quite good performances on most tasks. However, in tasks like albuterol_similarity, semi-synthetic training outperforms this baseline by a large margin. We hypothesize that the underlying objective in albuterol_similarity is far from the intrinsic functions used to train LICO, leading to poor generalization. Finally, training with small ($0.1$) to moderate ($0.5$) ratios of synthetic data achieves similarly good performance.

Figure: Table 4: Performance of pretrained vs randomly initialized LLMs.
Refer to caption: x2.png

#### 5.2.3 Randomly initialized vs Pretrained LLMs

To understand the importance of using a pretrained LLM, we compare LICO with an autoregressive transformer model of the same size (7B). The transformer architecture is the same as in [], and we train this model to perform in-context learning on the semi-synthetic data from scratch. Table 4 shows the comparison. The scratch model performs much worse than LICO with a pretrained LLM on all tasks despite sharing the same number of parameters. This highlights the importance of the pattern-matching capabilities that LLMs like Llama-2 acquire through extensive language pretraining.

#### 5.2.4 LICO with different LLM sizes

Previous works have shown the favorable scaling laws of Large Language Models where larger models consistently perform better on downstream tasks []. In this section, we investigate the scaling properties of LLMs but in the context of black-box optimization. Specifically, we compare $4$ different base LLMs with different sizes – Qwen-1.5 1.8B and 4B [], Phi-2 2.7B [], and Llama-2 7B []. We use the same language instructions for all models. We evaluate each model on the first $8$ tasks in Table 1 and average the results across $5$ random seeds. We report the sum of performance across $8$ tasks.

The comparison in Figure 3 shows that the optimization performance scales consistently with the model size, with Llama-2 7B being the best method. This experiment indicates that larger LLMs not only perform better in language tasks but also obtain stronger pattern-matching capabilities that can be transferred to a completely different domain. Given this scaling, we can further improve the current performance of LICO by scaling up the base LLM size.

## 6 Conclusion and Future Work

We develop LICO, a new method that leverages pretrained Large Language Models for black-box optimization. LICO extends existing LLMs to non-language domains with separate embedding and prediction layers. To enable efficient generalization to various optimization tasks, we train LICO on a diverse set of semi-synthetic functions for few-shot predictions. LICO achieves state-of-the-art performance on PMO, a challenging molecular optimization benchmark with over 20 objective functions. Ablation analyses highlight the importance of incorporating language instruction to guide in-context learning and semi-synthetic training for better generalization.

One limitation of our method is the assumption of an accessible set of intrinsic functions. While this is true for molecular optimization, it may not apply to other scientific domains. In such cases, a better synthetic data generation process incorporating domain knowledge is needed to aid generalization.

Future directions include evaluating LICO in other domains to test its applicability and generality, exploring other prompts that better exploit the capabilities of pretrained LLMs, and using LLMs for other aspects of optimization, such as candidate suggestion or exploration.

## Acknowledgements

This work is supported by grants from Amazon, Cisco, Microsoft, and Samsung.

## Appendix A LICO implementation details

### A.1 Molecular intrinsic functions

We utilize $47$ intrinsic properties of molecules for pretraining LICO. Table 5 shows the intrinsic properties and their explanation.

**Table 5: Inherent Properties of Molecules and their Explanations**
| Property | Explanation |
| --- | --- |
| Molecular Weight | Total mass of all atoms in the molecule. |
| Number of Rotatable Bonds | Bonds that allow free rotation around themselves. |
| Number of Rings | Count of ring structures in the molecule. |
| Number of H Donors | Atoms in the molecule that can donate a hydrogen atom. |
| Number of H Acceptors | Atoms in the molecule capable of accepting a hydrogen atom. |
| Num Aromatic Rings | Count of rings with a pattern of alternating single and double bonds. |
| Num Aliphatic Rings | Count of non-aromatic rings in the molecule. |
| Num Saturated Rings | Rings with single bonds only. |
| Num Heteroatoms | Atoms other than carbon or hydrogen. |
| Fraction Csp3 | Fraction of carbon atoms bonded with a single pair of electrons. |
| Heavy Atom Count | Count of all atoms except hydrogen. |
| Num Valence Electrons | Total number of electrons that can participate in the formation of chemical bonds. |
| Num Aromatic CarboRings | Aromatic rings composed solely of carbon atoms. |
| Num Aromatic HeteroRings | Aromatic rings containing at least one heteroatom. |
| Num Saturated CarboRings | Saturated rings made only of carbon atoms. |
| Num Saturated HeteroRings | Saturated rings containing at least one heteroatom. |
| BalabanJ | Topological index to quantify molecular branching. |
| BertzCT | A measure of structural complexity of the molecule. |
| Ipc | Information content on the vertex degree. |
| HallKierAlpha | Valence connectivity index used in molecular shape analysis. |
| Kappa1 | Shape descriptor based on the skeleton of the molecule. |
| Kappa2 | Hydrogen suppressed graph descriptor. |
| Kappa3 | Hydrogen complete graph descriptor. |
| Chi0 | Randić molecular connectivity index. |
| Chi1 | Valence modified Randić molecular connectivity index. |
| Chi0n | Randić connectivity index normalized. |
| Chi1n | Valence modified Randić connectivity index normalized. |
| Chi2n | Second order Randić connectivity index normalized. |
| Chi3n | Third order Randić connectivity index normalized. |
| Chi4n | Fourth order Randić connectivity index normalized. |
| Chi0v | Randić connectivity index for valence electrons. |
| Chi1v | First order valence molecular connectivity index. |
| Chi2v | Second order valence molecular connectivity index. |
| Chi3v | Third order valence molecular connectivity index. |
| Chi4v | Fourth order valence molecular connectivity index. |
| Molar Refractivity | Measure of the molecule’s polarizability. |
| AMW | Average molecular weight of all atoms in the molecule. |
| Max Partial Charge | Maximum partial charge in the molecule. |
| Min Partial Charge | Minimum partial charge in the molecule. |
| Max Abs Partial Charge | Maximum absolute value of the partial charges in the molecule. |
| Min Abs Partial Charge | Minimum absolute value of the partial charges in the molecule. |
| Labute ASA | Labute’s Approximate Surface Area, an estimate of the molecular surface area. |
| Max EState Index | Maximum electrotopological state index of the atoms in the molecule. |
| Min EState Index | Minimum electrotopological state index of the atoms in the molecule. |
| Max Abs EState Index | Maximum absolute value of the electrotopological state indices in the molecule. |
| Min Abs EState Index | Minimum absolute value of the electrotopological state indices in the molecule. |
| fr_C_O | Frequency of carbon-oxygen bonds in the molecule. |

### A.2 Training details

The $x$ embedding layer, $y$ embedding layer, and prediction layer in LICO are MLPs with a hidden dimension of $1024$. We train LICO for $20000$ steps with a batch size of $4$. For each data point in the batch, we randomly decide whether to sample an intrinsic or a synthetic function, with the probability of choosing synthetic functions being $0.1$. Each data point is a sequence of $(x,y)$ pairs with length $n\sim\mathcal{U}[64,800]$. If the function is an intrinsic function, we uniformly sample a property from Table 5, otherwise sample synthetic data following Equation (4).

We use Llama-2-7b [] as the base LLM, and use LoRA [] for parameter-efficient finetuning. We use a base learning rate of $5e-4$ with a linear warmup for $1000$ steps and a cosine decay for the remaining $19000$ steps. We use LoRA with a rank of $16$ and $\alpha$ scale of $16$.

### A.3 Black-box optimization hyperparameters

We use Algorithm 1 to optimize a black-box function with LICO. We initialize the observed dataset $\mathcal{D}_{\text{obs}}$ with a population of $34$ molecules sampled randomly from ZINC. At each iteration, we use the best $34$ candidates in $\mathcal{D}_{\text{obs}}$ to generate new candidates via crossover and mutation operations, with the mutation rate being $0.01$. The candidate pool size $C$ is $100$. We predict the mean $\mu_{i}$ and standard deviation $\sigma_{i}$ for each candidate $x_{i}$ in the pool using LICO. We employ a UCB acquisition function to compute the utility score $u_{i}=\mu_{i}+\beta\sigma_{i}$, which balances exploration and exploitation. Following [], we set $\beta=10^{b}$, where $b\sim\mathcal{U}[-0.5,1.5]$. We then pick $k=15$ candidates with the highest utility scores. We evaluate each selected candidate $x_{j}$ using the black-box function $f$, and add the new data point $(x_{j},y_{j})$ to the observed dataset $\mathcal{D}_{\text{obs}}$. The process continues with the updated observed dataset, and stops when $|\mathcal{D}_{\text{obs}}|=1000.$

When predicting $\mu_{i},\sigma_{i}=f_{\theta}(x_{i},\mathcal{D}_{\text{obs}})$, we normalize all the $y^{\prime}s$ values in $\mathcal{D}_{\text{obs}}$ to have mean 0 0 and standard deviation $1$. This is to resemble the finetuning data distribution of LICO. We then denormalize $\mu_{i}$ and $\sigma_{i}$ to the original space.

### A.4 Black-box optimization with LICO

Algorithm 1 outlines the optimization algorithm using LICO as the surrogate model.

Figure: Algorithm 1 Black-box optimization with LICO

## Appendix B Baseline details

##### TNP

is a transformer-based architecture for in-context learning. We refer to Nguyen and Grover [] for more details about TNP. We train a TNP model with $16$ attention layers and $2048$ hidden dimensions. Other hyperparameters are the same as for LICO. After training, we use TNP for black-box optimization using Algorithm 1 with the same optimization hyperparameters but replace LICO with TNP.

##### GP BO

replaces the LICO surrogate model in Algorithm 1 with a Gaussian Process with a Tanimoto kernel. We optimize the Gaussian Process hyperparameters via maximum likelihood estimation on the initial population sampled from ZINC. Other optimization hyperparameters are the same as for LICO.

##### Graph GA

is a model-free variant of Algorithm 1. Specifically, at each iteration, Graph GA generates $15$ candidates using the same crossover and mutation operations, and directly evaluates and adds them to $\mathcal{D}_{\text{obs}}$, since it does not employ a surrogate model.

##### REINVENT

adopts a policy-based RL approach to finetune a pretrained RNN to generate SMILES strings with high returns. At each optimization iteration, we sample $16$ molecules from the finetuned RNN, evaluate these molecules using the black-box function $f$, and add the new data points to $\mathcal{D}_{\text{obs}}$. We refer to Gao et al. [] for more details of the algorithm and other hyperparameters.

## Appendix C Additional results

### C.1 Additional metrics

In addition to AUC Average Top-10, we measure the optimization performance of different methods on AUC Average Top-1 and AUC Average Top-100 for a more comprehensive comparison. Table 6 and 7 show AUC Average Top-1 and AUC Average Top-100 performances, respectively.

**Table 6: The performance of LICO and the baselines on $21$ optimization tasks in PMO with AUC Average Top-1 metric. A higher score is better. We report the mean and stddev of scores averaged over $5$ random seeds. We use blue and violet to denote the best and second-best method for each task.**
| Task | GP BO | Graph GA | LICO | REINVENT | TNP |
| --- | --- | --- | --- | --- | --- |
| albuterol_similarity | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.672\pm 0.109}}$ | $0.647\pm 0.080$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.69<br>5\pm 0.150}}$ | $0.572\pm 0.026$ | $0.611\pm 0.042$ |
| amlodipine_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.538\pm 0.016}}$ | $0.526\pm 0.017$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.56<br>0\pm 0.026}}$ | $0.500\pm 0.016$ | $0.513\pm 0.016$ |
| celecoxib_rediscovery | $0.434\pm 0.052$ | $0.466\pm 0.062$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.49<br>2\pm 0.079}}$ | $0.415\pm 0.031$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.482\pm 0.067}}$ |
| deco_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.598\pm 0.013}}$ | $0.590\pm 0.005$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.60<br>3\pm 0.012}}$ | $0.585\pm 0.010$ | $0.597\pm 0.002$ |
| drd2_current | $0.895\pm 0.067$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.898\pm 0.048}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.90<br>2\pm 0.055}}$ | $0.867\pm 0.077$ | $0.831\pm 0.043$ |
| fexofenadine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.72<br>8\pm 0.022}}$ | $0.691\pm 0.011$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.719\pm 0.025}}$ | $0.696\pm 0.012$ | $0.706\pm 0.014$ |
| isomers_c7h8n2o2 | $0.576\pm 0.154$ | $0.815\pm 0.120$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.834\pm 0.109}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.84<br>6\pm 0.070}}$ | $0.761\pm 0.145$ |
| isomers_c9h10n2o2pf2cl | $0.644\pm 0.053$ | $0.708\pm 0.083$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.714\pm 0.084}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.72<br>4\pm 0.043}}$ | $0.701\pm 0.086$ |
| median1 | $0.235\pm 0.016$ | $0.233\pm 0.018$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.24<br>2\pm 0.020}}$ | $0.229\pm 0.015$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.238\pm 0.015}}$ |
| median2 | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.21<br>2\pm 0.010}}$ | $0.193\pm 0.011$ | $0.201\pm 0.009$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.209\pm 0.013}}$ | $0.200\pm 0.018$ |
| mestranol_similarity | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.44<br>9\pm 0.028}}$ | $0.387\pm 0.020$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.445\pm 0.014}}$ | $0.433\pm 0.034$ | $0.406\pm 0.011$ |
| osimertinib_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.78<br>8\pm 0.008}}$ | $0.777\pm 0.008$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.781\pm 0.007}}$ | $0.780\pm 0.009$ | $0.776\pm 0.007$ |
| perindopril_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.475\pm 0.019}}$ | $0.460\pm 0.025$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.49<br>2\pm 0.011}}$ | $0.432\pm 0.010$ | $0.457\pm 0.012$ |
| qed | $0.926\pm 0.011$ | $0.930\pm 0.004$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.93<br>5\pm 0.002}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.934\pm 0.003}}$ | $0.931\pm 0.001$ |
| ranolazine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.72<br>9\pm 0.024}}$ | $0.684\pm 0.015$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.711\pm 0.028}}$ | $0.657\pm 0.048$ | $0.669\pm 0.032$ |
| scaffold_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.486\pm 0.010}}$ | $0.475\pm 0.008$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.49<br>1\pm 0.013}}$ | $0.468\pm 0.010$ | $0.484\pm 0.019$ |
| sitagliptin_mpo | $0.268\pm 0.098$ | $0.281\pm 0.069$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.36<br>3\pm 0.114}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.333\pm 0.030}}$ | $0.274\pm 0.044$ |
| thiothixene_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.37<br>1\pm 0.046}}$ | $0.351\pm 0.029$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.368\pm 0.041}}$ | $0.345\pm 0.026$ | $0.332\pm 0.041$ |
| troglitazone_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.32<br>9\pm 0.019}}$ | $0.289\pm 0.021$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.309\pm 0.033}}$ | $0.276\pm 0.009$ | $0.286\pm 0.012$ |
| valsartan_smarts | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.000\pm 0.000}}$ | $0.000\pm 0.000$ | $0.000\pm 0.000$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.00<br>0\pm 0.000}}$ | $0.000\pm 0.000$ |
| zaleplon_mpo | $0.431\pm 0.031$ | $0.418\pm 0.022$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.435\pm 0.027}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.45<br>6\pm 0.020}}$ | $0.428\pm 0.022$ |
| Sum of scores ($\uparrow$) | $10.784$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>10.818}}$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{11.2<br>91}}$ | $10.755$ | $10.683$ |
| Mean rank ($\downarrow$) | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>2.52}}$ | $3.57$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{1.62}}$ | $3.48$ | $3.75$ |

**Table 7: The performance of LICO and the baselines on $21$ optimization tasks in PMO with AUC Average Top-100 metric. A higher score is better. We report the mean and stddev of scores averaged over $5$ random seeds. We use blue and violet to denote the best and second-best method for each task.**
| Task | GP BO | Graph GA | LICO | REINVENT | TNP |
| --- | --- | --- | --- | --- | --- |
| albuterol_similarity | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.548\pm 0.100}}$ | $0.470\pm 0.042$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.56<br>3\pm 0.093}}$ | $0.395\pm 0.012$ | $0.448\pm 0.028$ |
| amlodipine_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.458\pm 0.008}}$ | $0.422\pm 0.014$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.48<br>6\pm 0.025}}$ | $0.407\pm 0.005$ | $0.420\pm 0.013$ |
| celecoxib_rediscovery | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.363\pm 0.040}}$ | $0.346\pm 0.036$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.37<br>2\pm 0.070}}$ | $0.296\pm 0.024$ | $0.346\pm 0.026$ |
| deco_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.579\pm 0.013}}$ | $0.563\pm 0.006$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.58<br>3\pm 0.009}}$ | $0.550\pm 0.006$ | $0.568\pm 0.004$ |
| drd2_current | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.74<br>1\pm 0.097}}$ | $0.605\pm 0.086$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.725\pm 0.092}}$ | $0.615\pm 0.098$ | $0.556\pm 0.095$ |
| fexofenadine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.64<br>5\pm 0.018}}$ | $0.588\pm 0.008$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.636\pm 0.022}}$ | $0.549\pm 0.004$ | $0.599\pm 0.016$ |
| isomers_c7h8n2o2 | $0.300\pm 0.142$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.53<br>5\pm 0.091}}$ | $0.450\pm 0.149$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.511\pm 0.058}}$ | $0.492\pm 0.115$ |
| isomers_c9h10n2o2pf2cl | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.474\pm 0.038}}$ | $0.441\pm 0.068$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.53<br>5\pm 0.067}}$ | $0.445\pm 0.027$ | $0.447\pm 0.049$ |
| median1 | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.17<br>5\pm 0.022}}$ | $0.168\pm 0.013$ | $0.166\pm 0.019$ | $0.162\pm 0.007$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.170\pm 0.008}}$ |
| median2 | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.18<br>4\pm 0.006}}$ | $0.158\pm 0.008$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.175\pm 0.010}}$ | $0.155\pm 0.006$ | $0.162\pm 0.009$ |
| mestranol_similarity | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.37<br>9\pm 0.020}}$ | $0.311\pm 0.016$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.361\pm 0.030}}$ | $0.302\pm 0.016$ | $0.314\pm 0.003$ |
| osimertinib_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.70<br>6\pm 0.006}}$ | $0.667\pm 0.008$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.694\pm 0.010}}$ | $0.623\pm 0.014$ | $0.671\pm 0.006$ |
| perindopril_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.405\pm 0.019}}$ | $0.357\pm 0.012$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.42<br>4\pm 0.007}}$ | $0.332\pm 0.011$ | $0.359\pm 0.010$ |
| qed | $0.853\pm 0.010$ | $0.854\pm 0.011$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.88<br>2\pm 0.007}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.874\pm 0.003}}$ | $0.857\pm 0.003$ |
| ranolazine_mpo | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.63<br>3\pm 0.020}}$ | $0.462\pm 0.022$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.617\pm 0.021}}$ | $0.436\pm 0.040$ | $0.468\pm 0.042$ |
| scaffold_hop | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.462\pm 0.006}}$ | $0.435\pm 0.008$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.46<br>2\pm 0.006}}$ | $0.415\pm 0.009$ | $0.440\pm 0.010$ |
| sitagliptin_mpo | $0.133\pm 0.062$ | $0.103\pm 0.032$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.17<br>1\pm 0.045}}$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.134\pm 0.016}}$ | $0.100\pm 0.023$ |
| thiothixene_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.31<br>1\pm 0.030}}$ | $0.270\pm 0.015$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.299\pm 0.026}}$ | $0.256\pm 0.015$ | $0.261\pm 0.024$ |
| troglitazone_rediscovery | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.28<br>3\pm 0.014}}$ | $0.228\pm 0.008$ | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.258\pm 0.024}}$ | $0.201\pm 0.008$ | $0.230\pm 0.005$ |
| valsartan_smarts | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.000\pm 0.000}}$ | $0.000\pm 0.000$ | $0.000\pm 0.000$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.00<br>0\pm 0.000}}$ | $0.000\pm 0.000$ |
| zaleplon_mpo | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>0.301\pm 0.036}}$ | $0.258\pm 0.016$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{0.31<br>8\pm 0.018}}$ | $0.296\pm 0.009$ | $0.257\pm 0.013$ |
| Sum of scores ($\uparrow$) | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>8.933}}$ | $8.242$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{9.17<br>5}}$ | $7.954$ | $8.167$ |
| Mean rank ($\downarrow$) | ${\color[rgb]{.5,0,.5}\definecolor[named]{pgfstrokecolor}{rgb}{.5,0,.5}\mathbf{<br>1.95}}$ | $3.62$ | ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathbf{1.76}}$ | $4.14$ | $3.45$ |

## Appendix D Broader impact

Our work studies the application of large language models to black-box optimization, particularly in the domain of molecular optimization. This intersection of machine learning and optimization holds significant promise for advancing our understanding of LLMs’ capabilities and limitations, and has significant potential in areas like material science and drug discovery. Our main goal is to enhance machine learning and optimization techniques, but it’s also important to consider how these advancements might affect society, such as speeding up the development of new medicines and materials.

## Appendix E Compute Resources

All experiments in this paper are run on a cluster of $4$ A6000 GPUs, each with 49GB of memory.

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## Peer Reviews

confidence: 5
contribution: 4
initial_rating: 5
presentation: 4
questions: **Suggestion:**
I am willing to increase my rating if the authors report results on the *original* PMO-10K, which will ensure fair comparison with the prior work. Even if the results are not SOTA anymore, the paper can still be accepted, as the methods of the paper are interesting on their own. 

The paper can have an additional table for PMO-1K, with either tuned baselines, or with a note that the baselines are not carefully tuned.
soundness: 3
strengths: * the "domain adaption" trick to convert the general purpose text-based LLMs into domain-specific in-context learners using synthetic data.
* detailed ablation studies. I really liked the analysis of the effect of the ratio of "intrinsic" and "synthetic" datasets. It gives an intuition on how to design synthetic datasets for other optimization tasks in other domains.
* the "scaling law" chart (Fig. 3) is a good indicator of the scaling abilities of the proposed approach. Unfortunately there is a diversity of underlying models which makes the claims less significant. Hopefully there will be many sizes of similarly pretrained LLMs at some point (e.g. Llama 4 1B, 3B, 8B, etc.).
summary: The paper focuses on one of the most promising directions of modern LLMs: LLM-enhanced optimization algorithms. It suggests a method to extend arbitrary pretrained LLMs with a couple of layers and train them to perform in-context learning for arbitrary functions. The idea is tested on molecular property prediction tasks, and the paper claims SOTA results on the famous PMO benchmark.
weaknesses: The main weakness is that the SOTA claim on PMO is misleading. **The results reported in this paper are not really PMO.** There are two major differences. 

a) PMO has 23 tasks, not 21. *jnk3* and *gsk3* are missing.

b) PMO uses 10K budget of oracle calls (as mentioned by the authors).

While a) does not make the comparison to prior art unfair, b) is critical. The main advantage of the PMO paper was that the authors performed a large-scale hyperparameter search for every method they tried, and even discovered hyperparameter values (e.g. for REINVENT) that were not covered even by the authors of the methods. So, all methods from PMO, and the subsequent methods like Genetic GFN have their hyperparameters tuned for the 10K budget. 

I agree with the authors that 1K budget can be more interesting, as 10K might feel saturated, but that's a different benchmark. I would suggest to name it something like **PMO-1K**, and then properly tune the hyperparameters of the baselines. I understand it's hard to do this in the review discussion period.

** Details of the optimization algorithm**
It took me a few days to understand that the sentence "At each iteration t, we generate a set of candidates" in Section 4.3 does not mean that the candidates are generated without the LLM. As seen in the Appendix, the authors actually used a manually designed genetic algorithm for generating the candidates, and the LLM is only used for scoring them. This is a critical component of the algorithm and has to be presented well in the main part of the paper. 

**Three other papers that could be cited and discussed:**
1. Optformer [1] is the earliest transformer to the best of my knowledge that used in-context learning for an optimization task. It did not use an initialization from a large pretrained model, and the data used there is not synthetic. Still, the concept is very close.
2. Another recent approach that produced good scores on PMO is from the Chemlactica/Chemma models [2]. It has the genetic algorithm idea, very similar to the one described in the Appendix A.3. Chemlactica's scores on PMO are still a bit unfair, as it uses a lot more molecules in the pretraining phase (way beyond ZINC250k).
3. MOLLEO [3] is another evolutionary algorithm that wraps an LLM. It has a few evaluations on 

A minor aspect that could be considered in the future iterations: use more realistic oracles, like molecular docking. Check [2] and [4] for new benchmarks.

[1] Chen, Yutian, et al. "Towards learning universal hyperparameter optimizers with transformers." Advances in Neural Information Processing Systems 35 (2022): 32053-32068.
[2] Guevorguian, Philipp, et al. "Small Molecule Optimization with Large Language Models." arXiv preprint arXiv:2407.18897 (2024).
[3] Wang, Haorui, et al. "Efficient evolutionary search over chemical space with large language models." arXiv preprint arXiv:2406.16976 (2024).
[4] Guo, Jeff, and Philippe Schwaller. "Saturn: Sample-efficient Generative Molecular Design using Memory Manipulation." arXiv preprint arXiv:2405.17066 (2024).

---

confidence: 4
contribution: 4
initial_rating: 6
presentation: 3
questions: See above.
soundness: 3
strengths: 1. The paper studies an important task of adapting LLMs for molecular optimization tasks, which has not been studied extensively. 

2. The paper presents a novel approach by integrating LLMs with specialized layers to address black-box optimization problems in the molecular domain.

3. The model achieves strong performance on the challenging PMO benchmark.
summary: This paper introduces LICO, a versatile model that enhances LLMs for black-box optimization, specifically in the molecular domain. LICO overcomes limitations related to domain-specific data scarcity and complex problem expression. It is trained to perform in-context predictions across diverse functions and, post-training, efficiently generalizes to new molecule properties through simple prompting. LICO achieves state-of-the-art PMO molecular optimization benchmark results, demonstrating its efficacy in complex scientific applications.
weaknesses: 1. While this paper demonstrates the strong performance of LLMs, the analysis of their specific benefits remains limited. It would be valuable to understand which particular characteristics of LLMs contribute to the success of this molecular optimization task. For instance, how do different LLM architectures or configurations impact performance? Would domain-adaptive training on chemistry corpora further enhance results? Expanding on these points with additional explanation would strengthen the understanding of LLMs' effectiveness in this context.

2. The study offers a limited exploration of prompt formats. Further investigation into how different prompt structures might influence model performance would be beneficial (e.g. Prompts that include more domain-specific chemistry terminology/Prompts that frame the task in different ways (e.g. as a prediction task vs. an optimization task/Testing different ways of structuring the input-output pairs within the prompt).

3. It would be better to discuss several recent works for using LLMs for molecule optimization: a) DrugAssist: A Large Language Model for Molecule Optimization; b) Domain-Agnostic Molecular Generation with Self-feedback; c) A Sober Look at LLMs for Material Discovery: Are They Actually Good for Bayesian Optimization Over Molecules?

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: 1. Can the authors argue why the additional input embedding layers are necessary here? considering that the LLM always comes with an existing embedding layers.

2. How the embedding and prediction layers are integrated into the existing LLM backbone?

3. Maybe I missed this, but what language representation is used in LICO?

4. What's the rationale behind using Tanimoto kernels for GPR synthetic data generation? Have the authors tried other types of kernels, and how do they perform?
soundness: 3
strengths: -The overall approach shows good efficacy, as shown in the benchmark scores. The combo of training data and modeling recipe is interesting and novel for surrogate modeling, as far as I know (this needs cross-confirmation).

-The scaling law analysis is interesting, indicating the power of scaling up the model size for better molecule optimization outcome.

-The ablation study and result analysis is helpful: the analysis of surrogate modeling accuracy, vs. the GPR baseline, confirms the efficacy of proposed LLM surrogate modeling approach. The discussion of the limitation of PMO benchmark numbers are also helpful and shows scientific rigor.
summary: This work proposes a semi-synthetic training approach for LLM-based surrogate modeling, with a specific focus on molecular optimization. By integrating a pretrained language model with embedding and prediction layers and training on both "intrinsic" and synthetic data, it shows promises of outperforming gold-standard Gaussian process regressors. As a result, the molecular optimization algorithm coupled with this LLM-based surrogate shows better performances than presented baselines, ranging from RL algorithms to GFN etc. The authors also presented analysis on different model sizes and training approach with varying data mixture.
weaknesses: -The authors selectively show the numbers with a different sampling budget (1k instead of 10k in the original PMO setting) with a reason. Can they also present the numbers with different sampling budget in the supplementary information? That will confirm the generalization of the proposed approach.

-The ablation and baseline should be more comprehensive: there are several concurrent works for LLM for molecular optimization[1,2], the authors should also add them as a baseline, if applicable, and thereafter discuss the efficacy of the proposed methods. For example, the MolLEO framework [1] (https://github.com/zoom-wang112358/MOLLEO) claims that they achieve superior performances than baselines on PMO as well, how does it compare with LICO? 

-Two more straightforward baselines I can come up with are: (1) drop the input embedding layers, simply extract the text embedding from prompts and train an MLP layer for the surrogate. (2) drop both the embedding and prediction layers, use the pretrained model to do in context learning only. This is similar to the LLAMBO work [3] that is cited in the paper. The authors should justify why they think the proposed approach is the most promising here.

-The description of the experimental details is a bit lacking: e.g. how the embedding and prediction layers are integrated into the existing LLM backbone? Please also provide code and pretrained models so that the reviewers can reproduce the results.

-The language models tested in this work, such as llama2 and qwen1.5, are slightly outdated. The authors should also add numbers on llama3/3.1, Qwen2 to further confirm their conclusions. 

-The related works section on LLM for molecular optimization is missing.

[1] Efficient Evolutionary Search Over Chemical Space with Large Language Models, arXiv:2406.16976 . 
[2] ChatGPT-powered Conversational Drug Editing Using Retrieval and Domain Feedback, ICLR 2024.
[3] https://github.com/tennisonliu/LLAMBO; Large Language Models to Enhance Bayesian Optimization, ICLR 2024.

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: - How do you obtain the uncertainties do you directly use the probabilities returned by the model? Are those probabilities well-calibrated? 
- The ordering of the examples seems important - what is the impact and how is this taken care of? 
- The approach is shown for a causal LM. But it seems that a masked approach (similar to https://www.nature.com/articles/s42256-023-00639-z) might be more effective in learning from the entire sequence
soundness: 3
strengths: - The authors use an established benchmark and perform competitive performance on this benchmark 
- Bayesian optimization is one of the most practically useful applications of machine learning in chemistry 
- The paper is well-written and easy to follow 
- The method is novel (but it is based on combining multiple existing techniques) 
- There are useful ablations (e.g., training with various amounts of synthetic data)
summary: The authors report an approach to using LLMs with additional embedding layers (similar to FPT) and text-encoding and semi-synthetic training (similar to ExPT) for molecular optimization. They report good performance on the PMO benchmark.
weaknesses: - In some places, the paper seems to indicate that ICL for Bayesian Opt has not been done in chemistry. This, however, is not the case as the following two reports show: 
    - https://arxiv.org/abs/2304.05341
    - https://www.researchgate.net/profile/Christoph-Voelker-4/publication/377722231_LLMs_can_Design_Sustainable_Concrete_-a_Systematic_Benchmark_re-submitted_version/links/65b408e934bbff5ba7c85ad8/LLMs-can-Design-Sustainable-Concrete-a-Systematic-Benchmark-re-submitted-version.pdf
- A bit related is the use of LLM-derived embeddings for Bayesian Opt in chemistry. This, for example, has been reported in https://openreview.net/forum?id=A1RVn1m3J3

Meta-review: The paper introduces LICO, a general-purpose model that extends arbitrary base Large Language Models (LLMs) for black-box optimization, with a particular focus on the molecular domain. The authors equip the language model with separate embedding and prediction layers, training it to perform in-context predictions on a diverse set of functions. LICO is shown to perform competitively on the PMO benchmark. The paper claims that LICO can generalize to unseen molecule properties via in-context prompting, leveraging the pattern-matching capabilities of pretrained LLMs.

Strengths:
* Novelty/Usefulness: The paper presents a novel approach by integrating LLMs with specialized layers for black-box optimization in molecular domains
* Detailed Experiments and Analysis: The authors provide extensive experiments and ablation studies, demonstrating the effectiveness of LICO on the PMO benchmark.
* Promising Scaling Laws: The scaling law analysis suggests the method should continue to improve as the underlying model grows.

Weaknesses:
* **Unusual Benchmarking**. The experiments focus (and did so exclusively before the rebuttal) on a non-standard use of the PMO benchmark, which unexplicably excluded two datasets and used a much-smaller-than-usual sampling budget (1K calls instead of 10K). Only after multiple reviewers raised concerns about the fairness of comparisons (most other methods have parameters tailored to the 10K setting) did the authors include the usual 10K budget results, where their method’s advantage is much less clear or completely disappears in some datasets.
* **Reproducibility**: The description of experimental details is somewhat lacking, making it difficult to reproduce the results.
* **Few Explaining Insights**: The paper provides little in the way of explanation for what aspects (architecture, pretraining, prompting) of the LLMs contribute to the success of this molecular optimization task. 
*  **Missing Baselines**: The paper does not adequately compare LICO with recent methods, limiting the understanding of its relative performance. Some of these were adding to the related work section during the rebuttal phase, but were not included as baselines in the experiments.

Overall, despite the potentially promising method proposed in this paper, there were various issues around benchmarking fairness, comparison, and selective result presentation that unfortunately cast a shadow over its contribution. Additionally, it has been brought to our attention that this paper had already been called out for non-standard use of the PMO benchmark during the NeurIPS 2024 rebuttal phase, where it was ultimately rejected. The same issues were brought up there: excluding two of the 23 tasks, and using a much more limited number of oracle calls than standard practice. After the reviewers raised those issues during that discussion phase, the authors included the missing datasets in the comparison and pledged to disclose the decision to focus on a smaller-than-usual oracle budget in the revised version of the paper. Unfortunately, they did not: in the version they originally submitted here to ICLR, which had a deadline more than a month after the NeurIPS rebuttal phase, the authors again left out those two tasks, and doubled down on the unusual 1K calls budget without fully disclosing its atypicality. The issue came up again in one of the reviews and was addressed anew in the rebuttal.

In our deliberation with SACs, we decided to give the authors the benefit of the doubt here. Overall, the decision to accept/reject this paper was very difficult due to the above reasons. In the end, we recommend acceptance mostly because of the potential interest and impact that this paper will have in the community, which given the novelty and results—even if partially clouded in uncertainty— is likely to be moderate to strong.

If the paper is accepted, the authors need to make sure that the revised results and the accompanying discussion of the oracle budget are indeed included in the camera-ready version. As a general advice for the authors: **Modifying evaluation conditions for standardized benchmarks should be carefully and transparently justified a priori, always**.

Decision: Accept (Poster)