Many crucial scientific problems involve designing novel molecules with desired properties, which can be formulated as a black-box optimization problem over the discrete chemical space. In practice, multiple conflicting objectives and costly evaluations (e.g., wet-lab experiments) make the diversity of candidates paramount. Computational methods have achieved initial success but still struggle with considering diversity in both objective and search space. To fill this gap, we propose a multi-objective Bayesian optimization (MOBO) algorithm leveraging the hypernetwork-based GFlowNets (HN-GFN) as an acquisition function optimizer, with the purpose of sampling a diverse batch of candidate molecular graphs from an approximate Pareto front. Using a single preference-conditioned hypernetwork, HN-GFN learns to explore various trade-offs between objectives. We further propose a hindsight-like off-policy strategy to share high-performing molecules among different preferences in order to speed up learning for HN-GFN. We empirically illustrate that HN-GFN has adequate capacity to generalize over preferences. Moreover, experiments in various real-world MOBO settings demonstrate that our framework predominantly outperforms existing methods in terms of candidate quality and sample efficiency. The code is available at https://github.com/violet-sto/HN-GFN.
Cyclic peptides are attractive therapeutic modalities because their closed-ring topology can improve stability and target specificity. However, de novo cyclic peptide design remains challenging for diffusion generators, as macrocyclization requires satisfying sparse, non-smooth, and compositional geometric constraints. Existing constraint-conditioned methods largely rely on inference-time guidance, which can steer samples toward desired closures but does not directly change the learned generative distribution. We propose GeoCycler, a reward-weighted diffusion alignment framework for training conditional latent diffusion models toward macrocyclization feasibility. GeoCycler introduces a type-gated stair reward that activates distance-based shaping only when prerequisite residue or linker types are satisfied, providing dense geometric feedback while avoiding misleading signals from chemically incompatible anchors. Together with positive-only reward weighting and replay-based stabilization, GeoCycler aligns a single generator across multiple cyclization topologies. On the LNR benchmark, GeoCycler improves pass@5 closure success over strong guidance-based baselines across stapled, head-to-tail, disulfide, and bicyclic settings. In particular, it improves head-to-tail success by 20.8 percentage points over CP-Composer while maintaining comparable amino-acid and backbone-dihedral statistics. These results suggest that training-time alignment to sparse geometric constraints is a promising alternative to relying solely on post hoc sampling-time correction for cyclic peptide generation.
Designing molecules with desirable physiochemical properties and functionalities is a long-standing challenge in chemistry, material science, and drug discovery. Recently, machine learning-based generative models have emerged as promising approaches for \emph{de novo} molecule design. However, further refinement of methodology is highly desired as most existing methods lack unified modeling of 2D topology and 3D geometry information and fail to effectively learn the structure-property relationship for molecule design. Here we present MolCode, a roto-translation equivariant generative framework for \underline{Mol}ecular graph-structure \underline{Co-de}sign. In MolCode, 3D geometric information empowers the molecular 2D graph generation, which in turn helps guide the prediction of molecular 3D structure. Extensive experimental results show that MolCode outperforms previous methods on a series of challenging tasks including \emph{de novo} molecule design, targeted molecule discovery, and structure-based drug design. Particularly, MolCode not only consistently generates valid (99.95$\%$ Validity) and diverse (98.75$\%$ Uniqueness) molecular graphs/structures with desirable properties, but also generate drug-like molecules with high affinity to target proteins (61.8$\%$ high-affinity ratio), which demonstrates MolCode's potential applications in material design and drug discovery. Our extensive investigation reveals that the 2D topology and 3D geometry contain intrinsically complementary information in molecule design, and provide new insights into machine learning-based molecule representation and generation.
Reliable molecular property prediction is essential for various scientific endeavors and industrial applications, such as drug discovery. However, the data scarcity, combined with the highly non-linear causal relationships between physicochemical and biological properties and conventional molecular featurization schemes, complicates the development of robust molecular machine learning models. Self-supervised learning (SSL) has emerged as a popular solution, utilizing large-scale, unannotated molecular data to learn a foundational representation of chemical space that might be advantageous for downstream tasks. Yet, existing molecular SSL methods largely overlook chemical knowledge, including molecular structure similarity, scaffold composition, and the context-dependent aspects of molecular properties when operating over the chemical space. They also struggle to learn the subtle variations in structure-activity relationship. This paper introduces a novel pre-training framework that learns robust and generalizable chemical knowledge. It leverages the structural hierarchy within the molecule, embeds them through distinct pre-training tasks across channels, and aggregates channel information in a task-specific manner during fine-tuning. Our approach demonstrates competitive performance across various molecular property benchmarks and offers strong advantages in particularly challenging yet ubiquitous scenarios like activity cliffs.
Directed evolution is a versatile technique in protein engineering that mimics the process of natural selection by iteratively alternating between mutagenesis and screening in order to search for sequences that optimize a given property of interest, such as catalytic activity and binding affinity to a specified target. However, the space of possible proteins is too large to search exhaustively in the laboratory, and functional proteins are scarce in the vast sequence space. Machine learning (ML) approaches can accelerate directed evolution by learning to map protein sequences to functions without building a detailed model of the underlying physics, chemistry and biological pathways. Despite the great potentials held by these ML methods, they encounter severe challenges in identifying the most suitable sequences for a targeted function. These failures can be attributed to the common practice of adopting a high-dimensional feature representation for protein sequences and inefficient search methods. To address these issues, we propose an efficient, experimental design-oriented closed-loop optimization framework for protein directed evolution, termed ODBO, which employs a combination of novel low-dimensional protein encoding strategy and Bayesian optimization enhanced with search space prescreening via outlier detection. We further design an initial sample selection strategy to minimize the number of experimental samples for training ML models. We conduct and report four protein directed evolution experiments that substantiate the capability of the proposed framework for finding of the variants with properties of interest. We expect the ODBO framework to greatly reduce the experimental cost and time cost of directed evolution, and can be further generalized as a powerful tool for adaptive experimental design in a broader context.
Significant interests have recently risen in leveraging sequence-based large language models (LLMs) for drug design. However, most current applications of LLMs in drug discovery lack the ability to comprehend three-dimensional (3D) structures, thereby limiting their effectiveness in tasks that explicitly involve molecular conformations. In this study, we introduced Token-Mol, a token-only 3D drug design model. This model encodes all molecular information, including 2D and 3D structures, as well as molecular property data, into tokens, which transforms classification and regression tasks in drug discovery into probabilistic prediction problems, thereby enabling learning through a unified paradigm. Token-Mol is built on the transformer decoder architecture and trained using random causal masking techniques. Additionally, we proposed the Gaussian cross-entropy (GCE) loss function to overcome the challenges in regression tasks, significantly enhancing the capacity of LLMs to learn continuous numerical values. Through a combination of fine-tuning and reinforcement learning (RL), Token-Mol achieves performance comparable to or surpassing existing task-specific methods across various downstream tasks, including pocket-based molecular generation, conformation generation, and molecular property prediction. Compared to existing molecular pre-trained models, Token-Mol exhibits superior proficiency in handling a wider range of downstream tasks essential for drug design. Notably, our approach improves regression task accuracy by approximately 30% compared to similar token-only methods. Token-Mol overcomes the precision limitations of token-only models and has the potential to integrate seamlessly with general models such as ChatGPT, paving the way for the development of a universal artificial intelligence drug design model that facilitates rapid and high-quality drug design by experts.
Proteins govern most biological functions essential for life, but achieving controllable protein discovery and optimization remains challenging. Recently, machine learning-assisted protein editing (MLPE) has shown promise in accelerating optimization cycles and reducing experimental workloads. However, current methods struggle with the vast combinatorial space of potential protein edits and cannot explicitly conduct protein editing using biotext instructions, limiting their interactivity with human feedback. To fill these gaps, we propose a novel method called ProtET for efficient CLIP-informed protein editing through multi-modality learning. Our approach comprises two stages: in the pretraining stage, contrastive learning aligns protein-biotext representations encoded by two large language models (LLMs), respectively. Subsequently, during the protein editing stage, the fused features from editing instruction texts and original protein sequences serve as the final editing condition for generating target protein sequences. Comprehensive experiments demonstrated the superiority of ProtET in editing proteins to enhance human-expected functionality across multiple attribute domains, including enzyme catalytic activity, protein stability and antibody specific binding ability. And ProtET improves the state-of-the-art results by a large margin, leading to significant stability improvements of 16.67% and 16.90%. This capability positions ProtET to advance real-world artificial protein editing, potentially addressing unmet academic, industrial, and clinical needs.
In the realm of drug discovery, DNA-encoded library (DEL) screening technology has emerged as an efficient method for identifying high-affinity compounds. However, DEL screening faces a significant challenge: noise arising from nonspecific interactions within complex biological systems. Neural networks trained on DEL libraries have been employed to extract compound features, aiming to denoise the data and uncover potential binders to the desired therapeutic target. Nevertheless, the inherent structure of DEL, constrained by the limited diversity of building blocks, impacts the performance of compound encoders. Moreover, existing methods only capture compound features at a single level, further limiting the effectiveness of the denoising strategy. To mitigate these issues, we propose a Multimodal Pretraining DEL-Fusion model (MPDF) that enhances encoder capabilities through pretraining and integrates compound features across various scales. We develop pretraining tasks applying contrastive objectives between different compound representations and their text descriptions, enhancing the compound encoders' ability to acquire generic features. Furthermore, we propose a novel DEL-fusion framework that amalgamates compound information at the atomic, submolecular, and molecular levels, as captured by various compound encoders. The synergy of these innovations equips MPDF with enriched, multi-scale features, enabling comprehensive downstream denoising. Evaluated on three DEL datasets, MPDF demonstrates superior performance in data processing and analysis for validation tasks. Notably, MPDF offers novel insights into identifying high-affinity molecules, paving the way for improved DEL utility in drug discovery.
Molecular de novo design is a critical yet challenging task in scientific fields, aiming to design novel molecular structures with desired property profiles. Significant progress has been made by resorting to generative models for graphs. However, limited attention is paid to hierarchical generative models, which can exploit the inherent hierarchical structure (with rich semantic information) of the molecular graphs and generate complex molecules of larger size that we shall demonstrate to be difficult for most existing models. The primary challenge to hierarchical generation is the non-differentiable issue caused by the generation of intermediate discrete coarsened graph structures. To sidestep this issue, we cast the tricky hierarchical generation problem over discrete spaces as the reverse process of hierarchical representation learning and propose MolHF, a new hierarchical flow-based model that generates molecular graphs in a coarse-to-fine manner. Specifically, MolHF first generates bonds through a multi-scale architecture, then generates atoms based on the coarsened graph structure at each scale. We demonstrate that MolHF achieves state-of-the-art performance in random generation and property optimization, implying its high capacity to model data distribution. Furthermore, MolHF is the first flow-based model that can be applied to model larger molecules (polymer) with more than 100 heavy atoms. The code and models are available at https://github.com/violet-sto/MolHF.
Protein is linked to almost every life process. Therefore, analyzing the biological structure and property of protein sequences is critical to the exploration of life, as well as disease detection and drug discovery. Traditional protein analysis methods tend to be labor-intensive and time-consuming. The emergence of deep learning models makes modeling data patterns in large quantities of data possible. Interdisciplinary researchers have begun to leverage deep learning methods to model large biological datasets, e.g. using long short-term memory and convolutional neural network for protein sequence classification. After millions of years of evolution, evolutionary information is encoded in protein sequences. Inspired by the similarity between natural language and protein sequences, we use large-scale language models to model evolutionary-scale protein sequences, encoding protein biology information in representation. Significant improvements are observed in both token-level and sequence-level tasks, demonstrating that our large-scale model can accurately capture evolution information from pretraining on evolutionary-scale individual sequences. Our code and model are available at https://github.com/THUDM/ProteinLM.
The idea of using deep-learning-based molecular generation to accelerate discovery of drug candidates has attracted extraordinary attention, and many deep generative models have been developed for automated drug design, termed molecular generation. In general, molecular generation encompasses two main strategies: de novo design, which generates novel molecular structures from scratch, and lead optimization, which refines existing molecules into drug candidates. Among them, lead optimization plays an important role in real-world drug design. For example, it can enable the development of me-better drugs that are chemically distinct yet more effective than the original drugs. It can also facilitate fragment-based drug design, transforming virtual-screened small ligands with low affinity into first-in-class medicines. Despite its importance, automated lead optimization remains underexplored compared to the well-established de novo generative models, due to its reliance on complex biological and chemical knowledge. To bridge this gap, we conduct a systematic review of traditional computational methods for lead optimization, organizing these strategies into four principal sub-tasks with defined inputs and outputs. This review delves into the basic concepts, goals, conventional CADD techniques, and recent advancements in AIDD. Additionally, we introduce a unified perspective based on constrained subgraph generation to harmonize the methodologies of de novo design and lead optimization. Through this lens, de novo design can incorporate strategies from lead optimization to address the challenge of generating hard-to-synthesize molecules; inversely, lead optimization can benefit from the innovations in de novo design by approaching it as a task of generating molecules conditioned on certain substructures.
The design of novel protein sequences with targeted functionalities underpins a central theme in protein engineering, impacting diverse fields such as drug discovery and enzymatic engineering. However, navigating this vast combinatorial search space remains a severe challenge due to time and financial constraints. This scenario is rapidly evolving as the transformative advancements in AI, particularly in the realm of generative models and optimization algorithms, have been propelling the protein design field towards an unprecedented revolution. In this survey, we systematically review recent advances in generative AI for controllable protein sequence design. To set the stage, we first outline the foundational tasks in protein sequence design in terms of the constraints involved and present key generative models and optimization algorithms. We then offer in-depth reviews of each design task and discuss the pertinent applications. Finally, we identify the unresolved challenges and highlight research opportunities that merit deeper exploration.
Most earlier 3D structure-based molecular generation approaches follow an atom-wise paradigm, incrementally adding atoms to a partially built molecular fragment within protein pockets. These methods, while effective in designing tightly bound ligands, often overlook other essential properties such as synthesizability. The fragment-wise generation paradigm offers a promising solution. However, a common challenge across both atom-wise and fragment-wise methods lies in their limited ability to co-design plausible chemical and geometrical structures, resulting in distorted conformations. In response to this challenge, we introduce the Deep Geometry Handling protocol, a more abstract design that extends the design focus beyond the model architecture. Through a comprehensive review of existing geometry-related models and their protocols, we propose a novel hybrid strategy, culminating in the development of FragGen - a geometry-reliable, fragment-wise molecular generation method. FragGen marks a significant leap forward in the quality of generated geometry and the synthesis accessibility of molecules. The efficacy of FragGen is further validated by its successful application in designing type II kinase inhibitors at the nanomolar level.
The design of protein sequences with desired functionalities is a fundamental task in protein engineering. Deep generative methods, such as autoregressive models and diffusion models, have greatly accelerated the discovery of novel protein sequences. However, these methods mainly focus on local or shallow residual semantics and suffer from low inference efficiency, large modeling space and high training cost. To address these challenges, we introduce ProtFlow, a fast flow matching-based protein sequence design framework that operates on embeddings derived from semantically meaningful latent space of protein language models. By compressing and smoothing the latent space, ProtFlow enhances performance while training on limited computational resources. Leveraging reflow techniques, ProtFlow enables high-quality single-step sequence generation. Additionally, we develop a joint design pipeline for the design scene of multichain proteins. We evaluate ProtFlow across diverse protein design tasks, including general peptides and long-chain proteins, antimicrobial peptides, and antibodies. Experimental results demonstrate that ProtFlow outperforms task-specific methods in these applications, underscoring its potential and broad applicability in computational protein sequence design and analysis.
Structural assessment of biomolecular complexes is vital for translating molecular models into functional insights, shaping our understanding of biology and aiding drug discovery. However, current structure-based scoring functions often lack generalizability across diverse biomolecular systems. We present BioScore, a foundational scoring function that addresses key challenges -- data sparsity, cross-system representation, and task compatibility -- through a dual-scale geometric graph learning framework with tailored modules for structure assessment and affinity prediction. BioScore supports a wide range of tasks, including affinity prediction, conformation ranking, and structure-based virtual screening. Evaluated on 16 benchmarks spanning proteins, nucleic acids, small molecules, and carbohydrates, BioScore consistently outperforms or matches 70 traditional and deep learning methods. Our newly proposed PPI Benchmark further enables comprehensive evaluation of protein-protein complex scoring. BioScore demonstrates broad applicability: (1) pretraining on mixed-structure data boosts protein-protein affinity prediction by up to 40% and antigen-antibody binding correlation by over 90%; (2) cross-system generalizability enables zero- and few-shot prediction with up to 71% correlation gain; and (3) its unified representation captures chemically challenging systems such as cyclic peptides, improving affinity prediction by over 60%. BioScore establishes a robust and generalizable framework for structural assessment across complex biomolecular landscapes.
DNA-encoded library (DEL) screening has revolutionized the detection of protein-ligand interactions through read counts, enabling rapid exploration of vast chemical spaces. However, noise in read counts, stemming from nonspecific interactions, can mislead this exploration process. We present DEL-Ranking, a novel distribution-correction denoising framework that addresses these challenges. Our approach introduces two key innovations: (1) a novel ranking loss that rectifies relative magnitude relationships between read counts, enabling the learning of causal features determining activity levels, and (2) an iterative algorithm employing self-training and consistency loss to establish model coherence between activity label and read count predictions. Furthermore, we contribute three new DEL screening datasets, the first to comprehensively include multi-dimensional molecular representations, protein-ligand enrichment values, and their activity labels. These datasets mitigate data scarcity issues in AI-driven DEL screening research. Rigorous evaluation on diverse DEL datasets demonstrates DEL-Ranking's superior performance across multiple correlation metrics, with significant improvements in binding affinity prediction accuracy. Our model exhibits zero-shot generalization ability across different protein targets and successfully identifies potential motifs determining compound binding affinity. This work advances DEL screening analysis and provides valuable resources for future research in this area.
Recombinant adeno-associated virus (rAAV) vectors have revolutionized gene therapy, but their broad tropism and suboptimal transduction efficiency limit their clinical applications. To overcome these limitations, researchers have focused on designing and screening capsid libraries to identify improved vectors. However, the large sequence space and limited resources present challenges in identifying viable capsid variants. In this study, we propose an end-to-end diffusion model to generate capsid sequences with enhanced viability. Using publicly available AAV2 data, we generated 38,000 diverse AAV2 viral protein (VP) sequences, and evaluated 8,000 for viral selection. The results attested the superiority of our model compared to traditional methods. Additionally, in the absence of AAV9 capsid data, apart from one wild-type sequence, we used the same model to directly generate a number of viable sequences with up to 9 mutations. we transferred the remaining 30,000 samples to the AAV9 domain. Furthermore, we conducted mutagenesis on AAV9 VP hypervariable regions VI and V, contributing to the continuous improvement of the AAV9 VP sequence. This research represents a significant advancement in the design and functional validation of rAAV vectors, offering innovative solutions to enhance specificity and transduction efficiency in gene therapy applications.
Retrosynthesis prediction is one of the fundamental challenges in organic synthesis. The task is to predict the reactants given a core product. With the advancement of machine learning, computer-aided synthesis planning has gained increasing interest. Numerous methods were proposed to solve this problem with different levels of dependency on additional chemical knowledge. In this paper, we propose Retroformer, a novel Transformer-based architecture for retrosynthesis prediction without relying on any cheminformatics tools for molecule editing. Via the proposed local attention head, the model can jointly encode the molecular sequence and graph, and efficiently exchange information between the local reactive region and the global reaction context. Retroformer reaches the new state-of-the-art accuracy for the end-to-end template-free retrosynthesis, and improves over many strong baselines on better molecule and reaction validity. In addition, its generative procedure is highly interpretable and controllable. Overall, Retroformer pushes the limits of the reaction reasoning ability of deep generative models.
Drug resistance is a major threat to the global health and a significant concern throughout the clinical treatment of diseases and drug development. The mutation in proteins that is related to drug binding is a common cause for adaptive drug resistance. Therefore, quantitative estimations of how mutations would affect the interaction between a drug and the target protein would be of vital significance for the drug development and the clinical practice. Computational methods that rely on molecular dynamics simulations, Rosetta protocols, as well as machine learning methods have been proven to be capable of predicting ligand affinity changes upon protein mutation. However, the severely limited sample size and heavy noise induced overfitting and generalization issues have impeded wide adoption of machine learning for studying drug resistance. In this paper, we propose a robust machine learning method, termed SPLDExtraTrees, which can accurately predict ligand binding affinity changes upon protein mutation and identify resistance-causing mutations. Especially, the proposed method ranks training data following a specific scheme that starts with easy-to-learn samples and gradually incorporates harder and diverse samples into the training, and then iterates between sample weight recalculations and model updates. In addition, we calculate additional physics-based structural features to provide the machine learning model with the valuable domain knowledge on proteins for this data-limited predictive tasks. The experiments substantiate the capability of the proposed method for predicting kinase inhibitor resistance under three scenarios, and achieves predictive accuracy comparable to that of molecular dynamics and Rosetta methods with much less computational costs.
The notion of word embedding plays a fundamental role in natural language processing (NLP). However, pre-training word embedding for very large-scale vocabulary is computationally challenging for most existing methods. In this work, we show that with merely a small fraction of contexts (Q-contexts)which are typical in the whole corpus (and their mutual information with words), one can construct high-quality word embedding with negligible errors. Mutual information between contexts and words can be encoded canonically as a sampling state, thus, Q-contexts can be fast constructed. Furthermore, we present an efficient and effective WEQ method, which is capable of extracting word embedding directly from these typical contexts. In practical scenarios, our algorithm runs 11$\sim$13 times faster than well-established methods. By comparing with well-known methods such as matrix factorization, word2vec, GloVeand fasttext, we demonstrate that our method achieves comparable performance on a variety of downstream NLP tasks, and in the meanwhile maintains run-time and resource advantages over all these baselines.
Guangyong Chen, Pengfei Chen, Chang-Yu Hsieh et al.
We introduce a new molecular dataset, named Alchemy, for developing machine learning models useful in chemistry and material science. As of June 20th 2019, the dataset comprises of 12 quantum mechanical properties of 119,487 organic molecules with up to 14 heavy atoms, sampled from the GDB MedChem database. The Alchemy dataset expands the volume and diversity of existing molecular datasets. Our extensive benchmarks of the state-of-the-art graph neural network models on Alchemy clearly manifest the usefulness of new data in validating and developing machine learning models for chemistry and material science. We further launch a contest to attract attentions from researchers in the related fields. More details can be found on the contest website \footnote{https://alchemy.tencent.com}. At the time of benchamrking experiment, we have generated 119,487 molecules in our Alchemy dataset. More molecular samples are generated since then. Hence, we provide a list of molecules used in the reported benchmarks.
Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned for the node feature updating. However, existing propagation schemes are far from being optimal since they do not fully utilize the relational information between nodes. We propose the information maximizing graph neural networks (IGNN), which maximizes the mutual information between edge states and transform parameters. We reformulate the mutual information as a differentiable objective via a variational approach. We compare our model against several recent variants of GNNs and show that our model achieves the state-of-the-art performance on multiple tasks including quantum chemistry regression on QM9 dataset, generalization capability from QM9 to larger molecular graphs, and prediction of molecular bioactivities relevant for drug discovery. The IGNN model is based on an elegant and fundamental idea in information theory as explained in the main text, and it could be easily generalized beyond the contexts of molecular graphs considered in this work. To encourage more future work in this area, all datasets and codes used in this paper will be released for public access.
In this work, we propose a novel technique to boost training efficiency of a neural network. Our work is based on an excellent idea that whitening the inputs of neural networks can achieve a fast convergence speed. Given the well-known fact that independent components must be whitened, we introduce a novel Independent-Component (IC) layer before each weight layer, whose inputs would be made more independent. However, determining independent components is a computationally intensive task. To overcome this challenge, we propose to implement an IC layer by combining two popular techniques, Batch Normalization and Dropout, in a new manner that we can rigorously prove that Dropout can quadratically reduce the mutual information and linearly reduce the correlation between any pair of neurons with respect to the dropout layer parameter $p$. As demonstrated experimentally, the IC layer consistently outperforms the baseline approaches with more stable training process, faster convergence speed and better convergence limit on CIFAR10/100 and ILSVRC2012 datasets. The implementation of our IC layer makes us rethink the common practices in the design of neural networks. For example, we should not place Batch Normalization before ReLU since the non-negative responses of ReLU will make the weight layer updated in a suboptimal way, and we can achieve better performance by combining Batch Normalization and Dropout together as an IC layer.
Jonathan Allcock, Chang-Yu Hsieh, Iordanis Kerenidis et al.
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine learning today. In this paper we present quantum algorithms for training and evaluating feedforward neural networks based on the canonical classical feedforward and backpropagation algorithms. Our algorithms rely on an efficient quantum subroutine for approximating the inner products between vectors in a robust way, and on implicitly storing large intermediate values in quantum random access memory for fast retrieval at later stages. The running times of our algorithms can be quadratically faster in the size of the network than their standard classical counterparts since they depend linearly on the number of neurons in the network, as opposed to the number of connections between neurons as in the classical case. This makes our algorithms suited for large-scale, highly-connected networks where the number of edges in the network dominates the classical algorithmic running time. Furthermore, networks trained by our quantum algorithm may have an intrinsic resilience to overfitting, as the algorithm naturally mimics the effects of classical techniques such as drop-out used to regularize networks. Our algorithms can also be used as the basis for new quantum-inspired classical algorithms which have the same dependence on the network dimensions as their quantum counterparts, but with quadratic overhead in other parameters that makes them relatively impractical.