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A Multi-Modal Contrastive Diffusion Model for Therapeutic Peptide Generation Yongkang Wang1, Xuan Liu1, Feng Huang1, Zhankun Xiong1, Wen Zhang1,2 3† 1College of Informatics, Huazhong Agricultural University, Wuhan 430070, China 2Hubei Key Laboratory of Agricultural Bioinformatics, Huazhong Agricultural University, Wuhan 430070, China 3Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education, Wuhan 430070,China {wyky481, lx666, fhuang233, xiongzk }@webmail.hzau.edu.cn, zhangwen@mail.hzau.edu.cn Abstract Therapeutic peptides represent a unique class of pharmaceu- tical agents crucial for the treatment of human diseases. Re- cently, deep generative models have exhibited remarkable potential for generating therapeutic peptides, but they only utilize sequence or structure information alone, which hin- ders the performance in generation. In this study, we pro- pose a Multi-Modal Contrastive Diffusion model (MMCD), fusing both sequence and structure modalities in a diffusion framework to co-generate novel peptide sequences and struc- tures. Specifically, MMCD constructs the sequence-modal and structure-modal diffusion models, respectively, and de- vises a multi-modal contrastive learning strategy with inter- contrastive and intra-contrastive in each diffusion timestep, aiming to capture the consistency between two modalities and boost model performance. The inter-contrastive aligns se- quences and structures of peptides by maximizing the agree- ment of their embeddings, while the intra-contrastive differ- entiates therapeutic and non-therapeutic peptides by max- imizing the disagreement of their sequence/structure em- beddings simultaneously. The extensive experiments demon- strate that MMCD performs better than other state-of-the- art deep generative methods in generating therapeutic pep- tides across various metrics, including antimicrobial/anti- cancer score, diversity, and peptide-docking. Introduction Therapeutic peptides, such as antimicrobial and anticancer peptides, are a unique class of pharmaceutical agents that comprise short chains of amino acids, exhibiting significant potential in treating complex human diseases (Jakubczyk et al. 2020). Traditionally, therapeutic peptides are discov- ered through a comprehensive screening of sequence spaces using phage/yeast display technologies (Muttenthaler et al. 2021) or computational tools trained for scoring desired properties (Lee et al. 2017; Lee, Wong, and Ferguson 2018). However, the combinatorial space of possible peptides is vast and only a small solution satisfies therapeutic require- ments; thus, such screening methods based on brute force can be time-consuming and costly. These authors contributed equally. †Corresponding authors. Copyright © 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.In recent years, deep generative models (DGMs) have demonstrated success in generating images (Liu and Chilton 2022), texts (Iqbal and Qureshi 2022), proteins (Wu et al. 2021), and also gained popularity in peptides. DGMs ex- plored a more expansive chemical space that affords the creation of structurally novel peptides, by training neu- ral networks to approximate the underlying distribution of observed or known ones (Wan, Kontogiorgos, and Fuente 2022). For example, autoregression-based methods depicted peptide sequences as sentences composed of residue tokens, so that the problem can be solved by predicting residue ar- rangement via recurrent neural networks (RNN) (M ¨uller, Hiss, and Schneider 2018; Capecchi et al. 2021). Variational autoencoder (V AE)-based methods generated new peptide sequences by sampling from the latent space learned through an encoder-decoder architecture, with or without therapeu- tic properties as conditional constraints (Ghorbani et al. 2022; Szymczak et al. 2023b). Generative adversarial net- work (GAN)-based methods trained the generator and dis- criminator using known data, which compete against each other to generate new peptides (Tucs et al. 2020; Oort et al. 2021; Lin, Lin, and Lane 2022). Nowadays, diffusion mod- els (Yang et al. 2023) are prevalent in the generation of pro- tein sequences and structures, owing to their superior capa- bility in fitting distributions compared to prior techniques (Shi et al. 2023; Wu et al. 2022). Likewise, these advanced diffusion models can be extended to peptide generation and are expected to deliver favorable outcomes. Despite the commendable progress of efforts above, they focused on generating either sequences (i.e., residue ar- rangements) or structures (i.e., spatial coordinates of back- bone atoms), ignoring that models fusing information from both modalities may outperform their uni-modal counter- parts (Huang et al. 2021). However, how to effectively in- tegrate the multi-modal information and capture their con- sistency in peptide generation is a major challenge. Addi- tionally, compared with generation tasks for images, texts, and proteins that involve millions of labeled samples, public datasets for therapeutic peptides typically contain only thou- sands of sequence or structure profiles, induced by the high cost of in vitro screening. This limited amount of available data may result in overfitting (Webster et al. 2019), which confines generated outcomes within a restricted distribution, consequently compromising the model’s generalization abil-arXiv:2312.15665v2 [q-bio.QM] 4 Jan 2024ity. How to fully leverage existing peptide data, such as ther- apeutic and non-therapeutic peptides, to enhance the gener- ation performance could be regarded as another challenge. To address these challenges, we propose a Multi-Modal Contrastive Diffusion model for therapeutic peptide genera- tion, named MMCD . Specifically, we build a multi-modal framework that integrates sequence-modal and structure- modal diffusion models for co-generating residue arrange- ments and backbone coordinates of peptides. To ensure con- sistency between the two modalities during the generation process, we bring in an inter-modal contrastive learning (Inter-CL) strategy. Inter-CL aligns sequences and struc- tures, by maximizing the agreement between their embed- dings derived from the same peptides at each diffusion timestep. Meanwhile, to avoid the issue of inferior per- formance caused by limited therapeutic peptide data, we incorporate substantial known non-therapeutic peptides as data augmentations to devise an intra-modal CL (Intra- CL). Intra-CL differentiates therapeutic and non-therapeutic peptides by maximizing the disagreement of their se- quence/structure embeddings at each diffusion timestep, driving the model to precisely fit the distribution of thera- peutic peptides. Overall, the main contributions of this work are described as follows: • We propose a multi-modal diffusion model that inte- grates both sequence and structure information to co- generate residue arrangements and backbone coordinates of therapeutic peptides, whereas previous works focused only on a single modality. • We design the inter-intra CL strategy at each diffusion timestep, which aims to maximize the agreement be- tween sequence and structure embeddings for aligning multi-modal information, and maximize the disagree- ment between therapeutic and non-therapeutic peptides for boosting model generalization. • Extensive experiments conducted on peptide datasets demonstrate that MMCD surpasses the current state-of- the-art baselines in generating therapeutic peptides, par- ticularly in terms of antimicrobial/anticancer score, di- versity, and pathogen-docking. Related works Diffusion Model for Protein Generation Diffusion models (Song and Ermon 2019; Trippe et al. 2023) devote to learning the noise that adequately destroys the source data and iteratively remove noise from the prior dis- tribution to generate new samples, which have emerged as cutting-edge methods for numerous generation tasks, es- pecially in proteins (Wu et al. 2022; Cao et al. 2023). For example, Liu et al. (2023) proposed a textual condi- tionally guided diffusion model for sequence generation. Hoogeboom et al. (2022) introduced ProtDiff with an E(3) equivariant graph neural network to learn a diverse distri- bution over backbone coordinates of structures. Luo et al. (2022) considered both the position and orientation of anti- body residues, achieving an equivariant diffusion model for sequence-structure co-generation. Despite their success, thefusion of both sequence and structure modalities in diffu- sion models has not been comprehensively investigated, and their potential for peptide generation remains unexplored. To fill this gap, we implement a peptide-oriented diffu- sion model capable of sequence-structure co-generation and multi-modal data fusion. Contrastive Learning Being popular in self-supervised learning, contrastive learn- ing (CL) allows models to learn the knowledge behind data without explicit labels (Xia et al. 2022; Zhu et al. 2023). It aims to bring an anchor (i.e., data sample) closer to a posi- tive/similar instance and away from many negative/dissimi- lar instances, by optimizing their mutual information in the embedding space. Strategies to yield the positive and neg- ative pairs often dominate the model performance (Zhang et al. 2022). For example, Yuan et al. (2021) proposed a multi-modal CL to align text and image data, which encour- ages the agreement of corresponding text-image pairs (posi- tive) to be greater than those of all non-corresponding pairs (negative). Wu, Luu, and Dong (2022) designed a CL frame- work that makes full use of semantic relations among text samples via efficient positive and negative sampling strate- gies, to mitigate data sparsity for short text modeling. Zhang et al. (2023b) augmented the protein structures using differ- ent conformers, and maximized the agreement/disagreement between the learned embeddings of same/different proteins, aiming to learn more discriminative representations. How- ever, these CL strategies have yet to be extended to peptide- related studies. Therefore, we devise the novel CL strategy in peptide generation, which serves as an auxiliary objective to enforce sequence-structure alignment and boost model performance. Methodology In this section, we formulate the peptide co-generation prob- lem for sequence and structure. Subsequently, we elabo- rately enumerate the components of our method MMCD, including the diffusion model for peptide generation and the multi-modal contrastive learning strategy. The overview of MMCD is illustrated in Figure 1. Problem Formulation A peptide with Nresidues (amino acids) can be repre- sented as a sequence-structure tuple, denoted as X= (S, C).S= [si]N i=1stands for the sequence with si∈ {ACDEFGHIKLMNPQRSTV WY }as the type of thei-th residue, and C= [ci]N i=1stands for the structure withci∈R3∗4as Cartesian coordinates of the i-th residue (involving four backbone atoms N-C α-C-O). Our goal is to model the joint distribution of Xbased on the known pep- tide data, so that sequences (i.e., residue types) and struc- tures (i.e., residue coordinates) of new peptides can be co- generated by sampling the distribution. Diffusion Model for Peptide Generation The diffusion model defines the Markov chains of processes, in which latent variables are encoded by a forward diffu- sion process and decoded by a reverse generative processembedding embeddingInter -contrastive learning... ... Intra-contrastive learning Therapeutic Non-therapeuticNoise prior Peptide positive pairs nega tive pairs MLP MLP EGNNTransformer ST ...St-1StS0 ...q(St \| St-1) p(St-1 \| St ) CT ... Ct-1CtC0 ... q(Ct \| Ct-1)p(Ct-1 \| Ct ) ...QVQ RWQ D SDDAMWV... ...**** ***** ... ... ... St St Ct... ... ... ...Intra-contrastive learningSequences Structures Marginal distribution Gaussian noiseMulti -Modal CL Multi -Modal CLDenoisingAdd noise Denoising Add noise Ct Figure 1: Overview of the MMCD. MMCD consists of a diffusion model for the peptide sequence-structure co-generation and multi-modal contrastive learning (CL). The diffusion model involves a forward process ( q(·\|·)) for adding noise and a reverse process ( p(·\|·)) for denoising at each timestep t. The reverse process utilizes a transformer encoder (or EGNN) to extract embeddings from sequences S(or structures C), and a sequence (or structure)-based MLP to map embeddings to the marginal distribution (or Gaussian) noise. The multi-modal CL includes an Inter-CL and an Intra-CL, which aims to align sequence and structure embeddings, and differentiate therapeutic and non-therapeutic peptide embeddings. (Sohl-Dickstein et al. 2015). Let X0= (S0, C0)denotes the ground-truth peptide and Xt= (St, Ct)fort= 1, ..., T to be the latent variable at timestep t. The peptide gener- ation can be modeled as an evolving thermodynamic sys- tem, where the forward process q(Xt\|Xt−1)gradually in- jects small noise to the data X0until reaching a random noise distribution at timestep T, and the reverse process pθ(Xt−1\|Xt)with learnable parameters θlearns to denoise the latent variable Xttowards the data distribution (Luo et al. 2022). Diffusion for Peptide Sequence. Following Anand and Achim (2022), we treat residue types as categorical data and apply discrete diffusion to sequences, where each residue type is characterized using one-hot encoding with 20 types. For the forward process, we add noise to residue types using the transition matrices with the marginal distribution (Austin et al. 2021; Vignac et al. 2023) (see details in Appendix A). For the reverse process, the diffusion trajectory is parame- terized by the probability q(St−1\|St, S0)and a network ˆpθis defined to predict the probability of S0(Austin et al.2021), that is: pθ St−1\|St =Y 1≤i≤Nq(st−1 i\|St,ˆS0)·ˆpθ(ˆS0\|St)(1) where st idenotes the one-hot feature for the i-th residue in the sequence Sat timestep t, and ˆS0is the predicted proba- bility of S0. In this work, we design the ˆpθas follows: ˆpθ ˆS0\|St =Y 1≤i≤NSoftmax ˆs0 i\| Fs ht i (2) where ht iis the input feature of residue iwith the diffusion noise at time t(the initialization of ht iis provided in Ap- pendix A). Fsis a hybrid neural network to predict the noise of residue types from the marginal distribution, and then the noise would be removed to compute the probability of ˆs0 i. Softmax is applied over all residue types. Here, we imple- mentFswith a transformer encoder and an MLP. The for- mer learns contextual embeddings of residues from the se- quence, while the latter maps these embeddings to the noises of residue types. The learned sequence embedding (defined asS) involves downstream contrastive learning strategies.Diffusion for Peptide Structure. As the coordinates of atoms are continuous variables in the 3D space, the forward process can be defined by adding Gaussian noise to atom coordinates (Ho, Jain, and Abbeel 2020) (see details in Ap- pendix A). Following Trippe et al. (2023), the reverse pro- cess can be defined as: pθ(ct−1 i\|Ct) =N(ct−1 i\|µθ(Ct, t), βtI) (3) µθ Ct, t =1√ αt ct i−βt √ 1−αtϵθ Ct, t (4) where cirefers to coordinates of the i-th residue in the structure C;βis the noise rate, formally αt= 1−βt, αt=Qt τ=1(1−βτ); the network ϵθis used to gradually recover the structural data by predicting the Gaussian noise. In this work, we design the ϵθas follows: ϵθ(Ct, t) =Fc rt i, ht i (5) where rirepresents the coordinates of residue i,hiis the residue feature, and Fcis a hybrid neural network for pre- dicting Gaussian noises at timestep t. Similar to sequence diffusion, we implement Fcwith an equivariant graph neu- ral network (EGNN) (Satorras, Hoogeboom, and Welling 2021) and an MLP. The former learns spatial embeddings of residues from the structure (formalized as a 3D graph), while the latter maps these embeddings to Gaussian noises. The learned structure embedding (defined as C) also involves downstream contrastive learning strategies. Diffusion Objective. Following previous work (Anand and Achim 2022), we decompose the objective of the pep- tide diffusion process into sequence loss and structure loss. For the sequence loss Lt S, we aim to minimize the cross- entropy (CE) loss between the actual and predicted residue types at timestep t: Lt S=1 NX 1≤i≤NCE s0 i,ˆpθ(ˆs0 i\|St) (6) For the structure loss Lt C, the objective is to calculate the mean squared error (MSE) between the predicted noise ϵθ and standard Gaussian noise ϵat timestep t: Lt C=1 NX 1≤i≤N ϵi−ϵθ(Ct, t) 2(7) Multi-Modal Contrastive Learning Strategy When multiple modal data (e.g., sequence and structure) co- exist, it becomes imperative to capture their consistency to reduce the heterogeneous differences between modalities, allowing them to be better fused in generation tasks. Mutual information (MI) is a straightforward solution to measure the non-linear dependency (consistency) between variables (Liu et al. 2023); thus, maximizing MI between modalities can force them to align and share more crucial information. Along this line, we bring in contrastive learning (CL) to align sequences and structures by maximizing their MI in the embedding space. Specifically, we devise CL strategies for each diffusion timestep t, as follows:Inter-CL. For a peptide, we define its sequence as the an- chor, its structure as the positive instance, and the structures of other peptides in a mini-batch as the negative instances. Then, we maximize the MI of positive pair (anchor and posi- tive instance) while minimizing the MI of negative pairs (an- chor and negative instances), based on embeddings learned from the networks ˆpθandϵθ. Further, we establish a ’dual’ contrast where the structure acts as an anchor and sequences are instances. The objective is to minimize the following InfoNCE-based (Chen et al. 2020) loss function: Lt inter=−1 2" logE St i,Ct i PM j=1E St i,Ct j+ logE Ct i,St i PM j=1E Ct i,St j# (8) where Si/Ciis the sequence/structure embeddings of i-th peptide in the mini-batch, E(·,·)is the cosine similarity function with the temperature coefficient to measure the MI score between two variables, Mis the size of a mini-batch. In addition, the used diffusion model can only remem- ber confined generation patterns if therapeutic peptide data for training is limited, which may lead to inferior general- ization towards novel peptides. To alleviate this issue, we introduce contrastive learning to boost the generative capac- ity of networks ˆpθandϵθby enriching the supervised sig- nals. However, it is unwise to construct positive instances by performing data augmentations on therapeutic peptides, as even minor perturbations may lead to significant functional changes (Yadav, Kumar, and Singh 2022). Hence, our fo- cus lies on employing effective strategies for selecting neg- ative instances. In this regard, we collect non-therapeutic peptides from public databases to treat them as negative in- stances, and maximize the disagreement between embed- dings of therapeutic and non-therapeutic peptides. In detail, we devise an Intra-CL strategy for each diffusion timestep t, as follows: Intra-CL. In a mini-batch, we define the sequence of a therapeutic peptide ias the anchor, and the sequence of an- other therapeutic peptide jas the positive instance, while the sequences of non-therapeutic peptides kare regarded as neg- ative instances. Similar to Inter-CL, we then maximize/mini- mize the MI of positive/negative pairs. And we also establish a structure-oriented contrast by using structures of therapeu- tic and non-therapeutic peptides to construct the anchor, pos- itive, and negative instances. The objective is to minimize the following loss function (Zheng et al. 2021): Lt intra=−1 MMX j=1,j̸=i1yi=yj logE St i,St j PM k=11yi̸=ykE(St i,St k) + logE Ct i,Ct j PM k=11yi̸=ykE(Ct i,Ct k)! (9) where yirepresents the class of peptide i(i.e., therapeutic or non-therapeutic). 1yi=yjand1yi̸=ykstand for the indicator functions, where the output is 1ifyi=yj(peptides iandj belong to the same class) or yi̸=yk(the types of peptides iandkare different); otherwise the output is 0. The indica- tor function filters therapeutic and non-therapeutic peptides from the data for creating positive and negative pairs.MethodsAMP ACP Similarity ↓ Instability ↓ Antimicrobial ↑ Similarity ↓ Instability ↓ Anticancer ↑ LSTM-RNN 39.6164 45.0862 0.8550 36.9302 47.0669 0.7336 AMPGAN∗38.3080 51.5236 0.8617 - - - HydrAMP∗31.0662 59.6340 0.8145 - - - WAE-PSO∗- - - 41.2524 42.5061 0.7443 DiffAB 28.9849 43.3607 0.8024 31.4220 36.0610 0.6669 SimDiff 25.5385 41.1629 0.8560 28.8245 33.0405 0.7222 MMCD 24.4107 39.9649 0.8810 27.4685 31.7381 0.7604 ’*’ represents that the method relies on domain-specific biological knowledge. ’-’ represents that the method is un- suitable for the current task. For example, AMPGAN and HydrAMP are only designed for the AMP generation. Table 1: Results for the sequence generation MethodsAMP ACP Ramachandran ↑ RMSD ↓ Docking ↑ Ramachandran ↑ RMSD ↓ APPTEST 69.6576 2.7918 1362 67.9826 2.8055 FoldingDiff 72.4681 2.5118 1574 72.0531 2.6033 ProtDiff 71.3078 2.5544 1533 69.7589 2.4960 DiffAB 72.9647 2.3844 1608 71.3225 2.5513 SimDiff 76.1378 2.1004 1682 76.6164 2.4118 MMCD 80.4661 1.8278 1728 78.2157 2.0847 Table 2: Results for the structure generation. The reason behind the design of Intra-CL is intuitive. First, the non-therapeutic class naturally implies opposite in- formation against the therapeutic class, and hence it makes the model more discriminative. Second, the fashion to max- imize the disagreement between classes (1) can induce bi- ases in the embedding distribution of therapeutic peptides, identifying more potential generation space, and (2) can ex- plicitly reinforce embedding-class correspondences during diffusion, maintaining high generation fidelity (Zhu et al. 2022). Further analysis is detailed in the ablation study. Model Training The ultimate objective function is the sum of the diffusion process for sequence and structure generation, along with the CL tasks for Intra-CL and Inter-CL: Ltotal=Et∼Uniform(1...T) α Lt S+Lt C + (1−α) Lt intra+Lt inter (10) where αrepresents a hyperparameter to balance the contri- butions of different tasks. The Uniform(1...T) shows the uni- form distribution for the diffusion timesteps. The implemen- tation details of MMCD and the sampling process of peptide generation can be found in Appendix A. Experiments Experimental Setups Datasets. Following previous studies (Thi Phan et al. 2022; Zhang et al. 2023a), we collected therapeutic pep- tide data from public databases, containing two biologi- cal types, i.e., antimicrobial peptides (AMP) and anticancer peptides (ACP). Among these collected peptides, a portion of them only have 1D sequence information, without 3Dstructure information. Then, we applied Rosetta-based com- putational tools (Chaudhury, Lyskov, and Gray 2010) to pre- dict the missing structures based on their sequences. Finally, we compiled two datasets, one containing 20,129 antimi- crobial peptides and the other containing 4,381 anticancer peptides. In addition, we paired an equal number of labeled non-therapeutic peptides (collected from public databases) with each of the two datasets, exclusively for the contrastive learning task. Baselines. We compared our method with the follow- ing advanced methods for peptide generation at sequence and structure levels. For the sequence generation, the autoregression-based method LSTM-RNN (M ¨uller, Hiss, and Schneider 2018), the GAN-based method AMPGAN (Oort et al. 2021), and the V AE-based methods including WAE-PSO (Yang et al. 2022) and HydrAMP (Szymczak et al. 2023a) are listed as baselines. For the structure gener- ation, we took APPTEST (Timmons and Hewage 2021) as a baseline, which combines the neural network and simulated annealing algorithm for structure prediction. Moreover, we extended diffusion-based methods for protein generation to peptides. The diffusion-based methods for structure genera- tion (e.g., FoldingDiff (Wu et al. 2022) and ProtDiff (Trippe et al. 2023)) and the sequence-structure co-design (e.g., Dif- fAB(Luo et al. 2022) and SimDiff(Zhang et al. 2023b)), are considered for the comparison separately in the sequence and structure generation. Evaluation protocol. Here, we required each model (ours and baselines) to generate 1,000 new peptides, and then evaluated the quality of generated peptides with the follow- ing metrics. For the sequence, similarity score is used toMMCD (w/o Inter -CL) on AMP MMCD on AMP MMCD (w/o Intra -CL) on AMP and non -AMP MMCD on AMP and non -AMP(a) (b) (a) (b) average averageFigure 2: (a) The sample ratio under different sequence lengths in the AMP dataset, where the red line is the average ratio. (b) The similarity and RMSD scores of MMCD and baselines across different sequence lengths. quantify how closely the generated sequences match exist- ing ones, with a lower score indicating higher novelty; insta- bility score (M ¨uller et al. 2017) indicates the degree of pep- tide instability; antimicrobial /anticancer score evaluates the probability of peptides having therapeutic properties. For the structure, Ramachandran score (Hollingsworth and Karplus 2010) accesses the reliability of peptide structures; RMSD score measures the structural similarity between generated and existing peptides, with a lower score indi- cating higher authenticity; docking score (Fl ´orez-Castillo et al. 2020) evaluates the binding degree of antimicro- bial peptides to bacterial membrane proteins (PDB ID: 6MI7). We only reported the average metrics over all gen- erated peptides for each method in the experimental re- sults. Detailed information about the datasets, baselines, metrics, and implementations can be found in Appendix B. Our code, data and appendix are available on GitHub (https://github.com/wyky481l/MMCD) Experimental Results Performance comparison. In the results of sequence gen- eration under two datasets (as shown in Table 1), MMCD ex- hibited lower similarity and instability scores than all base- lines, suggesting its good generalization ability in generating diverse and stable peptides. Meanwhile, MMCD surpassed all baselines with higher antimicrobial and anticancer scores across AMP and ACP datasets, highlighting its strong po- tential for generating therapeutic peptides. Beyond that, we noticed that diffusion-based baselines (e.g., SimDiff, Dif- fAB) exhibit higher stability and diversity but lower ther- apeutic scores compared to baselines that incorporate bio- logical knowledge (e.g., AMPGAN, HydrAMP, WAE-PSO, details in Appendix B). By contrast, MMCD introduced bio- logical knowledge into the diffusion model by designing the contrastive learning of therapeutic and non-therapeutic pep- tides, thereby delivering optimality across various metrics. For the results of structure generation (as shown in Ta- ble 2), MMCD also outperformed all the baselines and ex- ceeded the best baselines (DiffAB and SimDiff) by 23.3 % and 12.9 %in RMSD scores, 10.2 %and 5.6 %in Ramachan- dran scores, and 7.4 %and 2.7 %in docking scores for AMP dataset. The higher Ramachandran score and lower RMSD score of MMCD underlined the reliability of our generated peptide structures. Especially in peptide docking, we foundthat MMCD shows the best docking score compared with baselines, which indicates great binding interactions with the target protein. Overall, MMCD is superior to all base- lines in both sequence and structure generation of peptides, and its impressive generative ability holds great promise to yield high-quality therapeutic peptides. Performance on different sequence lengths. In our dataset, sequence lengths of different peptides exhibited sub- stantial variation, with the number of residues ranging from 5 to 50 (Figure 2-a). We required models to generate 20 new peptides (sequences or structures) at each sequence length. Note that two methods, AMPGAN and HydrAMP, were excluded from the comparison because they cannot generate peptides with fixed lengths. From the generated re- sults on the AMP dataset (Figure 2-b), MMCD exceeded the baselines in terms of similarity and RMSD scores at each sequence length. With the increasing sequence lengths, there is a general trend of increased similarity and RMSD scores across all methods. One possible reason for this trend is that designing longer peptides becomes more complex, given the more prominent search space involved. Addition- ally, the scarcity of long-length peptides poses challenges in accurately estimating the similarity between generated and known peptides. In summary, these observations supported that MMCD excels at generating diverse peptides across dif- ferent lengths, especially shorter ones. Ablation study To investigate the necessity of each module in MMCD, we conducted several comparisons between MMCD with its variants: (1) MMCD (w/o Inter-CL) that removes the Inter- CL task, (2) MMCD (w/o Intra-CL) that removes the Intra- CL task, and (3) MMCD (w/o Inter-CL & Intra-CL) that re- moves both Inter-CL and Intra-CL tasks. The comparisons were operated on both AMP and ACP datasets, and the re- sults are shown in Table 3 and Appendix Table 1. When the Inter-CL was removed (w/o Inter-CL), we observed a de- cline in all metrics for peptide sequence and structure gen- eration, implying the importance of aligning two modalities via CL. The variant (w/o Intra-CL) results signified that us- ing the CL to differentiate therapeutic and non-therapeutic peptides contributes to the generation. As expected, the per- formance of MMCD dropped significantly after removingMethodsAMP ACP Similarity ↓Instability ↓Antimicrobial ↑Similarity ↓Instability ↓Anticancer ↑ MMCD (w/o InterCL & IntraCL) 27.4794 42.5359 0.8013 31.2820 34.6888 0.6996 MMCD (w/o IntraCL) 26.6889 41.2631 0.8584 28.9782 33.0268 0.7513 MMCD (w/o InterCL) 24.9079 41.7646 0.8494 28.0143 33.9816 0.7352 MMCD 24.4107 39.9649 0.8810 27.4685 31.7381 0.7604 Table 3: Ablation study on the sequence-level generation task. MMCD (w/o InterCL) on AMP MMCD on AMP MMCD (w/o IntraCL) on AMP and non -AMP MMCD on AMP and non -AMP(a) (b) Figure 3: (a) The t-SNE for structure and sequence em- beddings of therapeutic peptides (AMP data) obtained from MMCD (w/o Inter-CL) and MMCD. (b) The t-SNE for em- beddings (including structures and sequences) of therapeutic (AMP) and non-therapeutic (non-AMP) peptides obtained from MMCD (w/o Intra-CL) and MMCD. both Inter-CL and Intra-CL (w/o Inter-CL & Intra-CL). To better understand the strengths of Inter-CL and Intra- CL, we performed the t-SNE (Van der Maaten and Hin- ton 2008) visualization using the learned embeddings of peptides on the AMP dataset. As illustrated in Figure 3- a, Inter-CL effectively promoted the alignment of sequence and structure embeddings, facilitating the shared crucial in- formation (dashed circle) to be captured during diffusion. The t-SNE of Intra-CL (Figure 3-b) also revealed that it bet- ter distinguished therapeutic peptides from non-therapeutic ones in the embedding distribution. And the resulting dis- tribution bias may identify more potential generation space, thus leading to higher quality and diversity of therapeutic peptides generated by MMCD. Overall, MMCD with all the modules fulfilled superior performance, and removing any modules will diminish its generation power. Peptide-docking analysis To test the validity of generated peptide structures, we con- ducted a molecular-docking simulation. Here, a peptide was randomly selected from the AMP dataset as the reference,and the methods (Figure 4) were employed to generate cor- responding structures based on the sequence of the reference peptide (see details in Appendix C). The lipopolysaccharide on the outer membrane of bacteria (Li, Orlando, and Liao 2019) was selected as the target protein for molecular dock- ing. Then, we extracted the residues within a 5 ˚A proxim- ity between peptides (i.e., the reference and generated struc- tures) and the active pocket of target protein in docking com- plexes, to visualize their binding interactions (Miller et al. 2021). Of these docking results, all methods yielded a new structure capable of binding to the target protein, and our method exhibited the highest docking scores and displayed binding residues most similar to the reference structure. This prominent result underscored the reliability and therapeutic potential of our method for peptide generation. Reference DockingMMCD SimDiff DiffABDocking score = 1754 RMSD = 1.76Docking score = 1726 RMSD = 2.04Docking score = 1690 RMSD = 2.32Docking score = 1597 FoldingDiff RMSD = 2.45Docking score = 1582 ProtDiff RMSD = 2.51Docking score = 1551 Figure 4: Docking analysis (interactive visualization be- tween target protein and peptides) of the reference and gen- erated structures by MMCD and baselines. Thick lines rep- resent the residues of peptides, and the thin lines show the binding residues for protein-peptide complexes. Conclusion In this work, we propose a multi-modal contrastive dif- fusion model for the co-generation of peptide sequences and structures, named MMCD. MMCD is dedicated to leveraging a multi-modal contrastive learning strategy to capture consensus-related and difference-related informa- tion behind the sequences/structures and therapeutic/non- therapeutic peptides, enhancing the diffusion model to gen- erate high-quality therapeutic peptides. The experimental results unequivocally demonstrate the capability of our method in co-generating peptide sequence and structure, surpassing state-of-the-art baseline methods with advanta- geous performance.Acknowledgments This work was supported by the National Natural Sci- ence Foundation of China (62372204, 62072206, 61772381, 62102158); Huazhong Agricultural University Scien- tific & Technological Self-innovation Foundation; Fun- damental Research Funds for the Central Universities (2662021JC008, 2662022JC004). The funders have no role in study design, data collection, data analysis, data interpre- tation, or writing of the manuscript. References Anand, N.; and Achim, T. 2022. Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models. arxiv:2205.15019. Austin, J.; Johnson, D. D.; Ho, J.; Tarlow, D.; and van den Berg, R. 2021. Structured Denoising Diffusion Models in Discrete State-Spaces. In Advances in Neural Information Processing Systems , volume 34, 17981–17993. Curran As- sociates, Inc. Cao, H.; Tan, C.; Gao, Z.; Xu, Y .; Chen, G.; Heng, P.-A.; and Li, S. Z. 2023. A Survey on Generative Diffusion Model. arxiv:2209.02646. Capecchi, A.; Cai, X.; Personne, H.; K ¨ohler, T.; van Delden, C.; and Reymond, J.-L. 2021. Machine Learning Designs Non-Hemolytic Antimicrobial Peptides. Chem Sci , 12(26): 9221–9232. Chaudhury, S.; Lyskov, S.; and Gray, J. J. 2010. PyRosetta: A Script-Based Interface for Implementing Molecular Mod- eling Algorithms Using Rosetta. Bioinformatics , 26(5): 689–691. Chen, T.; Kornblith, S.; Norouzi, M.; and Hinton, G. 2020. A simple framework for contrastive learning of visual repre- sentations. In International conference on machine learning , 1597–1607. PMLR. Fl´orez-Castillo, J. M.; Rond ´on-Villareal, P.; Ropero-Vega, J. L.; Mendoza-Espinel, S. Y .; Moreno-Am ´ezquita, J. A.; M´endez-Jaimes, K. D.; Farf ´an-Garc ´ıa, A. E.; G ´omez- Rangel, S. Y .; and G ´omez-Duarte, O. G. 2020. Ib-M6 An- timicrobial Peptide: Antibacterial Activity against Clinical Isolates of Escherichia Coli and Molecular Docking. Antibi- otics , 9(2): 79. Ghorbani, M.; Prasad, S.; Brooks, B. R.; and Klauda, J. B. 2022. Deep Attention Based Variational Autoencoder for Antimicrobial Peptide Discovery. Ho, J.; Jain, A.; and Abbeel, P. 2020. Denoising Diffusion Probabilistic Models. In Advances in Neural Information Processing Systems , volume 33, 6840–6851. Curran Asso- ciates, Inc. Hollingsworth, S. A.; and Karplus, P. A. 2010. A Fresh Look at the Ramachandran Plot and the Occurrence of Standard Structures in Proteins. 1(3-4): 271–283. Hoogeboom, E.; Satorras, V . G.; Vignac, C.; and Welling, M. 2022. Equivariant Diffusion for Molecule Generation in 3D. In Proceedings of the 39th International Conference on Machine Learning , 8867–8887. PMLR.Huang, Y .; Du, C.; Xue, Z.; Chen, X.; Zhao, H.; and Huang, L. 2021. What makes multi-modal learning better than sin- gle (provably). Advances in Neural Information Processing Systems , 34: 10944–10956. Iqbal, T.; and Qureshi, S. 2022. The Survey: Text Generation Models in Deep Learning. J King Saud Univ-com , 34(6, Part A): 2515–2528. Jakubczyk, A.; Kara ´s, M.; Rybczy ´nska-Tkaczyk, K.; Zieli ´nska, E.; and Zieli ´nski, D. 2020. Current Trends of Bioactive Peptides—New Sources and Therapeutic Effect. Foods , 9(7): 846. Lee, E. Y .; Lee, M. W.; Fulan, B. M.; Ferguson, A. L.; and Wong, G. C. L. 2017. What Can Machine Learning Do for Antimicrobial Peptides, and What Can Antimicrobial Peptides Do for Machine Learning? Interface Focus , 7(6): 20160153. Lee, E. Y .; Wong, G. C. L.; and Ferguson, A. L. 2018. Machine Learning-Enabled Discovery and Design of Membrane-Active Peptides. Bioorgan Med Chem , 26(10): 2708–2718. Li, Y .; Orlando, B. J.; and Liao, M. 2019. Structural Basis of Lipopolysaccharide Extraction by the LptB2FGC Complex. Nature , 567(7749): 486–490. Lin, E.; Lin, C.-H.; and Lane, H.-Y . 2022. De novo peptide and protein design using generative adversarial networks: an update. Journal of Chemical Information and Modeling , 62(4): 761–774. Liu, S.; Zhu, Y .; Lu, J.; Xu, Z.; Nie, W.; Gitter, A.; Xiao, C.; Tang, J.; Guo, H.; and Anandkumar, A. 2023. A Text-guided Protein Design Framework. arxiv:2302.04611. Liu, V .; and Chilton, L. B. 2022. Design Guidelines for Prompt Engineering Text-to-Image Generative Models. In Proceedings of the 2022 CHI Conference on Human Fac- tors in Computing Systems , CHI ’22, 1–23. New York, NY , USA: Association for Computing Machinery. ISBN 978-1- 4503-9157-3. Luo, S.; Su, Y .; Peng, X.; Wang, S.; Peng, J.; and Ma, J. 2022. Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Struc- tures. Miller, E. B.; Murphy, R. B.; Sindhikara, D.; Borrelli, K. W.; Grisewood, M. J.; Ranalli, F.; Dixon, S. L.; Jerome, S.; Boyles, N. A.; Day, T.; Ghanakota, P.; Mondal, S.; Rafi, S. B.; Troast, D. M.; Abel, R.; and Friesner, R. A. 2021. Reliable and Accurate Solution to the Induced Fit Docking Problem for Protein–Ligand Binding. J Chem Theory Com- put, 17(4): 2630–2639. M¨uller, A. T.; Gabernet, G.; Hiss, J. A.; and Schneider, G. 2017. modlAMP: Python for Antimicrobial Peptides. Bioin- formatics , 33(17): 2753–2755. M¨uller, A. T.; Hiss, J. A.; and Schneider, G. 2018. Recurrent Neural Network Model for Constructive Peptide Design. J Chem Inf Model , 58(2): 472–479. Muttenthaler, M.; King, G. F.; Adams, D. J.; and Alewood, P. F. 2021. Trends in peptide drug discovery. Nature reviews Drug discovery , 20(4): 309–325.Oort, C. M. V .; Ferrell, J. B.; Remington, J. M.; Wshah, S.; and Li, J. 2021. AMPGAN v2: Machine Learning Guided Design of Antimicrobial Peptides. Satorras, V . G.; Hoogeboom, E.; and Welling, M. 2021. E(n) Equivariant Graph Neural Networks. In Proceedings of the 38th International Conference on Machine Learning , 9323– 9332. PMLR. Shi, C.; Wang, C.; Lu, J.; Zhong, B.; and Tang, J. 2023. Protein Sequence and Structure Co-Design with Equivariant Translation. arxiv:2210.08761. Sohl-Dickstein, J.; Weiss, E.; Maheswaranathan, N.; and Ganguli, S. 2015. Deep Unsupervised Learning Using Nonequilibrium Thermodynamics. In Proceedings of the 32nd International Conference on Machine Learning , 2256– 2265. PMLR. Song, Y .; and Ermon, S. 2019. Generative Modeling by Es- timating Gradients of the Data Distribution. In Advances in Neural Information Processing Systems , volume 32. Curran Associates, Inc. Szymczak, P.; Mo ˙zejko, M.; Grzegorzek, T.; Jurczak, R.; Bauer, M.; Neubauer, D.; Sikora, K.; Michalski, M.; Sroka, J.; Setny, P.; Kamysz, W.; and Szczurek, E. 2023a. Discov- ering Highly Potent Antimicrobial Peptides with Deep Gen- erative Model HydrAMP. Nat Commun , 14(1): 1453. Szymczak, P.; Mo ˙zejko, M.; Grzegorzek, T.; Jurczak, R.; Bauer, M.; Neubauer, D.; Sikora, K.; Michalski, M.; Sroka, J.; Setny, P.; et al. 2023b. Discovering highly potent an- timicrobial peptides with deep generative model HydrAMP. Nature Communications , 14(1): 1453. Thi Phan, L.; Woo Park, H.; Pitti, T.; Madhavan, T.; Jeon, Y .-J.; and Manavalan, B. 2022. MLACP 2.0: An Updated Machine Learning Tool for Anticancer Peptide Prediction. Comput Struct Biotec , 20: 4473–4480. Timmons, P. B.; and Hewage, C. M. 2021. APPTEST Is a Novel Protocol for the Automatic Prediction of Peptide Tertiary Structures. Brief Bioinform , 22(6): bbab308. Trippe, B. L.; Yim, J.; Tischer, D.; Baker, D.; Broderick, T.; Barzilay, R.; and Jaakkola, T. 2023. Diffusion Proba- bilistic Modeling of Protein Backbones in 3D for the Motif- Scaffolding Problem. arxiv:2206.04119. Tucs, A.; Tran, D. P.; Yumoto, A.; Ito, Y .; Uzawa, T.; and Tsuda, K. 2020. Generating Ampicillin-Level Antimicrobial Peptides with Activity-Aware Generative Adversarial Net- works. ACS Omega , 5(36): 22847–22851. Van der Maaten, L.; and Hinton, G. 2008. Visualizing data using t-SNE. Journal of machine learning research , 9(11). Vignac, C.; Krawczuk, I.; Siraudin, A.; Wang, B.; Cevher, V .; and Frossard, P. 2023. DiGress: Discrete Denoising Dif- fusion for Graph Generation. arxiv:2209.14734. Wan, F.; Kontogiorgos, H. D.; and Fuente, d. l. N. C. 2022. Deep Generative Models for Peptide Design. Digital Dis- covery , 1(3): 195–208. Webster, R.; Rabin, J.; Simon, L.; and Jurie, F. 2019. Detect- ing overfitting of deep generative networks via latent recov- ery. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition , 11273–11282.Wu, K. E.; Yang, K. K.; van den Berg, R.; Zou, J. Y .; Lu, A. X.; and Amini, A. P. 2022. Protein Structure Generation via Folding Diffusion. arxiv:2209.15611. Wu, X.; Luu, A. T.; and Dong, X. 2022. Mitigating Data Sparsity for Short Text Topic Modeling by Topic-Semantic Contrastive Learning. In Proceedings of the 2022 Confer- ence on Empirical Methods in Natural Language Process- ing, 2748–2760. Wu, Z.; Johnston, K. E.; Arnold, F. H.; and Yang, K. K. 2021. Protein sequence design with deep generative mod- els.Current Opinion in Chemical Biology , 65: 18–27. Xia, C.; Feng, S.-H.; Xia, Y .; Pan, X.; and Shen, H.-B. 2022. Fast protein structure comparison through effective repre- sentation learning with contrastive graph neural networks. PLoS computational biology , 18(3): e1009986. Yadav, N. S.; Kumar, P.; and Singh, I. 2022. Structural and functional analysis of protein. In Bioinformatics , 189–206. Elsevier. Yang, L.; Yang, G.; Bing, Z.; Tian, Y .; Huang, L.; Niu, Y .; and Yang, L. 2022. Accelerating the Discovery of Anti- cancer Peptides Targeting Lung and Breast Cancers with the Wasserstein Autoencoder Model and PSO Algorithm. Brief Bioinform , 23(5): bbac320. Yang, L.; Zhang, Z.; Song, Y .; Hong, S.; Xu, R.; Zhao, Y .; Zhang, W.; Cui, B.; and Yang, M.-H. 2023. Diffusion Mod- els: A Comprehensive Survey of Methods and Applications. arxiv:2209.00796. Yuan, X.; Lin, Z.; Kuen, J.; Zhang, J.; Wang, Y .; Maire, M.; Kale, A.; and Faieta, B. 2021. Multimodal contrastive train- ing for visual representation learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , 6995–7004. Zhang, H.; Saravanan, K. M.; Wei, Y .; Jiao, Y .; Yang, Y .; Pan, Y .; Wu, X.; and Zhang, J. Z. H. 2023a. Deep Learning-Based Bioactive Therapeutic Peptide Generation and Screening. J Chem Inf Model , 63(3): 835–845. Zhang, Z.; Xu, M.; Lozano, A.; Chenthamarakshan, V .; Das, P.; and Tang, J. 2023b. Pre-Training Protein Encoder via Siamese Sequence-Structure Diffusion Trajectory Predic- tion. arxiv:2301.12068. Zhang, Z.; Zhao, Y .; Chen, M.; and He, X. 2022. Label An- chored Contrastive Learning for Language Understanding. InProceedings of the 2022 Conference of the North Ameri- can Chapter of the Association for Computational Linguis- tics: Human Language Technologies , 1437–1449. Zheng, M.; Wang, F.; You, S.; Qian, C.; Zhang, C.; Wang, X.; and Xu, C. 2021. Weakly Supervised Contrastive Learn- ing. In Proceedings of the IEEE/CVF International Confer- ence on Computer Vision , 10042–10051. Zhu, Y .; Wu, Y .; Olszewski, K.; Ren, J.; Tulyakov, S.; and Yan, Y . 2022. Discrete contrastive diffusion for cross-modal and conditional generation. arXiv preprint arXiv:2206.07771 . Zhu, Y .; Wu, Y .; Olszewski, K.; Ren, J.; Tulyakov, S.; and Yan, Y . 2023. Discrete Contrastive Diffusion for Cross- Modal Music and Image Generation. arxiv:2206.07771.
Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning Christian Szegedy Google Inc. 1600 Amphitheatre Pkwy, Mountain View, CA szegedy@google.comSergey Ioffe sioffe@google.comVincent Vanhoucke vanhoucke@google.com Alex Alemi alemi@google.com Abstract Very deep convolutional networks have been central to the largest advances in image recognition performance in recent years. One example is the Inception architecture that has been shown to achieve very good performance at rel- atively low computational cost. Recently, the introduction of residual connections in conjunction with a more tradi- tional architecture has yielded state-of-the-art performance in the 2015 ILSVRC challenge; its performance was similar to the latest generation Inception-v3 network. This raises the question of whether there are any beneﬁt in combining the Inception architecture with residual connections. Here we give clear empirical evidence that training with residual connections accelerates the training of Inception networks signiﬁcantly. There is also some evidence of residual Incep- tion networks outperforming similarly expensive Inception networks without residual connections by a thin margin. We also present several new streamlined architectures for both residual and non-residual Inception networks. These varia- tions improve the single-frame recognition performance on the ILSVRC 2012 classiﬁcation task signiﬁcantly. We fur- ther demonstrate how proper activation scaling stabilizes the training of very wide residual Inception networks. With an ensemble of three residual and one Inception-v4, we achieve 3.08% top-5 error on the test set of the ImageNet classiﬁcation (CLS) challenge. 1. Introduction Since the 2012 ImageNet competition [11] winning en- try by Krizhevsky et al [8], their network “AlexNet” has been successfully applied to a larger variety of computer vision tasks, for example to object-detection [4], segmen- tation [10], human pose estimation [17], video classiﬁca-tion [7], object tracking [18], and superresolution [3]. These examples are but a few of all the applications to which deep convolutional networks have been very successfully applied ever since. In this work we study the combination of the two most recent ideas: Residual connections introduced by He et al. in [5] and the latest revised version of the Inception archi- tecture [15]. In [5], it is argued that residual connections are of inherent importance for training very deep architectures. Since Inception networks tend to be very deep, it is natu- ral to replace the ﬁlter concatenation stage of the Inception architecture with residual connections. This would allow Inception to reap all the beneﬁts of the residual approach while retaining its computational efﬁciency. Besides a straightforward integration, we have also stud- ied whether Inception itself can be made more efﬁcient by making it deeper and wider. For that purpose, we designed a new version named Inception-v4 which has a more uni- form simpliﬁed architecture and more inception modules than Inception-v3. Historically, Inception-v3 had inherited a lot of the baggage of the earlier incarnations. The techni- cal constraints chieﬂy came from the need for partitioning the model for distributed training using DistBelief [2]. Now, after migrating our training setup to TensorFlow [1] these constraints have been lifted, which allowed us to simplify the architecture signiﬁcantly. The details of that simpliﬁed architecture are described in Section 3. In this report, we will compare the two pure Inception variants, Inception-v3 and v4, with similarly expensive hy- brid Inception-ResNet versions. Admittedly, those mod- els were picked in a somewhat ad hoc manner with the main constraint being that the parameters and computa- tional complexity of the models should be somewhat similar to the cost of the non-residual models. In fact we have tested bigger and wider Inception-ResNet variants and they per- formed very similarly on the ImageNet classiﬁcation chal- 1arXiv:1602.07261v2 [cs.CV] 23 Aug 2016lenge [11] dataset. The last experiment reported here is an evaluation of an ensemble of all the best performing models presented here. As it was apparent that both Inception-v4 and Inception- ResNet-v2 performed similarly well, exceeding state-of- the art single frame performance on the ImageNet valida- tion dataset, we wanted to see how a combination of those pushes the state of the art on this well studied dataset. Sur- prisingly, we found that gains on the single-frame perfor- mance do not translate into similarly large gains on ensem- bled performance. Nonetheless, it still allows us to report 3.1% top-5 error on the validation set with four models en- sembled setting a new state of the art, to our best knowl- edge. In the last section, we study some of the classiﬁcation failures and conclude that the ensemble still has not reached the label noise of the annotations on this dataset and there is still room for improvement for the predictions. 2. Related Work Convolutional networks have become popular in large scale image recognition tasks after Krizhevsky et al. [8]. Some of the next important milestones were Network-in- network [9] by Lin et al., VGGNet [12] by Simonyan et al. and GoogLeNet (Inception-v1) [14] by Szegedy et al. Residual connection were introduced by He et al. in [5] in which they give convincing theoretical and practical ev- idence for the advantages of utilizing additive merging of signals both for image recognition, and especially for object detection. The authors argue that residual connections are inherently necessary for training very deep convolutional models. Our ﬁndings do not seem to support this view, at least for image recognition. However it might require more measurement points with deeper architectures to understand the true extent of beneﬁcial aspects offered by residual con- nections. In the experimental section we demonstrate that it is not very difﬁcult to train competitive very deep net- works without utilizing residual connections. However the use of residual connections seems to improve the training speed greatly, which is alone a great argument for their use. The Inception deep convolutional architecture was intro- duced in [14] and was called GoogLeNet or Inception-v1 in our exposition. Later the Inception architecture was reﬁned in various ways, ﬁrst by the introduction of batch normaliza- tion [6] (Inception-v2) by Ioffe et al. Later the architecture was improved by additional factorization ideas in the third iteration [15] which will be referred to as Inception-v3 in this report. Conv +Relu activation Relu activation Conv Figure 1. Residual connections as introduced in He et al. [5]. Conv +Relu activation Relu activation 1x1 Conv Figure 2. Optimized version of ResNet connections by [5] to shield computation. 3. Architectural Choices 3.1. Pure Inception blocks Our older Inception models used to be trained in a par- titioned manner, where each replica was partitioned into a multiple sub-networks in order to be able to ﬁt the whole model in memory. However, the Inception architecture is highly tunable, meaning that there are a lot of possible changes to the number of ﬁlters in the various layers that do not affect the quality of the fully trained network. In order to optimize the training speed, we used to tune the layer sizes carefully in order to balance the computation be- tween the various model sub-networks. In contrast, with the introduction of TensorFlow our most recent models can be trained without partitioning the replicas. This is enabled in part by recent optimizations of memory used by backprop- agation, achieved by carefully considering what tensors are needed for gradient computation and structuring the compu-tation to reduce the number of such tensors. Historically, we have been relatively conservative about changing the archi- tectural choices and restricted our experiments to varying isolated network components while keeping the rest of the network stable. Not simplifying earlier choices resulted in networks that looked more complicated that they needed to be. In our newer experiments, for Inception-v4 we decided to shed this unnecessary baggage and made uniform choices for the Inception blocks for each grid size. Plase refer to Figure 9 for the large scale structure of the Inception-v4 net- work and Figures 3, 4, 5, 6, 7 and 8 for the detailed struc- ture of its components. All the convolutions not marked with “V” in the ﬁgures are same-padded meaning that their output grid matches the size of their input. Convolutions marked with “V” are valid padded, meaning that input patch of each unit is fully contained in the previous layer and the grid size of the output activation map is reduced accord- ingly. 3.2. Residual Inception Blocks For the residual versions of the Inception networks, we use cheaper Inception blocks than the original Inception. Each Inception block is followed by ﬁlter-expansion layer (11convolution without activation) which is used for scaling up the dimensionality of the ﬁlter bank before the addition to match the depth of the input. This is needed to compensate for the dimensionality reduction induced by the Inception block. We tried several versions of the residual version of In- ception. Only two of them are detailed here. The ﬁrst one “Inception-ResNet-v1” roughly the computational cost of Inception-v3, while “Inception-ResNet-v2” matches the raw cost of the newly introduced Inception-v4 network. See Figure 15 for the large scale structure of both varianets. (However, the step time of Inception-v4 proved to be signif- icantly slower in practice, probably due to the larger number of layers.) Another small technical difference between our resid- ual and non-residual Inception variants is that in the case of Inception-ResNet, we used batch-normalization only on top of the traditional layers, but not on top of the summa- tions. It is reasonable to expect that a thorough use of batch- normalization should be advantageous, but we wanted to keep each model replica trainable on a single GPU. It turned out that the memory footprint of layers with large activa- tion size was consuming disproportionate amount of GPU- memory. By omitting the batch-normalization on top of those layers, we were able to increase the overall number of Inception blocks substantially. We hope that with bet- ter utilization of computing resources, making this trade-off will become unecessary. 3x3 Conv (32 stride 2 V ) Input (299x299x3) 3x3 Conv (32 V) 3x3 Conv (64)3x3 MaxPool (stride 2 V) 3x3 Conv (96 stride 2 V) Filter concat 1x1 Conv (64)3x3 Conv (96 V) 1x1 Conv (64)7x1 Conv (64)1x7 Conv (64)Filter concat 3x3 Conv (96 V) MaxPool (stride=2 V) 3x3 Conv (192 V) Filter concat 299x299x3 149x149x32 147x147x32 147x147x64 73x73x160 71x71x192 35x35x384 Figure 3. The schema for stem of the pure Inception-v4 and Inception-ResNet-v2 networks. This is the input part of those net- works. Cf. Figures 9 and 151x1 Conv (96)1x1 Conv (64)1x1 Conv (64)3x3 Conv (96)3x3 Conv (96)3x3 Conv (96)Filter concat Filter concat Avg Pooling 1x1 Conv (96)Figure 4. The schema for 3535grid modules of the pure Inception-v4 network. This is the Inception-A block of Figure 9. 1x1 Conv (384) 1x1 Conv (192) 1x1 Conv (192) 1x7 Conv (224) 1x7 Conv (192) 7x1 Conv (224) Filter concat Filter concat Avg Pooling 1x1 Conv (128) 1x7 Conv (256) 1x7 Conv (224) 7x1 Conv (256) Figure 5. The schema for 1717grid modules of the pure Inception-v4 network. This is the Inception-B block of Figure 9. 1x1 Conv (256) 1x1 Conv (384) 1x1 Conv (384) 3x1 Conv (256) 1x3 Conv (448) 3x1 Conv (512) Filter concat Filter concat Avg Pooling 1x1 Conv (256) 1x3 Conv (256) 1x3 Conv (256) 3x1 Conv (256) Figure 6. The schema for 88grid modules of the pure Inception- v4 network. This is the Inception-C block of Figure 9. 1x1 Conv (k)3x3 Conv (n stride 2 V) 3x3 Conv (l)3x3 Conv (m stride 2 V) Filter concat Filter concat 3x3 MaxPool (stride 2 V) Figure 7. The schema for 3535to1717reduction module. Different variants of this blocks (with various number of ﬁlters) are used in Figure 9, and 15 in each of the new Inception(-v4, - ResNet-v1, -ResNet-v2) variants presented in this paper. The k,l, m,nnumbers represent ﬁlter bank sizes which can be looked up in Table 1. 1x1 Conv (256) 1x1 Conv (192) 1x7 Conv (256) 3x3 Conv (320 stride 2 V) Filter concat Filter concat 3x3 MaxPool (stride 2 V) 3x3 Conv (192 stride 2 V) 7x1 Conv (320) Figure 8. The schema for 1717to88grid-reduction mod- ule. This is the reduction module used by the pure Inception-v4 network in Figure 9.Stem Input (299x299x3) 299x299x3 4 x Inception-A Output: 35x35x384 Output: 35x35x384 Reduction-A Output: 17x17x1024 7 x Inception-B 3 x Inception-C Reduction-B Avarage Pooling Dropout (keep 0.8) Output: 17x17x1024 Output: 8x8x1536 Output: 8x8x1536 Output: 1536 Softmax Output: 1536 Output: 1000 Figure 9. The overall schema of the Inception-v4 network. For the detailed modules, please refer to Figures 3, 4, 5, 6, 7 and 8 for the detailed structure of the various components. 1x1 Conv (32) 1x1 Conv (32)1x1 Conv (32)3x3 Conv (32)3x3 Conv (32)3x3 Conv (32)1x1 Conv (256 Linear) +Relu activation Relu activation Figure 10. The schema for 3535grid (Inception-ResNet-A) module of Inception-ResNet-v1 network. 1x1 Conv (128) 1x1 Conv (128) 1x7 Conv (128) 7x1 Conv (128) 1x1 Conv (896 Linear) +Relu activation Relu activation Figure 11. The schema for 1717grid (Inception-ResNet-B) module of Inception-ResNet-v1 network. 1x1 Conv (256) 3x3 Conv (256 stride 2 V) Filter concat Previous Layer 3x3 MaxPool (stride 2 V) 3x3 Conv (384 stride 2 V) 3x3 Conv (256) 1x1 Conv (256) 3x3 Conv (256 stride 2 V) 1x1 Conv (256) Figure 12. “Reduction-B” 1717to88grid-reduction module. This module used by the smaller Inception-ResNet-v1 network in Figure 15.1x1 Conv (192) 1x1 Conv (192) 1x3 Conv (192) 3x1 Conv (192) 1x1 Conv (1792 Linear) +Relu activation Relu activation Figure 13. The schema for 88grid (Inception-ResNet-C) module of Inception-ResNet-v1 network. 3x3 Conv (32 stride 2 V ) Input (299x299x3) 3x3 Conv (32 V) 3x3 Conv (64)3x3 MaxPool (stride 2 V) 1x1 Conv (80) 299x299x3 149x149x32 147x147x32 147x147x64 73x73x64 73x73x80 3x3 Conv (192 V) 71x71x192 3x3 Conv (256 stride 2 V) 35x35x256 Figure 14. The stem of the Inception-ResNet-v1 network.Stem Input (299x299x3) 299x299x3 5 x Inception-resnet-A Output: 35x35x256 Output: 35x35x256 Reduction-A Output: 17x17x896 10 x Inception-resnet-B 5 x Inception-resnet-C Reduction-B Average Pooling Dropout (keep 0.8) Output: 17x17x896 Output: 8x8x1792 Output: 8x8x1792 Output: 1792 Softmax Output: 1792 Output: 1000 Figure 15. Schema for Inception-ResNet-v1 and Inception- ResNet-v2 networks. This schema applies to both networks but the underlying components differ. Inception-ResNet-v1 uses the blocks as described in Figures 14, 10, 7, 11, 12 and 13. Inception- ResNet-v2 uses the blocks as described in Figures 3, 16, 7,17, 18 and 19. The output sizes in the diagram refer to the activation vector tensor shapes of Inception-ResNet-v1.1x1 Conv (32) 1x1 Conv (32)1x1 Conv (32)3x3 Conv (32)3x3 Conv (48)3x3 Conv (64)1x1 Conv (384 Linear) +Relu activation Relu activation Figure 16. The schema for 3535grid (Inception-ResNet-A) module of the Inception-ResNet-v2 network. 1x1 Conv (192) 1x1 Conv (128) 1x7 Conv (160) 7x1 Conv (192) 1x1 Conv (1154 Linear) +Relu activation Relu activation Figure 17. The schema for 1717grid (Inception-ResNet-B) module of the Inception-ResNet-v2 network. 1x1 Conv (256) 3x3 Conv (320 stride 2 V) Filter concat Previous Layer 3x3 MaxPool (stride 2 V) 3x3 Conv (384 stride 2 V) 3x3 Conv (288) 1x1 Conv (256) 3x3 Conv (288 stride 2 V) 1x1 Conv (256) Figure 18. The schema for 1717to88grid-reduction mod- ule. Reduction-B module used by the wider Inception-ResNet-v1 network in Figure 15. 1x1 Conv (192) 1x1 Conv (192) 1x3 Conv (224) 3x1 Conv (256) 1x1 Conv (2048 Linear) +Relu activation Relu activation Figure 19. The schema for 88grid (Inception-ResNet-C) module of the Inception-ResNet-v2 network. Network k l m n Inception-v4 192 224 256 384 Inception-ResNet-v1 192 192 256 384 Inception-ResNet-v2 256 256 384 384 Table 1. The number of ﬁlters of the Reduction-A module for the three Inception variants presented in this paper. The four numbers in the colums of the paper parametrize the four convolutions of Figure 7Activation Scaling +Relu activation Relu activation Inception Figure 20. The general schema for scaling combined Inception- resnet moduels. We expect that the same idea is useful in the gen- eral resnet case, where instead of the Inception block an arbitrary subnetwork is used. The scaling block just scales the last linear activations by a suitable constant, typically around 0.1. 3.3. Scaling of the Residuals Also we found that if the number of ﬁlters exceeded 1000, the residual variants started to exhibit instabilities and the network has just “died” early in the training, meaning that the last layer before the average pooling started to pro- duce only zeros after a few tens of thousands of iterations. This could not be prevented, neither by lowering the learn- ing rate, nor by adding an extra batch-normalization to this layer. We found that scaling down the residuals before adding them to the previous layer activation seemed to stabilize the training. In general we picked some scaling factors between 0.1 and 0.3 to scale the residuals before their being added to the accumulated layer activations (cf. Figure 20). A similar instability was observed by He et al. in [5] in the case of very deep residual networks and they suggested a two-phase training where the ﬁrst “warm-up” phase is done with very low learning rate, followed by a second phase with high learning rata. We found that if the number of ﬁlters is very high, then even a very low (0.00001) learning rate is not sufﬁcient to cope with the instabilities and the training with high learning rate had a chance to destroy its effects. We found it much more reliable to just scale the residuals. Even where the scaling was not strictly necessary, it never seemed to harm the ﬁnal accuracy, but it helped to stabilize the training. 4. Training Methodology We have trained our networks with stochastic gradient utilizing the TensorFlow [1] distributed machine learning system using 20replicas running each on a NVidia Kepler GPU. Our earlier experiments used momentum [13] with a decay of 0:9, while our best models were achieved using 20 40 60 80 100 120 140 160 180 200 Epoch151617181920212223242526272829Error (top-1) % inception-v3 inception-resnet-v1Figure 21. Top-1 error evolution during training of pure Inception- v3 vs a residual network of similar computational cost. The eval- uation is measured on a single crop on the non-blacklist images of the ILSVRC-2012 validation set. The residual model was train- ing much faster, but reached slightly worse ﬁnal accuracy than the traditional Inception-v3. RMSProp [16] with decay of 0:9and= 1:0. We used a learning rate of 0:045, decayed every two epochs using an exponential rate of 0:94. Model evaluations are performed using a running average of the parameters computed over time. 5. Experimental Results First we observe the top-1 and top-5 validation-error evo- lution of the four variants during training. After the exper- iment was conducted, we have found that our continuous evaluation was conducted on a subset of the validation set which omitted about 1700 blacklisted entities due to poor bounding boxes. It turned out that the omission should have been only performed for the CLSLOC benchmark, but yields somewhat incomparable (more optimistic) numbers when compared to other reports including some earlier re- ports by our team. The difference is about 0.3% for top- 1 error and about 0.15% for the top- 5error. However, since the differences are consistent, we think the comparison be- tween the curves is a fair one. On the other hand, we have rerun our multi-crop and en- semble results on the complete validation set consisting of 50000 images. Also the ﬁnal ensemble result was also per- formed on the test set and sent to the ILSVRC test server for validation to verify that our tuning did not result in an over-ﬁtting. We would like to stress that this ﬁnal validation was done only once and we have submitted our results only twice in the last year: once for the BN-Inception paper and later during the ILSVR-2015 CLSLOC competition, so we believe that the test set numbers constitute a true estimate of the generalization capabilities of our model. Finally, we present some comparisons, between various versions of Inception and Inception-ResNet. The models Inception-v3 and Inception-v4 are deep convolutional net-20 40 60 80 100 120 140 160 180 200 Epoch3.03.54.04.55.05.56.06.57.07.58.08.59.09.5Error (top-5) % inception-v3 inception-resnet-v1Figure 22. Top-5 error evolution during training of pure Inception- v3 vs a residual Inception of similar computational cost. The eval- uation is measured on a single crop on the non-blacklist images of the ILSVRC-2012 validation set. The residual version has trained much faster and reached slightly better ﬁnal recall on the valida- tion set. 20 40 60 80 100 120 140 160 Epoch1516171819202122232425262728293031323334Error (top-1) % inception-v4 inception-resnet-v2 Figure 23. Top-1 error evolution during training of pure Inception- v3 vs a residual Inception of similar computational cost. The eval- uation is measured on a single crop on the non-blacklist images of the ILSVRC-2012 validation set. The residual version was train- ing much faster and reached slightly better ﬁnal accuracy than the traditional Inception-v4. Network Top-1 Error Top-5 Error BN-Inception [6] 25.2% 7.8% Inception-v3 [15] 21.2% 5.6% Inception-ResNet-v1 21.3% 5.5% Inception-v4 20.0% 5.0% Inception-ResNet-v2 19.9% 4.9% Table 2. Single crop - single model experimental results. Reported on the non-blacklisted subset of the validation set of ILSVRC 2012. works not utilizing residual connections while Inception- ResNet-v1 and Inception-ResNet-v2 are Inception style net- works that utilize residual connections instead of ﬁlter con- catenation. Table 2 shows the single-model, single crop top-1 and top-5 error of the various architectures on the validation set. 20 40 60 80 100 120 140 160 Epoch3456789Error (top-5) % inception-v4 inception-resnet-v2Figure 24. Top-5 error evolution during training of pure Inception- v4 vs a residual Inception of similar computational cost. The eval- uation is measured on a single crop on the non-blacklist images of the ILSVRC-2012 validation set. The residual version trained faster and reached slightly better ﬁnal recall on the validation set. 20 40 60 80 100 120 140 160 Epoch2.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5Error (top-5) % inception-v4 inception-resnet-v2 inception-v3 inception-resnet-v1 Figure 25. Top-5 error evolution of all four models (single model, single crop). Showing the improvement due to larger model size. Although the residual version converges faster, the ﬁnal accuracy seems to mainly depend on the model size. 20 40 60 80 100 120 140 160 Epoch181920212223242526272829Error (top-1) % inception-v4 inception-resnet-v2 inception-v3 inception-resnet-v1 Figure 26. Top-1 error evolution of all four models (single model, single crop). This paints a similar picture as the top-5 evaluation. Table 3 shows the performance of the various models with a small number of crops: 10 crops for ResNet as was reported in [5]), for the Inception variants, we have used the 12 crops evaluation as as described in [14].Network Crops Top-1 Error Top-5 Error ResNet-151 [5] 10 21.4% 5.7% Inception-v3 [15] 12 19.8% 4.6% Inception-ResNet-v1 12 19.8% 4.6% Inception-v4 12 18.7% 4.2% Inception-ResNet-v2 12 18.7% 4.1% Table 3. 10/12 crops evaluations - single model experimental re- sults. Reported on the all 50000 images of the validation set of ILSVRC 2012. Network Crops Top-1 Error Top-5 Error ResNet-151 [5] dense 19.4% 4.5% Inception-v3 [15] 144 18.9% 4.3% Inception-ResNet-v1 144 18.8% 4.3% Inception-v4 144 17.7% 3.8% Inception-ResNet-v2 144 17.8% 3.7% Table 4. 144 crops evaluations - single model experimental results. Reported on the all 50000 images of the validation set of ILSVRC 2012. Network Models Top-1 Error Top-5 Error ResNet-151 [5] 6 – 3.6% Inception-v3 [15] 4 17.3% 3.6% Inception-v4 + 3Inception-ResNet-v24 16.5% 3.1% Table 5. Ensemble results with 144 crops/dense evaluation. Re- ported on the all 50000 images of the validation set of ILSVRC 2012. For Inception-v4(+Residual), the ensemble consists of one pure Inception-v4 and three Inception-ResNet-v2 models and were evaluated both on the validation and on the test-set. The test-set performance was 3:08% top-5 error verifying that we don’t over- ﬁt on the validation set. Table 4 shows the single model performance of the var- ious models using. For residual network the dense evalua- tion result is reported from [5]. For the inception networks, the 144 crops strategy was used as described in [14]. Table 5 compares ensemble results. For the pure resid- ual network the 6 models dense evaluation result is reported from [5]. For the inception networks 4 models were ensem- bled using the 144 crops strategy as described in [14]. 6. Conclusions We have presented three new network architectures in detail: Inception-ResNet-v1: a hybrid Inception version that has a similar computational cost to Inception-v3 from [15]. Inception-ResNet-v2: a costlier hybrid Inception ver- sion with signiﬁcantly improved recognition perfor- mance.Inception-v4: a pure Inception variant without residual connections with roughly the same recognition perfor- mance as Inception-ResNet-v2. We studied how the introduction of residual connections leads to dramatically improved training speed for the Incep- tion architecture. Also our latest models (with and without residual connections) outperform all our previous networks, just by virtue of the increased model size. References [1] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghe- mawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y . Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Man ´e, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V . Vanhoucke, V . Vasudevan, F. Vi ´egas, O. Vinyals, P. War- den, M. Wattenberg, M. Wicke, Y . Yu, and X. Zheng. Tensor- Flow: Large-scale machine learning on heterogeneous sys- tems, 2015. Software available from tensorﬂow.org. [2] J. Dean, G. Corrado, R. Monga, K. Chen, M. Devin, M. Mao, A. Senior, P. Tucker, K. Yang, Q. V . Le, et al. Large scale dis- tributed deep networks. In Advances in Neural Information Processing Systems , pages 1223–1231, 2012. [3] C. Dong, C. C. Loy, K. He, and X. Tang. Learning a deep convolutional network for image super-resolution. In Com- puter Vision–ECCV 2014 , pages 184–199. Springer, 2014. [4] R. Girshick, J. Donahue, T. Darrell, and J. Malik. Rich fea- ture hierarchies for accurate object detection and semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 2014. [5] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learn- ing for image recognition. arXiv preprint arXiv:1512.03385 , 2015. [6] S. Ioffe and C. Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In Proceedings of The 32nd International Conference on Ma- chine Learning , pages 448–456, 2015. [7] A. Karpathy, G. Toderici, S. Shetty, T. Leung, R. Sukthankar, and L. Fei-Fei. Large-scale video classiﬁcation with con- volutional neural networks. In Computer Vision and Pat- tern Recognition (CVPR), 2014 IEEE Conference on , pages 1725–1732. IEEE, 2014. [8] A. Krizhevsky, I. Sutskever, and G. E. Hinton. Imagenet classiﬁcation with deep convolutional neural networks. In Advances in neural information processing systems , pages 1097–1105, 2012. [9] M. Lin, Q. Chen, and S. Yan. Network in network. arXiv preprint arXiv:1312.4400 , 2013. [10] J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recogni- tion, pages 3431–3440, 2015. [11] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein,et al. Imagenet large scale visual recognition challenge. 2014. [12] K. Simonyan and A. Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 , 2014. [13] I. Sutskever, J. Martens, G. Dahl, and G. Hinton. On the importance of initialization and momentum in deep learning. InProceedings of the 30th International Conference on Ma- chine Learning (ICML-13) , volume 28, pages 1139–1147. JMLR Workshop and Conference Proceedings, May 2013. [14] C. Szegedy, W. Liu, Y . Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V . Vanhoucke, and A. Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages 1–9, 2015. [15] C. Szegedy, V . Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna. Rethinking the inception architecture for computer vision. arXiv preprint arXiv:1512.00567 , 2015. [16] T. Tieleman and G. Hinton. Divide the gradient by a run- ning average of its recent magnitude. COURSERA: Neural Networks for Machine Learning, 4, 2012. Accessed: 2015- 11-05. [17] A. Toshev and C. Szegedy. Deeppose: Human pose estima- tion via deep neural networks. In Computer Vision and Pat- tern Recognition (CVPR), 2014 IEEE Conference on , pages 1653–1660. IEEE, 2014. [18] N. Wang and D.-Y . Yeung. Learning a deep compact image representation for visual tracking. In Advances in Neural Information Processing Systems , pages 809–817, 2013.
Neural Embeddings for kNN Search in Biological Sequence Zhihao Chang1, Linzhu Yu2, Yanchao Xu2, Wentao Hu3 1The State Key Laboratory of Blockchain and Data Security, Zhejiang University, Hangzhou, China 2College of Computer Science and Technology, Zhejiang University, Hangzhou, China 3Zhejiang Police College, Hangzhou, China {changzhihao, linzhu, xuyanchao, wthu}@zju.edu.cn Abstract Biological sequence nearest neighbor search plays a fun- damental role in bioinformatics. To alleviate the pain of quadratic complexity for conventional distance computa- tion, neural distance embeddings, which project sequences into geometric space, have been recognized as a promising paradigm. To maintain the distance order between sequences, these models all deploy triplet loss and use intuitive methods to select a subset of triplets for training from a vast selection space. However, we observed that such training often enables models to distinguish only a fraction of distance orders, leav- ing others unrecognized. Moreover, naively selecting more triplets for training under the state-of-the-art network not only adds costs but also hampers model performance. In this paper, we introduce Bio-kNN: a kNN search frame- work for biological sequences. It includes a systematic triplet selection method and a multi-head network, enhancing the discernment of all distance orders without increasing training expenses. Initially, we propose a clustering-based approach to partition all triplets into several clusters with similar prop- erties, and then select triplets from these clusters using an innovative strategy. Meanwhile, we noticed that simultane- ously training different types of triplets in the same network cannot achieve the expected performance, thus we propose a multi-head network to tackle this. Our network employs a convolutional neural network (CNN) to extract local fea- tures shared by all clusters, and then learns a multi-layer per- ception (MLP) head for each cluster separately. Besides, we treat CNN as a special head, thereby integrating crucial lo- cal features which are neglected in previous models into our model for similarity recognition. Extensive experiments show that our Bio-kNN significantly outperforms the state-of-the- art methods on two large-scale datasets without increasing the training cost. Introduction Biological sequence nearest neighbor search plays a fun- damental role in bioinformatics research and serves as the cornerstone for numerous tasks, including gene predic- tion (Chothia and Lesk 1986), homology analysis (Sander and Schneider 1991), sequence clustering (Steinegger and S¨oding 2018; Li and Godzik 2021), etc. Traditional methods for measuring global or local similarity between sequences Copyright © 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.rely on alignment based on dynamic programming. In this paper, we focus on the global similarity between sequences, evaluated by the widely used Needleman-Wunsch (NW) al- gorithm (Needleman and Wunsch 1970). While the NW al- gorithm is proficient in calculating sequence similarity with precision, its inherent quadratic complexity poses signifi- cant challenges for rapid analysis, particularly when dealing with large-scale datasets comprising sequences that extend to hundreds or even thousands of amino acids or nucleotides. In recent years, embedding-based approaches have emerged as a promising paradigm for expediting sequence similarity analysis. These approaches involve projecting se- quences into a geometric embedding space through an em- bedding function, such that the distance between sequences can be approximated by the distance in the embedding space, which offers a computationally efficient alternative. These approaches can be broadly divided into two categories based on the core idea of the embedding function: rule-based and neural network-based. Rule-based approaches (Sims et al. 2009; Gao and Qi 2007; Ulitsky et al. 2006; Haubold et al. 2009; Leimeister and Morgenstern 2014) often rely on some predefined encoding rules. Several studies (Corso et al. 2021; Chen et al. 2022) have indicated that, in multiple tasks, these approaches exhibit inferior performance com- pared to neural network-based ones. Given this context, we will not delve into rule-based approaches, and instead con- centrate on exploring neural network-based approaches. Existing research on neural network-based meth- ods (Zheng et al. 2019; Chen et al. 2022; Zhang, Yuan, and Indyk 2019; Dai et al. 2020; Corso et al. 2021) primarily focused on various components such as encoding models and loss functions. These components are tailored to the task for which the learned embeddings are used. Notably, certain approaches (Zhang, Yuan, and Indyk 2019; Dai et al. 2020) focus on the learning objective aimed at preserving distance orders within the embedding space to facilitate kNN searches. To achieve this goal, these approaches employ triplet loss (Weinberger and Saul 2009; Hermans, Beyer, and Leibe 2017) and use intuitive methods to select triplets in the form (Sacr, Spos, Sneg)for training, in which Sacris the anchor sequence, Sposis the positive sequence that has smaller distance to Sacrthan the negative sequence Sneg. However, we found that the models trained by these methods exhibit proficiency in distance order recognition The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 38A1 2 3 4 5Triplet-Selection: GRU Embedding Embedding6 A1 2 3 4 56A12 3 4 56 A12 3 4 56 Anchor PositiveNegative Not SelectedPull PushTrain-Pair Wrong -Rank-PairTriplet-Selection: CNNED The white numbers in the point indicate the order of distance from the anchorFigure 1: The triplet selection methods used by GRU (Zhang, Yuan, and Indyk 2019) and CNNED (Dai et al. 2020). For GRU, the Top-N closest to the anchor is positive and the others are negative; for CNNED, two sequences are randomly selected from the Top-K closest to the anchor, the closer is positive, and the farther is negative. In this example we set N equal to 2 and K equal to 4. for only a limited subset of triplets, rather than the entire set. As illustrated in Figure 1, while certain order relations may be accurately identified after encoding, overlooked relations during training can substantially compromise the results. Such complications stem from that each sequence lacks a definitive category label, rendering existing tech- niques ineffective in this context. It might be hypothesized that increasing the number of triplets for training could ameliorate this issue. However, our assessments within a state-of-the-art network indicate that such problem has not been alleviated while suffering additional training expanses. In this paper, we introduce Bio-kNN, a biological se- quence kNN search framework. Bio-kNN aims to notably improve the recognition accuracy of distance order dis- tributed throughout the whole space without augmenting training expenses. The core idea of Bio-kNN is to par- tition all triplets into several clusters based on certain properties and learn a feature extraction network for each cluster. Specifically, Bio-kNN features two main modules: (1)Triplet selection method. A notable limitation of pre- vious models is that only a subset of the triplets is consid- ered during training. In this module, we consider all possi- ble combinations of triplets. We partition the selection space into small cells and merge cells with similar distance distri- butions into several clusters. We then employ an innovative strategy to select training triplets from these clusters with-out external samples. (2)Multi-head network. We noticed that merely adding more triplets in the SOTA network does not improve the performance, we thus propose a multi-head network to address it. Our network uses CNN as the back- bone to extract local features, and learns a multi-layer per- ception head for each cluster to extract global features. Fur- thermore, we integrate previously overlooked local features derived from the CNN, which are crucial in discernment. To summarize, we made four contributions in this paper. 1. We consider the entire selection space instead of subsets, and propose a clustering-based triplet selection method. 2. We notice that the performance of SOTA network de- grades when simultaneously training different types of triplets. A multi-head network is designed to alleviate it. 3. We treat CNN as a special head and integrate crucial local features into our model for sequence similarity. 4. We conduct extensive experiments on two large-scale datasets, and the results show that our method signifi- cantly outperforms the state-of-the-art methods. Related Work Rule-Based Approaches. Numerous rule-based approaches have been proposed over the past few decades, which can be broadly classified into two categories. The first cate- gory typically utilizes word frequency statistics with a pre- defined length (Kariin and Burge 1995) or the information content of word frequency distribution (Sims et al. 2009; Gao and Qi 2007) as features to characterize sequence sim- ilarity. On the other hand, the second category of meth- ods is based on the concept of sub-strings (Ulitsky et al. 2006; Haubold et al. 2009; Leimeister and Morgenstern 2014). However, it should be noted that all these approaches are data-independent, and their distance measures rely on heuristic rules. Several studies have shown that these ap- proaches exhibit weaker performance compared to neural network-based approaches across various tasks. Neural Network-Based Approaches. Notable efforts in neural networks have been made to approximate distances for biological sequences in recent years. SENSE (Zheng et al. 2019) is the first attempt to employ neural networks for comparison-free sequence analysis by utilizing a con- volutional neural network. However, SENSE is restricted to handling sequences of the same length. To address it, As- Mac (Chen et al. 2022) was proposed, which employs an ap- proximate string matching algorithm to extract relevant fea- tures through neural network. Regrettably, the performance of this approach degrades when dealing with protein se- quences, primarily due to the massive search space involved. A research domain closely aligned with our work fo- cuses on edit distance embedding. The distinction lies in the NW algorithm’s requirement to normalize the edit dis- tance by a dynamically varying length, thereby amplifying the complexity of discerning similarities. CGK (Ostrovsky and Rabani 2007) embeds the edit distance into the ham- ming space with a distortion of 2O(√logllog log l), however, this algorithm is excessively intricate for practical applica- tion. Zhang et al. (Zhang, Yuan, and Indyk 2019) propose a The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 39Figure 2: Motivating example. For the convenience of observation, the bottom subfigures are the results after comparing with the model trained by randomly selecting triplets, i.e., for each Sacr, two sequences are randomly selected from the training set, the closer to SacrisSpos, and the farther is Sneg. two-layer GRU structure to encode sequences, dividing the training process into three stages and utilizing three differ- ent loss functions. Nonetheless, the embedding dimension generated by this method is relatively high, resulting in sub- stantial memory consumption. CNNED (Dai et al. 2020) dis- covers that an untrained random CNN performs comparable to GRU models, leading to the belief that the CNN is more suitable for the edit distance embedding than RNN-based models. NeuroSEED (Corso et al. 2021) explores the poten- tial of employing global and local transformers to encode biological sequences, and experimental results also affirm that convolutional models surpass feedforward and recurrent models for biological sequence edit distance tasks. Further- more, NeuroSEED proposes that the hyperbolic space can better capture the data dependencies among biological se- quences from the perspective of embedded geometry. Motivating Example In this section, we use an example to reveal the limitations of existing methods. We first model the entire selection space as an upper triangular area. Then we visualize the distribu- tion of training triplets and the performance of the trained model, thus we can easily observe the relationship between them. Example details are as follows. Example Setting We first randomly select 3000 sequences from UniProtKB1 and use 1500 of them as the training set, while the remain- ing1500 as the test set. Then, we employ the state-of-the- art pipeline proposed by CNNED (Dai et al. 2020) as the common training framework, and replace the triplet selec- tion method with five other methods respectively during training, including two methods adopted by previous mod- els: the methods used by CNNED (Dai et al. 2020) and GRU (Zhang, Yuan, and Indyk 2019), and three methods de- signed for comparison: Method-3, Method-4, and Method-5. In Figure 2, we plot the distribution of triplets selected by these five methods on the training set (top subfigures) and the distance order recognition results on the test set (bottom subfigures) respectively. The horizontal and verti- cal coordinates (i, j)of each subfigure in Figure 2 are all 1https://www.uniprot.org/determined by the triplet (Sacr, Spos, Sneg). For each Sacr, we first sort other sequences according to the distance be- tween them and Sacrfrom small to large to form a list, and the indices iandjofSposandSnegin the list are used as the abscissa and ordinate, respectively. The difference be- tween the top and the bottom subfigures is the triplets used for visualization: (1) We plot top subfigures according to the triplets obtained in the training set by the five triplet se- lection methods. The depth of the color indicates the fre- quency of the corresponding triplet is selected. (2) For the bottom subfigures, the triplets are all triplets combinations in the test set, and these subfigures are used to visualize the results of distance order recognition in the test set. We iter- ated all triplet combinations in the test set to check whether the distance between SacrandSposis smaller than the dis- tance between SacrandSnegafter encoding by model f, i.e.,diste(f(Sacr), f(Spos))< dist e(f(Sacr), f(Sneg)), the more frequency of the match, the more vivid the color. Phenomenon From Figure 2, we can observe three following phenomena, including one expected and two inconsistent with the expec- tation but interesting: 1.Expected. Figure 2(a)-(d) illustrate that sequence dis- tance order recognition in the test set is highly correlated with the training triplets. This phenomenon is expected, as the more triplets the model learns for a region in the training set, the better it helps distinguish the order of that region in the test set. However, we can clearly ob- serve that the model trained by these methods can only recognize the order of a small part of the whole area. This observation shows that the model is very limited in identifying crucial regions that lie beyond its training re- gion(e.g., let the model in Figure 2(a) recognize the or- der of the region determined by Method-3). Such limita- tion greatly affects the effectiveness of the model. 2.UnExpected. Inspired by phenomenon 1, an intuitive idea is to select more training regions. We thus trained Method-5, which simultaneously trains the regions se- lected by Method-1, Method-3, and Method-4. However, the recognition results are not consistent with our expec- tation, as shown in the Figure 2(e), although certain re- The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 40gions have been trained, the corresponding regions in the test set do not have better distance order recognition. 3.UnExpected. These figures also illustrate that the model has a radiation effect on regions outside the training re- gion, i.e. even if some regions are not selected, the model is also better able to recognize the order of this region. Furthermore, the radiation region produced by the train- ing region in different positions varies greatly. Method To address the issues arising in phenomenon 2, we propose Bio-kNN, which includes a triplet selection method and a multi-head network. Its framework is shown in Figure 3. Triplet Selection Method Partition Selection Space. As shown in Figure 3(b), we par- tition the entire selection space formed by the training set into small cells. Specifically, we use the same setting as that in the motivating example to model the entire selection space as an upper triangular area, and the length of two legs of the triangle is the number of sequences in the training set. In this setting, for each Sacr, each point in the triangle represents a triplet, where the abscissa represents the index of the Spos, and the ordinate represents the index of the Sneg. Then, we divide the horizontal and vertical axes into Bgroups respectively based on an equal interval δ, where the hori- zontal axis is divided into [[x0, x1),[x1, x2), ...,[xB−1, xB)] and the vertical is [[y0, y1),[y1, y2), ...,[yB−1, yB)]. Thus the upper triangular area is divided intoPB i=1ismall cells, where most of the cells are grids and few are triangles. Then, the coordinates of each cell can be described as (Xi, Yj), where Ximeans [xi, xi+1), and Yjmeans [yj, yj+1). Distribution Statistics in Cell. For each cell after parti- tioning, we use the interval of the coordinates to count the horizontal and vertical distributions. This step is inspired by phenomenon 3 in the motivating example, which shows that some properties between adjacent regions may be similar. In this step, we try to use the intuitive distance distribu- tion as this property. It is worth noting that the possibility of other properties is not ruled out, which can be studied in the future. Next, we use an example to illustrate the details of our approach. Suppose there is a cell with coordinates (X500,600, Y700,800), we use each sequence in the training set as Sacrin turn. For each Sacr, we sort other sequences in the training set according to the NW distance between them andSacrfrom small to large to form a list l. We then count the horizontal distance distribution between all sequences in the list l[500 : 600] andSacrforX500,600, while count l[700 : 800] forY700,800. In this way, the coordinates of each cell can be further described as (Xi, Yj), where Ximeans count ([xi, xi+1)), and Yjmeans count ([yj, yj+1)). Subse- quent cell coordinates will use this definition by default. Distance Measurement between Cells. How to measure the distance between cells with distributions as coordinates becomes a new problem. Currently, there are many functions to measure the distance between two distributions, such as Kullback–Leibler divergence (Kullback and Leibler 1951), Jensen-Shannon divergence (Fuglede and Topsøe 2004), (a) Multi-Head Network (Training) (b) Triplet Selection MethodDistance MeasurementClusteringGrid & CountingOne-hot… … … … Index of Triplet Selection For Index of CNNFigure 3: The Framework of Bio-kNN. Earth mover’s distance (EMD) (Rubner, Tomasi, and Guibas 2000), etc. However, we noticed that when two distributions do not overlap, the KL divergence is meaningless, and the JS divergence is a constant, so neither of these functions is suitable for measuring the distance between cells in our ap- plication scenario. Considering that EMD as a metric sat- isfies non-negativity, symmetry, and triangle inequality, we define the distance between two cells on the basis of EMD. Specifically, given any two cells pandq, their coordinates are(Xpi, Ypj)and(Xqi, Yqj)respectively, then we define the distance dcell(p, q)between pandqis: dcell(p, q) =EMD (Xpi, Xqi) +EMD (Ypj, Yqj)(1) We prove that dcell(p, q)between cells is still a metric. Theorem 1 The distance dcellcomputed by Equation 1 is a metric. Given three any cells p,q, and r, we have: (1) Non-negativity. Ifp!=q, then dcell(p, q)>0. (2) Symmetry. dcell(p, q)=dcell(p, q). (3) Triangle inequality. dcell(p, r)≤dcell(p, q)+dcell(q, r) Proof 1 According to the non-negativity and symmetry of the EMD, it can be easily obtained that dcellalso satisfies the non-negativity and symmetry, so we will only prove the triangle inequality of dcell. dcell(p, r) =EMD (Xpi, Xri) +EMD (Ypj, Yrj) ≤(EMD (Xpi, Xqi) +EMD (Xqi, Xri)) + (EMD (Ypj, Yqj) +EMD (Yqj, Yrj)) = (EMD (Xpi, Xqi) +EMD (Ypj, Yqj) + (EMD (Xqi, Xri) +EMD (Yqj, Yrj)) =dcell(p, q) +dcell(q, r) Cell Clustering. Our last step is to merge those cells that have a similar distance distribution. We achieve this using unsupervised clustering, which is naturally suited to distin- guishing similar items such that distributions vary widely across clusters, while the distribution of cells within a single cluster is very close. In this paper, we do not propose a new clustering algorithm, but directly deploy existing cluster- ing algorithms. In following, we evaluated the performance of commonly used clustering algorithms such as k-means The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 41(Forgy 1965), agglomerative(Murtagh and Contreras 2012), and spectral clustering(von Luxburg 2007). Subsequent ex- periments will show more detailed results. Selection Strategy. Suppose there are mtraining se- quences and nclusters are obtained based on the above method. An intuitive selection strategy is that for each Sacr, We randomly select one point from each of the nclusters at each epoch, and the abscissa of these npoints is the index of the Spos, the ordinate is the index of the Sneg. However, this strategy needs to select m∗ntriplets for training at each epoch. Clearly, the training cost of this strategy increases lin- early with mandn, and it will bring burden to the expansion of the dataset when nhave a large value. We employ a novel selection strategy that can achieve good performance without adding more cost. Specifically, before each epoch of training, we first randomly shuffle all anchor sequences. Then for each batch, we divide all anchor sequences in the current batch evenly into nlists, and assign thenclusters to the nlists as candidate clusters respectively. The strategy at this time is that for each Sacr, we only ran- domly select a point from its corresponding candidate clus- ters instead of all clusters, and the number of training triplets for each epoch is also changed from m∗nton. Multi-Head Network Network Structure. In recent years, several works (Dai et al. 2020; Corso et al. 2021) have shown that convolutional models outperform feedforward and recurrent models for se- quence embedding, so our learning model utilizes the CNN submodule in CNNED (Dai et al. 2020) as a general back- bone. Subsequently, multiple multi-layer perceptron (MLP) heads are deployed in parallel following the convolutional layers, thereby facilitating the fusion of local features from different perspectives to extract global features. In this struc- ture, the number of heads is the same as the number of can- didate clusters k. Each head has exactly the same structure and is trained in parallel without communicating with each other. The core idea of our multi-head model is that we hope to learn one head for each candidate cluster, thus avoiding potential contradictions between candidate selection clusters during training. It is imperative to highlight that our model exhibits an obvious distinction between the training and in- ference phases, we introduce them separately below. Training Phase. During the training phase as shown in Figure 3(a), we first use the selection method introduced in the previous section to select a triplet (Si acr, Si pos, Si neg) for each anchor sequence in a batch. Then, the one-hot em- bedding representations (Xi acr,Xi pos,Xi neg)of all these triplets are simultaneously fed into the CNN, which is en- coded as (yi acr,yi pos,yi neg). After CNN encoding, the flow of these triplets starts to fork, and triplets selected from dif- ferent clusters are fed to different MLP heads. Specifically, The embedding function of our multi-head network during the training phase can be expressed as follows: yi acr,yi pos,yi neg=CNN (Xi acr,Xi pos,Xi neg) zi acr,zi pos,zi neg=MLPi(yi acr,yi pos,yi neg) seq…… …CNNFigure 4: Multi-head Network (Inference). after all triplets are encoded by the model, the final loss is: loss=kX i=1Loss(zi acr,zi pos,zi neg) (2) where krepresents both the number of candidate selection clusters and the number of heads, and Loss is the combina- tion of triplet loss and MSE loss. Inference Phase. As depicted in Figure 4, we feed all se- quences into the trained neutral network one by one during the inference phase. For each sequence, we use the one-hot representation Xof this sequence and encode it through CNN, then feed the feature youtput by CNN to all the MLP heads simultaneously. The outputs [z1, ...,zk]of these heads are then all cascaded together. In addition, we treat CNN as a special head and concatenate the feature youtput by CNN to the end. We will explain the reason for cascad- ing CNN features below. The embedding function during the inference phase can be expressed as follows: y=CNN (X) (3) zi=MLPi(y) (4) the representation of the sequence in embedding space is: Embedding = [z1, ...,zk,y] (5) CNN Serves as a Special Head. The core idea of our net- work is to train distinct MLP heads for each candidate clus- ter. Each of these heads aims to learn unique weights for the local features extracted by the CNN, essentially learning the most discriminative features that can distinguish different sequences within each cluster. However, fine-grained details can easily be ignored during learning. To alleviate the po- tential impact of these fine-grained feature losses, we intro- duce a compensation measure using CNN as a special head in the inference stage. Specifically, we concatenate local fea- tures with the final embedding, which is similar to the effect of fully connected layers with identity matrix and frozen weights. This approach effectively counteracts the adverse consequences of fine-grained features being ignored. Embedding Geometry. There are many studies using various functions to calculate the distance between two em- bedding vectors, including Euclidean distance (Dai et al. 2020), Jaccard distance (Zheng et al. 2019), Hyperbolic dis- tance (Corso et al. 2021), etc. However, for the multi-head network we designed, the final embedding of the sequence is the concatenation of vectors output by multiple heads. In order to make the features of each head play a bigger role in the distance calculation, we use a new metric instead of The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 42directly using the Euclidean distance to calculate the dis- tance between vectors. Specifically, we first calculate the Eu- clidean distance between the vectors output by a single head, and then sum the Euclidean distances of multiple heads as the final distance. Suppose there are two embedding vectors x= [x1, ...,xk,xcnn]andy= [y1, ...,yk,ycnn], then the distance between them can be described as: diste(x,y) =Euc(xcnn,ycnn) +kX i=1Euc(xi,yi)(6) Experiments Experimental Settings Datasets. We evaluate our neural embeddings through the utilization of two extensively recognized datasets(Dai et al. 2020; Zhang, Yuan, and Indyk 2019), i.e., the Uniprot and Uniref. These datasets exhibit varying sizes and sequence lengths, and their properties are shown in the Table 1. Con- sistent with existing works, we partition each dataset into distinct subsets, namely the training set, query set, and base set. Both the training set and the query set are composed of 1,000 sequences, and the other items belong to the base set. Dataset Uniprot Uniref Alphabet Size 25 24 # Items 474741 395869 Avg-Length 376.47 442.84 Min-Length 2 201 Max-Length 4998 4998 Table 1: Dataset Statistics Metrics. We follow existing works (Zhang, Yuan, and In- dyk 2019; Dai et al. 2020) and use the task of nearest neigh- bor search to evaluate the effectiveness of our model, i.e. whether the distance order in the embedding space still pre- serves. Specifically, we use: (1) Top-k hitting ratio (HR@k ). This metric is used to detect the overlap percentage of the top-k results and the ground truth. (2) Top-1 Recall. This one evaluates the performance of finding the most similar sequence to the query sequence by different methods. Baselines. We adopt previous network-based approaches as baselines, including GRU (Zhang, Yuan, and Indyk 2019), CNNED (Dai et al. 2020), NeuroSEED (Corso et al. 2021), AsMac (Chen et al. 2022), where NeuroSEED can be fur- ther divided into Global (Global T.) and Local Transformer (Local T.). Since SENSE (Zheng et al. 2019) cannot be used for unequal-length datasets, and its performance has been proven to be weaker than AsMac, we will not use it as a baseline. To demonstrate the effectiveness of the selection method and multi-head network, we use Bio-kNN-Base to denote the method without cascading CNN features, and re- fer to the complete method as Bio-kNN. Implementation Details. We use the EMBOSS1to com- pute the NW distance between sequences. In our implemen- 1https://www.ebi.ac.uk/Tools/emboss/tation, we set the split interval δ= 100 and experimen- tally tested the effect of various clustering algorithms and the number of clusters. Besides, we directly used the CNN submodule in CNNED. Code and datasets are available at https://github.com/Proudc/Bio-KNN. Experimental results Clustering-Based Triplet Selection. Tables 2 and 3 show the performance of Bio-kNN-Base under various cluster- ing algorithms and the number of clusters, including k- means, agglomerative (HAC), spectral clustering, and non- clustering. These results show that:(1) With a fixed output dimension (128), the performance of Bio-kNN-Base con- sistently surpasses the non-clustering counterpart in various algorithms and the number of clusters, reaffirming the in- dispensability of segmenting the selection space. (2) HAC shows superior performance within certain configurations in contrast to the other two methods. This may be attributed to the ability of HAC to handle outlier cells more efficiently relative to other techniques, which also prompted us to use the HAC by default in subsequent experiments. #Clusters(D/h) Method HR@1 HR@10 HR@50 1∗128 None 48.30 35.48 24.21 2∗64 K-Means 48.60 36 .51 25. 19 2∗64 HAC 48.60 36. 51 25. 19 2∗64 Spectral 48.60 36. 51 25. 19 4∗32 K-Means 49.90 38. 58 26. 98 4 32 HAC 50.50 39.13 27.28 4∗32 Spectral 49.00 36. 60 25. 23 8∗16 K-Means 49.70 37. 90 26. 00 8∗16 HAC 48.80 37. 52 25. 70 8∗16 Spectral 48.30 36. 23 24. 86 Note: D/h indicates the output dimension of each head. Table 2: Uniprot: various clustering methods and # clusters # Clusters(D/h) Method HR@1 HR@10 HR@50 1∗128 None 28.30 24.39 15.60 2∗64 K-Means 31.10 26 .91 17. 54 2 64 HAC 33.90 29.88 19.58 2∗64 Spectral 29.30 25. 88 16. 84 4∗32 K-Means 30.70 25. 83 16. 63 4∗32 HAC 32.40 26. 92 17. 42 4∗32 Spectral 30.00 25. 93 16. 91 8∗16 K-Means 31.70 26. 80 17. 41 8∗16 HAC 32.20 26. 57 17. 34 8∗16 Spectral 31.20 25. 67 16. 90 Table 3: Uniref: various clustering methods and # clusters Embedding Effectiveness. Table 4 presents an overview of the performance exhibited by different methods concern- ing the top-k similarity search task. As shown, on both datasets, our method Bio-kNN significantly outperforms all methods on all metrics. Using the Uniprot dataset as an ex- ample, Bio-kNN yields a remarkable enhancement across The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 43Unipr ot Uniref Model HR@1 HR@5 HR@10 HR@50 HR@1 HR@5 HR@10 HR@50 AsMac 47.07 32 .60 24. 25 9. 93 20.57 11 .93 8. 08 2. 68 GRU 40.83 40 .05 34. 53 23. 16 30.73 26 .53 22. 73 13. 62 CNNED 47.70 40 .43 34. 58 23. 37 35.13 32 .51 28. 55 18. 72 Global T. 48.76 39 .97 34. 16 22. 29 27.80 22 .38 18. 67 10. 47 Local T. 49.10 40 .11 34. 27 22. 43 27.07 21 .23 17. 94 10. 20 Bio-kNN 54.00 48.31 42.69 30.28 37.60 36.18 32.51 21.13 Gap With SOTA +4.90 +7.88 +8.11 +6 .91 +2.47 +3.67 +3.96 +2 .41 Table 4: Embedding Results (repeat three times and report average results) 100101102103104 # Items [k]405060708090100 T op-1 Recall (a) Uniprot100101102103104 # Items [k]20406080100 T op-1 Recall (b) UnirefAsMac GRUGlocal T. Local T.CNNED Bio-kNN Figure 5: Top-1 Recall curves for multiple methods. metrics, ranging from 4.9% to 8.11% when compared to the state-of-the-art counterparts. Notably, a substantial ma- jority of metrics experience an augmentation of over 6%. This non-negligible improvement is impressive given the fact that, unlike previous methods that only focus on partial subsets of triplets, Bio-kNN essentially partitions the entire selection space and learns individual heads for each distinct subspace. Besides, Bio-kNN incorporates the fine-grained local features extracted by CNN, which further improves its ability to distinguish similarities between sequences. We plot the curves of Top-1 recall for various methods on dif- ferent datasets in Figure 5. We observe that our model also achieves significant performance gains on the task of finding the most similar sequence compared to other methods. Ablation Studies. Our Bio-kNN comprises three mod- ules: clustering-based triplet selection, a multi-head net- work, and CNN features. We conduct the following exper- iments to validate the contributions of these modules: (1) Considering that the necessity of segmenting the space has been verified in Table 2 and 3, we exclusively explore spe- cific segmentation methods. We thus independently evaluate the segmentation outcomes on both sides of Figure 6. (2) Re- placing the multi-head (M) network with a single-head (S) network. (3) Omitting the features extracted by CNN. The results in Table 5 demonstrate that neglecting any of the three modules leads to a reduction in performance. The reason is that we take into account the distance distri- bution among cells when segmenting the selection space. 0 200 400 600 800 1000 Index of Spos02004006008001000 Index of Sneg (a) Uniprot: HAC-Based0 200 400 600 800 1000 Index of Spos02004006008001000 Index of Sneg (b) Uniprot: Average-Based 0 200 400 600 800 1000 Index of Spos02004006008001000 Index of Sneg (c) Uniref: HAC-Based0 200 400 600 800 1000 Index of Spos02004006008001000 Index of Sneg (d) Uniref: Average-BasedFigure 6: Segmentation Results of HAC(H) and Average(A) Datasets Method HR@1 HR@10 HR@50 UniprotH+ S + CNN 53.20 41. 02 28. 56 A+ M + CNN 52.03 40. 31 27. 93 H+ M 50.40 39. 01 27. 26 H+ M + CNN 54.00 42.69 30.28 UnirefH+ S + CNN 35.63 30. 31 19. 75 A+ M + CNN 35.43 30. 19 19. 60 H+ M 33.67 28. 95 18. 86 H+ M + CNN 37.60 32.51 21.13 Table 5: Ablation Studies Results Separate heads are assembled for clusters with large dif- ferences in distribution, making training more targeted. The fine-grained features extracted by CNN also effectively en- hance the model’s ability to distinguish sequence similarity. Conclusion We propose Bio-kNN for biological nearest neighbor search, which includes a clustering-based triplet selection method and a CNN-based multi-head network. It also incorporates local features extracted by CNN. Experimental results show that Bio-kNN outperforms the state-of-the-art. The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 44Acknowledgments This work is supported by the Fundamental Research Funds for the Central Universities(No.226-2022-00028). The au- thors would like to thank Zepeng Li for his help with this work, including analysis and discussions. References Chen, J.; Yang, L.; Li, L.; Goodison, S.; and Sun, Y . 2022. Alignment-free comparison of metagenomics sequences via approximate string matching. Bioinformatics Advances, 2(1): vbac077. Chothia, C.; and Lesk, A. M. 1986. The relation between the divergence of sequence and structure in proteins. The EMBO journal, 5(4): 823–826. Corso, G.; Ying, Z.; P ´andy, M.; Velickovic, P.; Leskovec, J.; and Li `o, P. 2021. Neural Distance Embeddings for Biologi- cal Sequences. In NeurIPS, 18539–18551. Dai, X.; Yan, X.; Zhou, K.; Wang, Y .; Yang, H.; and Cheng, J. 2020. Convolutional Embedding for Edit Distance. In ACM SIGIR, 599–608. ACM. Forgy, E. W. 1965. Cluster analysis of multivariate data: ef- ficiency versus interpretability of classifications. biometrics, 21: 768–769. Fuglede, B.; and Topsøe, F. 2004. Jensen-Shannon diver- gence and Hilbert space embedding. In ISIT, 31. IEEE. Gao, L.; and Qi, J. 2007. Whole genome molecular phy- logeny of large dsDNA viruses using composition vector method. BMC evolutionary biology, 7(1): 1–7. Haubold, B.; Pfaffelhuber, P.; Domazet-Los˘ o, M.; and Wiehe, T. 2009. Estimating mutation distances from un- aligned genomes. Journal of Computational Biology, 16(10): 1487–1500. Hermans, A.; Beyer, L.; and Leibe, B. 2017. In defense of the triplet loss for person re-identification. arXiv preprint arXiv:1703.07737. Kariin, S.; and Burge, C. 1995. Dinucleotide relative abun- dance extremes: a genomic signature. Trends in genetics, 11(7): 283–290. Kullback, S.; and Leibler, R. A. 1951. On information and sufficiency. The annals of mathematical statistics, 22(1): 79–86. Leimeister, C.-A.; and Morgenstern, B. 2014. Kmacs: the k-mismatch average common substring approach to alignment-free sequence comparison. Bioinformatics, 30(14): 2000–2008. Li, W.; and Godzik, A. 2021. Cd-hit: a fast program for clustering and comparing large sets of protein or nucleotide sequences. Bioinformatics 22, 1658–1659 (2006). Scientific Reports, 11: 3702. Murtagh, F.; and Contreras, P. 2012. Algorithms for hierar- chical clustering: an overview. WIREs Data Mining Knowl. Discov., 2(1): 86–97. Needleman, S. B.; and Wunsch, C. D. 1970. A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of molecular biology, 48(3): 443–453.Ostrovsky, R.; and Rabani, Y . 2007. Low distortion embed- dings for edit distance. J. ACM, 54(5): 23. Rubner, Y .; Tomasi, C.; and Guibas, L. J. 2000. The Earth Mover’s Distance as a Metric for Image Retrieval. IJCV, 40(2): 99–121. Sander, C.; and Schneider, R. 1991. Database of homology- derived protein structures and the structural meaning of se- quence alignment. Proteins: Structure, Function, and Bioin- formatics, 9(1): 56–68. Sims, G. E.; Jun, S.-R.; Wu, G. A.; and Kim, S.-H. 2009. Alignment-free genome comparison with feature frequency profiles (FFP) and optimal resolutions. Proceedings of the National Academy of Sciences, 106(8): 2677–2682. Steinegger, M.; and S ¨oding, J. 2018. Clustering huge protein sequence sets in linear time. Nature communications, 9(1): 1–8. Ulitsky, I.; Burstein, D.; Tuller, T.; and Chor, B. 2006. The average common substring approach to phylogenomic re- construction. Journal of Computational Biology, 13(2): 336–350. von Luxburg, U. 2007. A tutorial on spectral clustering. Stat. Comput., 17(4): 395–416. Weinberger, K. Q.; and Saul, L. K. 2009. Distance met- ric learning for large margin nearest neighbor classification. Journal of machine learning research, 10(2). Zhang, X.; Yuan, Y .; and Indyk, P. 2019. Neural embeddings for nearest neighbor search under edit distance. Zheng, W.; Yang, L.; Genco, R. J.; Wactawski-Wende, J.; Buck, M.; and Sun, Y . 2019. SENSE: Siamese neural net- work for sequence embedding and alignment-free compari- son. Bioinform., 35(11): 1820–1828. The Thirty-Eighth AAAI Conference on Artiﬁcial Intelligence (AAAI-24) 45
Provided proper attribution is provided, Google hereby grants permission to reproduce the tables and figures in this paper solely for use in journalistic or scholarly works. Attention Is All You Need Ashish Vaswani∗ Google Brain avaswani@google.comNoam Shazeer∗ Google Brain noam@google.comNiki Parmar∗ Google Research nikip@google.comJakob Uszkoreit∗ Google Research usz@google.com Llion Jones∗ Google Research llion@google.comAidan N. Gomez∗ † University of Toronto aidan@cs.toronto.eduŁukasz Kaiser∗ Google Brain lukaszkaiser@google.com Illia Polosukhin∗ ‡ illia.polosukhin@gmail.com Abstract The dominant sequence transduction models are based on complex recurrent or convolutional neural networks that include an encoder and a decoder. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English- to-German translation task, improving over the existing best results, including ensembles, by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data. ∗Equal contribution. Listing order is random. Jakob proposed replacing RNNs with self-attention and started the effort to evaluate this idea. Ashish, with Illia, designed and implemented the first Transformer models and has been crucially involved in every aspect of this work. Noam proposed scaled dot-product attention, multi-head attention and the parameter-free position representation and became the other person involved in nearly every detail. Niki designed, implemented, tuned and evaluated countless model variants in our original codebase and tensor2tensor. Llion also experimented with novel model variants, was responsible for our initial codebase, and efficient inference and visualizations. Lukasz and Aidan spent countless long days designing various parts of and implementing tensor2tensor, replacing our earlier codebase, greatly improving results and massively accelerating our research. †Work performed while at Google Brain. ‡Work performed while at Google Research. 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA.arXiv:1706.03762v7 [cs.CL] 2 Aug 20231 Introduction Recurrent neural networks, long short-term memory [ 13] and gated recurrent [ 7] neural networks in particular, have been firmly established as state of the art approaches in sequence modeling and transduction problems such as language modeling and machine translation [ 35,2,5]. Numerous efforts have since continued to push the boundaries of recurrent language models and encoder-decoder architectures [38, 24, 15]. Recurrent models typically factor computation along the symbol positions of the input and output sequences. Aligning the positions to steps in computation time, they generate a sequence of hidden states ht, as a function of the previous hidden state ht−1and the input for position t. This inherently sequential nature precludes parallelization within training examples, which becomes critical at longer sequence lengths, as memory constraints limit batching across examples. Recent work has achieved significant improvements in computational efficiency through factorization tricks [ 21] and conditional computation [ 32], while also improving model performance in case of the latter. The fundamental constraint of sequential computation, however, remains. Attention mechanisms have become an integral part of compelling sequence modeling and transduc- tion models in various tasks, allowing modeling of dependencies without regard to their distance in the input or output sequences [ 2,19]. In all but a few cases [ 27], however, such attention mechanisms are used in conjunction with a recurrent network. In this work we propose the Transformer, a model architecture eschewing recurrence and instead relying entirely on an attention mechanism to draw global dependencies between input and output. The Transformer allows for significantly more parallelization and can reach a new state of the art in translation quality after being trained for as little as twelve hours on eight P100 GPUs. 2 Background The goal of reducing sequential computation also forms the foundation of the Extended Neural GPU [16], ByteNet [ 18] and ConvS2S [ 9], all of which use convolutional neural networks as basic building block, computing hidden representations in parallel for all input and output positions. In these models, the number of operations required to relate signals from two arbitrary input or output positions grows in the distance between positions, linearly for ConvS2S and logarithmically for ByteNet. This makes it more difficult to learn dependencies between distant positions [ 12]. In the Transformer this is reduced to a constant number of operations, albeit at the cost of reduced effective resolution due to averaging attention-weighted positions, an effect we counteract with Multi-Head Attention as described in section 3.2. Self-attention, sometimes called intra-attention is an attention mechanism relating different positions of a single sequence in order to compute a representation of the sequence. Self-attention has been used successfully in a variety of tasks including reading comprehension, abstractive summarization, textual entailment and learning task-independent sentence representations [4, 27, 28, 22]. End-to-end memory networks are based on a recurrent attention mechanism instead of sequence- aligned recurrence and have been shown to perform well on simple-language question answering and language modeling tasks [34]. To the best of our knowledge, however, the Transformer is the first transduction model relying entirely on self-attention to compute representations of its input and output without using sequence- aligned RNNs or convolution. In the following sections, we will describe the Transformer, motivate self-attention and discuss its advantages over models such as [17, 18] and [9]. 3 Model Architecture Most competitive neural sequence transduction models have an encoder-decoder structure [ 5,2,35]. Here, the encoder maps an input sequence of symbol representations (x1, ..., x n)to a sequence of continuous representations z= (z1, ..., z n). Given z, the decoder then generates an output sequence (y1, ..., y m)of symbols one element at a time. At each step the model is auto-regressive [10], consuming the previously generated symbols as additional input when generating the next. 2Figure 1: The Transformer - model architecture. The Transformer follows this overall architecture using stacked self-attention and point-wise, fully connected layers for both the encoder and decoder, shown in the left and right halves of Figure 1, respectively. 3.1 Encoder and Decoder Stacks Encoder: The encoder is composed of a stack of N= 6 identical layers. Each layer has two sub-layers. The first is a multi-head self-attention mechanism, and the second is a simple, position- wise fully connected feed-forward network. We employ a residual connection [ 11] around each of the two sub-layers, followed by layer normalization [ 1]. That is, the output of each sub-layer is LayerNorm( x+ Sublayer( x)), where Sublayer( x)is the function implemented by the sub-layer itself. To facilitate these residual connections, all sub-layers in the model, as well as the embedding layers, produce outputs of dimension dmodel = 512 . Decoder: The decoder is also composed of a stack of N= 6identical layers. In addition to the two sub-layers in each encoder layer, the decoder inserts a third sub-layer, which performs multi-head attention over the output of the encoder stack. Similar to the encoder, we employ residual connections around each of the sub-layers, followed by layer normalization. We also modify the self-attention sub-layer in the decoder stack to prevent positions from attending to subsequent positions. This masking, combined with fact that the output embeddings are offset by one position, ensures that the predictions for position ican depend only on the known outputs at positions less than i. 3.2 Attention An attention function can be described as mapping a query and a set of key-value pairs to an output, where the query, keys, values, and output are all vectors. The output is computed as a weighted sum 3Scaled Dot-Product Attention Multi-Head Attention Figure 2: (left) Scaled Dot-Product Attention. (right) Multi-Head Attention consists of several attention layers running in parallel. of the values, where the weight assigned to each value is computed by a compatibility function of the query with the corresponding key. 3.2.1 Scaled Dot-Product Attention We call our particular attention "Scaled Dot-Product Attention" (Figure 2). The input consists of queries and keys of dimension dk, and values of dimension dv. We compute the dot products of the query with all keys, divide each by√dk, and apply a softmax function to obtain the weights on the values. In practice, we compute the attention function on a set of queries simultaneously, packed together into a matrix Q. The keys and values are also packed together into matrices KandV. We compute the matrix of outputs as: Attention( Q, K, V ) = softmax(QKT √dk)V (1) The two most commonly used attention functions are additive attention [ 2], and dot-product (multi- plicative) attention. Dot-product attention is identical to our algorithm, except for the scaling factor of1√dk. Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. While the two are similar in theoretical complexity, dot-product attention is much faster and more space-efficient in practice, since it can be implemented using highly optimized matrix multiplication code. While for small values of dkthe two mechanisms perform similarly, additive attention outperforms dot product attention without scaling for larger values of dk[3]. We suspect that for large values of dk, the dot products grow large in magnitude, pushing the softmax function into regions where it has extremely small gradients4. To counteract this effect, we scale the dot products by1√dk. 3.2.2 Multi-Head Attention Instead of performing a single attention function with dmodel-dimensional keys, values and queries, we found it beneficial to linearly project the queries, keys and values htimes with different, learned linear projections to dk,dkanddvdimensions, respectively. On each of these projected versions of queries, keys and values we then perform the attention function in parallel, yielding dv-dimensional 4To illustrate why the dot products get large, assume that the components of qandkare independent random variables with mean 0and variance 1. Then their dot product, q·k=Pdk i=1qiki, has mean 0and variance dk. 4output values. These are concatenated and once again projected, resulting in the final values, as depicted in Figure 2. Multi-head attention allows the model to jointly attend to information from different representation subspaces at different positions. With a single attention head, averaging inhibits this. MultiHead( Q, K, V ) = Concat(head 1, ...,head h)WO where head i= Attention( QWQ i, KWK i, V WV i) Where the projections are parameter matrices WQ i∈Rdmodel×dk,WK i∈Rdmodel×dk,WV i∈Rdmodel×dv andWO∈Rhdv×dmodel. In this work we employ h= 8 parallel attention layers, or heads. For each of these we use dk=dv=dmodel/h= 64 . Due to the reduced dimension of each head, the total computational cost is similar to that of single-head attention with full dimensionality. 3.2.3 Applications of Attention in our Model The Transformer uses multi-head attention in three different ways: •In "encoder-decoder attention" layers, the queries come from the previous decoder layer, and the memory keys and values come from the output of the encoder. This allows every position in the decoder to attend over all positions in the input sequence. This mimics the typical encoder-decoder attention mechanisms in sequence-to-sequence models such as [38, 2, 9]. •The encoder contains self-attention layers. In a self-attention layer all of the keys, values and queries come from the same place, in this case, the output of the previous layer in the encoder. Each position in the encoder can attend to all positions in the previous layer of the encoder. •Similarly, self-attention layers in the decoder allow each position in the decoder to attend to all positions in the decoder up to and including that position. We need to prevent leftward information flow in the decoder to preserve the auto-regressive property. We implement this inside of scaled dot-product attention by masking out (setting to −∞) all values in the input of the softmax which correspond to illegal connections. See Figure 2. 3.3 Position-wise Feed-Forward Networks In addition to attention sub-layers, each of the layers in our encoder and decoder contains a fully connected feed-forward network, which is applied to each position separately and identically. This consists of two linear transformations with a ReLU activation in between. FFN( x) = max(0 , xW 1+b1)W2+b2 (2) While the linear transformations are the same across different positions, they use different parameters from layer to layer. Another way of describing this is as two convolutions with kernel size 1. The dimensionality of input and output is dmodel = 512 , and the inner-layer has dimensionality dff= 2048 . 3.4 Embeddings and Softmax Similarly to other sequence transduction models, we use learned embeddings to convert the input tokens and output tokens to vectors of dimension dmodel. We also use the usual learned linear transfor- mation and softmax function to convert the decoder output to predicted next-token probabilities. In our model, we share the same weight matrix between the two embedding layers and the pre-softmax linear transformation, similar to [ 30]. In the embedding layers, we multiply those weights by√dmodel. 5Table 1: Maximum path lengths, per-layer complexity and minimum number of sequential operations for different layer types. nis the sequence length, dis the representation dimension, kis the kernel size of convolutions and rthe size of the neighborhood in restricted self-attention. Layer Type Complexity per Layer Sequential Maximum Path Length Operations Self-Attention O(n2·d) O(1) O(1) Recurrent O(n·d2) O(n) O(n) Convolutional O(k·n·d2) O(1) O(logk(n)) Self-Attention (restricted) O(r·n·d) O(1) O(n/r) 3.5 Positional Encoding Since our model contains no recurrence and no convolution, in order for the model to make use of the order of the sequence, we must inject some information about the relative or absolute position of the tokens in the sequence. To this end, we add "positional encodings" to the input embeddings at the bottoms of the encoder and decoder stacks. The positional encodings have the same dimension dmodel as the embeddings, so that the two can be summed. There are many choices of positional encodings, learned and fixed [9]. In this work, we use sine and cosine functions of different frequencies: PE(pos,2i)=sin(pos/100002i/d model) PE(pos,2i+1)=cos(pos/100002i/d model) where posis the position and iis the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from 2πto10000 ·2π. We chose this function because we hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset k,PEpos+kcan be represented as a linear function of PEpos. We also experimented with using learned positional embeddings [ 9] instead, and found that the two versions produced nearly identical results (see Table 3 row (E)). We chose the sinusoidal version because it may allow the model to extrapolate to sequence lengths longer than the ones encountered during training. 4 Why Self-Attention In this section we compare various aspects of self-attention layers to the recurrent and convolu- tional layers commonly used for mapping one variable-length sequence of symbol representations (x1, ..., x n)to another sequence of equal length (z1, ..., z n), with xi, zi∈Rd, such as a hidden layer in a typical sequence transduction encoder or decoder. Motivating our use of self-attention we consider three desiderata. One is the total computational complexity per layer. Another is the amount of computation that can be parallelized, as measured by the minimum number of sequential operations required. The third is the path length between long-range dependencies in the network. Learning long-range dependencies is a key challenge in many sequence transduction tasks. One key factor affecting the ability to learn such dependencies is the length of the paths forward and backward signals have to traverse in the network. The shorter these paths between any combination of positions in the input and output sequences, the easier it is to learn long-range dependencies [ 12]. Hence we also compare the maximum path length between any two input and output positions in networks composed of the different layer types. As noted in Table 1, a self-attention layer connects all positions with a constant number of sequentially executed operations, whereas a recurrent layer requires O(n)sequential operations. In terms of computational complexity, self-attention layers are faster than recurrent layers when the sequence 6length nis smaller than the representation dimensionality d, which is most often the case with sentence representations used by state-of-the-art models in machine translations, such as word-piece [38] and byte-pair [ 31] representations. To improve computational performance for tasks involving very long sequences, self-attention could be restricted to considering only a neighborhood of size rin the input sequence centered around the respective output position. This would increase the maximum path length to O(n/r). We plan to investigate this approach further in future work. A single convolutional layer with kernel width k < n does not connect all pairs of input and output positions. Doing so requires a stack of O(n/k)convolutional layers in the case of contiguous kernels, orO(logk(n))in the case of dilated convolutions [ 18], increasing the length of the longest paths between any two positions in the network. Convolutional layers are generally more expensive than recurrent layers, by a factor of k. Separable convolutions [ 6], however, decrease the complexity considerably, to O(k·n·d+n·d2). Even with k=n, however, the complexity of a separable convolution is equal to the combination of a self-attention layer and a point-wise feed-forward layer, the approach we take in our model. As side benefit, self-attention could yield more interpretable models. We inspect attention distributions from our models and present and discuss examples in the appendix. Not only do individual attention heads clearly learn to perform different tasks, many appear to exhibit behavior related to the syntactic and semantic structure of the sentences. 5 Training This section describes the training regime for our models. 5.1 Training Data and Batching We trained on the standard WMT 2014 English-German dataset consisting of about 4.5 million sentence pairs. Sentences were encoded using byte-pair encoding [ 3], which has a shared source- target vocabulary of about 37000 tokens. For English-French, we used the significantly larger WMT 2014 English-French dataset consisting of 36M sentences and split tokens into a 32000 word-piece vocabulary [ 38]. Sentence pairs were batched together by approximate sequence length. Each training batch contained a set of sentence pairs containing approximately 25000 source tokens and 25000 target tokens. 5.2 Hardware and Schedule We trained our models on one machine with 8 NVIDIA P100 GPUs. For our base models using the hyperparameters described throughout the paper, each training step took about 0.4 seconds. We trained the base models for a total of 100,000 steps or 12 hours. For our big models,(described on the bottom line of table 3), step time was 1.0 seconds. The big models were trained for 300,000 steps (3.5 days). 5.3 Optimizer We used the Adam optimizer [ 20] with β1= 0.9,β2= 0.98andϵ= 10−9. We varied the learning rate over the course of training, according to the formula: lrate =d−0.5 model·min(step_num−0.5, step _num·warmup _steps−1.5) (3) This corresponds to increasing the learning rate linearly for the first warmup _steps training steps, and decreasing it thereafter proportionally to the inverse square root of the step number. We used warmup _steps = 4000 . 5.4 Regularization We employ three types of regularization during training: 7Table 2: The Transformer achieves better BLEU scores than previous state-of-the-art models on the English-to-German and English-to-French newstest2014 tests at a fraction of the training cost. ModelBLEU Training Cost (FLOPs) EN-DE EN-FR EN-DE EN-FR ByteNet [18] 23.75 Deep-Att + PosUnk [39] 39.2 1.0·1020 GNMT + RL [38] 24.6 39.92 2.3·10191.4·1020 ConvS2S [9] 25.16 40.46 9.6·10181.5·1020 MoE [32] 26.03 40.56 2.0·10191.2·1020 Deep-Att + PosUnk Ensemble [39] 40.4 8.0·1020 GNMT + RL Ensemble [38] 26.30 41.16 1.8·10201.1·1021 ConvS2S Ensemble [9] 26.36 41.29 7.7·10191.2·1021 Transformer (base model) 27.3 38.1 3.3·1018 Transformer (big) 28.4 41.8 2.3·1019 Residual Dropout We apply dropout [ 33] to the output of each sub-layer, before it is added to the sub-layer input and normalized. In addition, we apply dropout to the sums of the embeddings and the positional encodings in both the encoder and decoder stacks. For the base model, we use a rate of Pdrop= 0.1. Label Smoothing During training, we employed label smoothing of value ϵls= 0.1[36]. This hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score. 6 Results 6.1 Machine Translation On the WMT 2014 English-to-German translation task, the big transformer model (Transformer (big) in Table 2) outperforms the best previously reported models (including ensembles) by more than 2.0 BLEU, establishing a new state-of-the-art BLEU score of 28.4. The configuration of this model is listed in the bottom line of Table 3. Training took 3.5days on 8P100 GPUs. Even our base model surpasses all previously published models and ensembles, at a fraction of the training cost of any of the competitive models. On the WMT 2014 English-to-French translation task, our big model achieves a BLEU score of 41.0, outperforming all of the previously published single models, at less than 1/4the training cost of the previous state-of-the-art model. The Transformer (big) model trained for English-to-French used dropout rate Pdrop= 0.1, instead of 0.3. For the base models, we used a single model obtained by averaging the last 5 checkpoints, which were written at 10-minute intervals. For the big models, we averaged the last 20 checkpoints. We used beam search with a beam size of 4and length penalty α= 0.6[38]. These hyperparameters were chosen after experimentation on the development set. We set the maximum output length during inference to input length + 50, but terminate early when possible [38]. Table 2 summarizes our results and compares our translation quality and training costs to other model architectures from the literature. We estimate the number of floating point operations used to train a model by multiplying the training time, the number of GPUs used, and an estimate of the sustained single-precision floating-point capacity of each GPU5. 6.2 Model Variations To evaluate the importance of different components of the Transformer, we varied our base model in different ways, measuring the change in performance on English-to-German translation on the 5We used values of 2.8, 3.7, 6.0 and 9.5 TFLOPS for K80, K40, M40 and P100, respectively. 8Table 3: Variations on the Transformer architecture. Unlisted values are identical to those of the base model. All metrics are on the English-to-German translation development set, newstest2013. Listed perplexities are per-wordpiece, according to our byte-pair encoding, and should not be compared to per-word perplexities. N d model dff h d k dvPdrop ϵlstrain PPL BLEU params steps (dev) (dev) ×106 base 6 512 2048 8 64 64 0.1 0.1 100K 4.92 25.8 65 (A)1 512 512 5.29 24.9 4 128 128 5.00 25.5 16 32 32 4.91 25.8 32 16 16 5.01 25.4 (B)16 5.16 25.1 58 32 5.01 25.4 60 (C)2 6.11 23.7 36 4 5.19 25.3 50 8 4.88 25.5 80 256 32 32 5.75 24.5 28 1024 128 128 4.66 26.0 168 1024 5.12 25.4 53 4096 4.75 26.2 90 (D)0.0 5.77 24.6 0.2 4.95 25.5 0.0 4.67 25.3 0.2 5.47 25.7 (E) positional embedding instead of sinusoids 4.92 25.7 big 6 1024 4096 16 0.3 300K 4.33 26.4 213 development set, newstest2013. We used beam search as described in the previous section, but no checkpoint averaging. We present these results in Table 3. In Table 3 rows (A), we vary the number of attention heads and the attention key and value dimensions, keeping the amount of computation constant, as described in Section 3.2.2. While single-head attention is 0.9 BLEU worse than the best setting, quality also drops off with too many heads. In Table 3 rows (B), we observe that reducing the attention key size dkhurts model quality. This suggests that determining compatibility is not easy and that a more sophisticated compatibility function than dot product may be beneficial. We further observe in rows (C) and (D) that, as expected, bigger models are better, and dropout is very helpful in avoiding over-fitting. In row (E) we replace our sinusoidal positional encoding with learned positional embeddings [ 9], and observe nearly identical results to the base model. 6.3 English Constituency Parsing To evaluate if the Transformer can generalize to other tasks we performed experiments on English constituency parsing. This task presents specific challenges: the output is subject to strong structural constraints and is significantly longer than the input. Furthermore, RNN sequence-to-sequence models have not been able to attain state-of-the-art results in small-data regimes [37]. We trained a 4-layer transformer with dmodel = 1024 on the Wall Street Journal (WSJ) portion of the Penn Treebank [ 25], about 40K training sentences. We also trained it in a semi-supervised setting, using the larger high-confidence and BerkleyParser corpora from with approximately 17M sentences [37]. We used a vocabulary of 16K tokens for the WSJ only setting and a vocabulary of 32K tokens for the semi-supervised setting. We performed only a small number of experiments to select the dropout, both attention and residual (section 5.4), learning rates and beam size on the Section 22 development set, all other parameters remained unchanged from the English-to-German base translation model. During inference, we 9Table 4: The Transformer generalizes well to English constituency parsing (Results are on Section 23 of WSJ) Parser Training WSJ 23 F1 Vinyals & Kaiser el al. (2014) [37] WSJ only, discriminative 88.3 Petrov et al. (2006) [29] WSJ only, discriminative 90.4 Zhu et al. (2013) [40] WSJ only, discriminative 90.4 Dyer et al. (2016) [8] WSJ only, discriminative 91.7 Transformer (4 layers) WSJ only, discriminative 91.3 Zhu et al. (2013) [40] semi-supervised 91.3 Huang & Harper (2009) [14] semi-supervised 91.3 McClosky et al. (2006) [26] semi-supervised 92.1 Vinyals & Kaiser el al. (2014) [37] semi-supervised 92.1 Transformer (4 layers) semi-supervised 92.7 Luong et al. (2015) [23] multi-task 93.0 Dyer et al. (2016) [8] generative 93.3 increased the maximum output length to input length + 300. We used a beam size of 21andα= 0.3 for both WSJ only and the semi-supervised setting. Our results in Table 4 show that despite the lack of task-specific tuning our model performs sur- prisingly well, yielding better results than all previously reported models with the exception of the Recurrent Neural Network Grammar [8]. In contrast to RNN sequence-to-sequence models [ 37], the Transformer outperforms the Berkeley- Parser [29] even when training only on the WSJ training set of 40K sentences. 7 Conclusion In this work, we presented the Transformer, the first sequence transduction model based entirely on attention, replacing the recurrent layers most commonly used in encoder-decoder architectures with multi-headed self-attention. For translation tasks, the Transformer can be trained significantly faster than architectures based on recurrent or convolutional layers. On both WMT 2014 English-to-German and WMT 2014 English-to-French translation tasks, we achieve a new state of the art. In the former task our best model outperforms even all previously reported ensembles. We are excited about the future of attention-based models and plan to apply them to other tasks. We plan to extend the Transformer to problems involving input and output modalities other than text and to investigate local, restricted attention mechanisms to efficiently handle large inputs and outputs such as images, audio and video. Making generation less sequential is another research goals of ours. The code we used to train and evaluate our models is available at https://github.com/ tensorflow/tensor2tensor . Acknowledgements We are grateful to Nal Kalchbrenner and Stephan Gouws for their fruitful comments, corrections and inspiration. References [1]Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450 , 2016. [2]Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. CoRR , abs/1409.0473, 2014. [3]Denny Britz, Anna Goldie, Minh-Thang Luong, and Quoc V . Le. Massive exploration of neural machine translation architectures. CoRR , abs/1703.03906, 2017. [4]Jianpeng Cheng, Li Dong, and Mirella Lapata. Long short-term memory-networks for machine reading. arXiv preprint arXiv:1601.06733 , 2016. 10[5]Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. CoRR , abs/1406.1078, 2014. [6]Francois Chollet. Xception: Deep learning with depthwise separable convolutions. arXiv preprint arXiv:1610.02357 , 2016. [7]Junyoung Chung, Çaglar Gülçehre, Kyunghyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks on sequence modeling. CoRR , abs/1412.3555, 2014. [8]Chris Dyer, Adhiguna Kuncoro, Miguel Ballesteros, and Noah A. Smith. Recurrent neural network grammars. In Proc. of NAACL , 2016. [9]Jonas Gehring, Michael Auli, David Grangier, Denis Yarats, and Yann N. Dauphin. Convolu- tional sequence to sequence learning. arXiv preprint arXiv:1705.03122v2 , 2017. [10] Alex Graves. Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850 , 2013. [11] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for im- age recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages 770–778, 2016. [12] Sepp Hochreiter, Yoshua Bengio, Paolo Frasconi, and Jürgen Schmidhuber. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies, 2001. [13] Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural computation , 9(8):1735–1780, 1997. [14] Zhongqiang Huang and Mary Harper. Self-training PCFG grammars with latent annotations across languages. In Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing , pages 832–841. ACL, August 2009. [15] Rafal Jozefowicz, Oriol Vinyals, Mike Schuster, Noam Shazeer, and Yonghui Wu. Exploring the limits of language modeling. arXiv preprint arXiv:1602.02410 , 2016. [16] Łukasz Kaiser and Samy Bengio. Can active memory replace attention? In Advances in Neural Information Processing Systems, (NIPS) , 2016. [17] Łukasz Kaiser and Ilya Sutskever. Neural GPUs learn algorithms. In International Conference on Learning Representations (ICLR) , 2016. [18] Nal Kalchbrenner, Lasse Espeholt, Karen Simonyan, Aaron van den Oord, Alex Graves, and Ko- ray Kavukcuoglu. Neural machine translation in linear time. arXiv preprint arXiv:1610.10099v2 , 2017. [19] Yoon Kim, Carl Denton, Luong Hoang, and Alexander M. Rush. Structured attention networks. InInternational Conference on Learning Representations , 2017. [20] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR , 2015. [21] Oleksii Kuchaiev and Boris Ginsburg. Factorization tricks for LSTM networks. arXiv preprint arXiv:1703.10722 , 2017. [22] Zhouhan Lin, Minwei Feng, Cicero Nogueira dos Santos, Mo Yu, Bing Xiang, Bowen Zhou, and Yoshua Bengio. A structured self-attentive sentence embedding. arXiv preprint arXiv:1703.03130 , 2017. [23] Minh-Thang Luong, Quoc V . Le, Ilya Sutskever, Oriol Vinyals, and Lukasz Kaiser. Multi-task sequence to sequence learning. arXiv preprint arXiv:1511.06114 , 2015. [24] Minh-Thang Luong, Hieu Pham, and Christopher D Manning. Effective approaches to attention- based neural machine translation. arXiv preprint arXiv:1508.04025 , 2015. 11[25] Mitchell P Marcus, Mary Ann Marcinkiewicz, and Beatrice Santorini. Building a large annotated corpus of english: The penn treebank. Computational linguistics , 19(2):313–330, 1993. [26] David McClosky, Eugene Charniak, and Mark Johnson. Effective self-training for parsing. In Proceedings of the Human Language Technology Conference of the NAACL, Main Conference , pages 152–159. ACL, June 2006. [27] Ankur Parikh, Oscar Täckström, Dipanjan Das, and Jakob Uszkoreit. A decomposable attention model. In Empirical Methods in Natural Language Processing , 2016. [28] Romain Paulus, Caiming Xiong, and Richard Socher. A deep reinforced model for abstractive summarization. arXiv preprint arXiv:1705.04304 , 2017. [29] Slav Petrov, Leon Barrett, Romain Thibaux, and Dan Klein. Learning accurate, compact, and interpretable tree annotation. In Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the ACL , pages 433–440. ACL, July 2006. [30] Ofir Press and Lior Wolf. Using the output embedding to improve language models. arXiv preprint arXiv:1608.05859 , 2016. [31] Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural machine translation of rare words with subword units. arXiv preprint arXiv:1508.07909 , 2015. [32] Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, and Jeff Dean. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. arXiv preprint arXiv:1701.06538 , 2017. [33] Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdi- nov. Dropout: a simple way to prevent neural networks from overfitting. Journal of Machine Learning Research , 15(1):1929–1958, 2014. [34] Sainbayar Sukhbaatar, Arthur Szlam, Jason Weston, and Rob Fergus. End-to-end memory networks. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems 28 , pages 2440–2448. Curran Associates, Inc., 2015. [35] Ilya Sutskever, Oriol Vinyals, and Quoc VV Le. Sequence to sequence learning with neural networks. In Advances in Neural Information Processing Systems , pages 3104–3112, 2014. [36] Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jonathon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. CoRR , abs/1512.00567, 2015. [37] Vinyals & Kaiser, Koo, Petrov, Sutskever, and Hinton. Grammar as a foreign language. In Advances in Neural Information Processing Systems , 2015. [38] Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint arXiv:1609.08144 , 2016. [39] Jie Zhou, Ying Cao, Xuguang Wang, Peng Li, and Wei Xu. Deep recurrent models with fast-forward connections for neural machine translation. CoRR , abs/1606.04199, 2016. [40] Muhua Zhu, Yue Zhang, Wenliang Chen, Min Zhang, and Jingbo Zhu. Fast and accurate shift-reduce constituent parsing. In Proceedings of the 51st Annual Meeting of the ACL (Volume 1: Long Papers) , pages 434–443. ACL, August 2013. 12Attention Visualizations Input-Input Layer5 It is in this spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult . <EOS> <pad> <pad> <pad> <pad> <pad> <pad> It is in this spirit that a majority of American governments have passed new laws since 2009 making the registration or voting process more difficult . <EOS> <pad> <pad> <pad> <pad> <pad> <pad> Figure 3: An example of the attention mechanism following long-distance dependencies in the encoder self-attention in layer 5 of 6. Many of the attention heads attend to a distant dependency of the verb ‘making’, completing the phrase ‘making...more difficult’. Attentions here shown only for the word ‘making’. Different colors represent different heads. Best viewed in color. 13Input-Input Layer5 The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> Input-Input Layer5 The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad>Figure 4: Two attention heads, also in layer 5 of 6, apparently involved in anaphora resolution. Top: Full attentions for head 5. Bottom: Isolated attentions from just the word ‘its’ for attention heads 5 and 6. Note that the attentions are very sharp for this word. 14Input-Input Layer5 The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> Input-Input Layer5 The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad> The Law will never be perfect , but its application should be just - this is what we are missing , in my opinion . <EOS> <pad>Figure 5: Many of the attention heads exhibit behaviour that seems related to the structure of the sentence. We give two such examples above, from two different heads from the encoder self-attention at layer 5 of 6. The heads clearly learned to perform different tasks. 15

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