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Applications · Chemistry and Drug Discovery

Austin Tripp, Krzysztof Maziarz, Sarah Lewis, Marwin Segler, José Miguel Hernández Lobato

Retrosynthesis is the task of planning a series of chemical reactions to create a desired molecule from simpler, buyable molecules. While previous works have proposed algorithms to find optimal solutions for a range of metrics (e.g. shortest, lowest-cost), these works generally overlook the fact that we have imperfect knowledge of the space of possible reactions, meaning plans created by algorithms may not work in a laboratory. In this paper we propose a novel formulation of retrosynthesis in terms of stochastic processes to account for this uncertainty. We then propose a novel greedy algorithm called retro-fallback which maximizes the probability that at least one synthesis plan can be executed in the lab. Using in-silico benchmarks we demonstrate that retro-fallback generally produces better sets of synthesis plans than the popular MCTS and retro* algorithms.

Theory · Learning Theory

Na Li, Yuchen Jiao, Hangguan Shan, Shefeng Yan

The thriving field of multi-agent reinforcement learning (MARL) studies how a group of interacting agents make decisions autonomously in a shared dynamic environment. Existing theoretical studies in this area suffer from at least two of the following obstacles: memory inefficiency, the heavy dependence of sample complexity on the long horizon and the large state space, the high computational complexity, non-Markov policy, non-Nash policy, and high burn-in cost. In this work, we take a step towards settling this problem by designing a model-free self-play algorithm \emph{Memory-Efficient Nash Q-Learning (ME-Nash-QL)} for two-player zero-sum Markov games, which is a specific setting of MARL. We prove that ME-Nash-QL can output an $\varepsilon$-approximate Nash policy with remarkable space complexity $O(SABH)$, sample complexity $\widetilde{O}(H^4SAB/\varepsilon^2)$, and computational complexity $O(T\mathrm{poly}(AB))$, where $S$ is the number of states, $\{A, B\}$ is the number of actions for the two players, $H$ is the horizon length, and $T$ is the number of samples. Notably, our approach outperforms in terms of space complexity compared to existing algorithms for tabular cases. It achieves the lowest computational complexity while preserving Markov policies, setting a new standard. Furthermore, our algorithm outputs a Nash policy and achieves the best sample complexity compared with the existing guarantee for long horizons, i.e. when $\min \\{ A, B \\} \ll H^2$. Our algorithm also achieves the best burn-in cost $O(SAB\,\mathrm{poly}(H))$, whereas previous algorithms need at least $O(S^3 AB\,\mathrm{poly}(H))$ to attain the same level of sample complexity with ours.

Theory · Learning Theory

Namjun Kim, Chanho Min, Sejun Park

It has been shown that deep neural networks of a large enough width are universal approximators but they are not if the width is too small.There were several attempts to characterize the minimum width $w_{\min}$ enabling the universal approximation property; however, only a few of them found the exact values.In this work, we show that the minimum width for $L^p$ approximation of $L^p$ functions from $[0,1]^{d_x}$ to $\mathbb R^{d_y}$ is exactly $\max\\{d_x,d_y,2\\}$ if an activation function is ReLU-Like (e.g., ReLU, GELU, Softplus).Compared to the known result for ReLU networks, $w_{\min}=\max\\{d_x+1,d_y\\}$ when the domain is ${\mathbb R^{d_x}}$, our result first shows that approximation on a compact domain requires smaller width than on ${\mathbb R^{d_x}}$.We next prove a lower bound on $w_{\min}$ for uniform approximation using general activation functions including ReLU: $w_{\min}\ge d_y+1$ if $d_x<d_y\le2d_x$. Together with our first result, this shows a dichotomy between $L^p$ and uniform approximations for general activation functions and input/output dimensions.

Applications · Chemistry and Drug Discovery

Yanqiao Zhu, Jeehyun Hwang, Keir Adams, Zhen Liu, Bozhao Nan, Brock Stenfors, Yuanqi Du, Jatin Chauhan, Olaf Wiest, Olexandr Isayev 等

Molecular Representation Learning (MRL) has proven impactful in numerous biochemical applications such as drug discovery and enzyme design. While Graph Neural Networks (GNNs) are effective at learning molecular representations from a 2D molecular graph or a single 3D structure, existing works often overlook the flexible nature of molecules, which continuously interconvert across conformations via chemical bond rotations and minor vibrational perturbations. To better account for molecular flexibility, some recent works formulate MRL as an ensemble learning problem, focusing on explicitly learning from a set of conformer structures. However, most of these studies have limited datasets, tasks, and models. In this work, we introduce the first MoleculAR Conformer Ensemble Learning (MARCEL) benchmark to thoroughly evaluate the potential of learning on con- former ensembles and suggest promising research directions. MARCEL includes four datasets covering diverse molecule- and reaction-level properties of chemically diverse molecules including organocatalysts and transition-metal catalysts, extending beyond the scope of common GNN benchmarks that are confined to drug-like molecules. In addition, we conduct a comprehensive empirical study, which benchmarks representative 1D, 2D, and 3D MRL models, along with two strategies that explicitly incorporate conformer ensembles into 3D models. Our findings reveal that direct learning from an accessible conformer space can improve performance on a variety of tasks and models.

Deep Learning · Large Language Models

Yanai Elazar, Akshita Bhagia, Ian Magnusson, Abhilasha Ravichander, Dustin Schwenk, Alane Suhr, Pete Walsh, Dirk Groeneveld, Luca Soldaini, Sameer Singh 等

Large text corpora are the backbone of language models.However, we have a limited understanding of the content of these corpora, including general statistics, quality, social factors, and inclusion of evaluation data (contamination).In this work, we propose What's In My Big Data? (WIMBD), a platform and a set of sixteen analyses that allow us to reveal and compare the contents of large text corpora. WIMBD builds on two basic capabilities---count and search---*at scale*, which allows us to analyze more than 35 terabytes on a standard compute node. We apply WIMBD to ten different corpora used to train popular language models, including *C4*, *The Pile*, and *RedPajama*.Our analysis uncovers several surprising and previously undocumented findings about these corpora, including the high prevalence of duplicate, synthetic, and low-quality content, personally identifiable information, toxic language, and benchmark contamination. For instance, we find that about 50% of the documents in *RedPajama* and *LAION-2B-en* are duplicates. In addition, several datasets used for benchmarking models trained on such corpora are contaminated with respect to important benchmarks, including the Winograd Schema Challenge and parts of GLUE and SuperGLUE.We open-source WIMBD's code and artifacts to provide a standard set of evaluations for new text-based corpora and to encourage more analyses and transparency around them.

Deep Learning · Generative Models and Autoencoders

Hugo Cui, Florent Krzakala, Eric Vanden-Eijnden, Lenka Zdeborova

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number $n$ of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the means of the generated mixture and the mean of the target mixture, which we show decays as $\Theta_n(\frac{1}{n})$. Finally, this rate is shown to be in fact Bayes-optimal.

Applications · Computer Vision

Zhen Yang, Ganggui Ding, Wen Wang, Hao Chen, Bohan Zhuang, Chunhua Shen

Diffusion-based image editing methods have achieved remarkable advances in text-driven image editing. The editing task aims to convert an input image with the original text prompt into the desired image that is well-aligned with the target text prompt. By comparing the original and target prompts, we can obtain numerous editing pairs, each comprising an object and its corresponding editing target. To allow editability while maintaining fidelity to the input image, existing editing methods typically involve a fixed number of inversion steps that project the whole input image to its noisier latent representation, followed by a denoising process guided by the target prompt. However, we find that the optimal number of inversion steps for achieving ideal editing results varies significantly among different editing pairs, owing to varying editing difficulties. Therefore, the current literature, which relies on a fixed number of inversion steps, produces sub-optimal generation quality, especially when handling multiple editing pairs in a natural image.To this end, we propose a new image editing paradigm, dubbed Object-aware Inversion and Reassembly (OIR), to enable object-level fine-grained editing. Specifically, we design a new search metric, which determines the optimal inversion steps for each editing pair, by jointly considering the editability of the target and the fidelity of the non-editing region. We use our search metric to find the optimal inversion step for each editing pair when editing an image. We then edit these editing pairs separately to avoid \concept. Subsequently, we propose an additional reassembly step to seamlessly integrate the respective editing results and the non-editing region to obtain the final edited image. To systematically evaluate the effectiveness of our method, we collect two datasets called OIRBench for benchmarking single- and multi-object editing, respectively. Experiments demonstrate that our method achieves superior performance in editing object shapes, colors, materials, categories, \textit{etc.}, especially in multi-object editing scenarios.The project page can be found in https://aim-uofa.github.io/OIR-Diffusion/.

Applications · Physics

Yehui Tang, Hao Xiong, Nianzu Yang, Tailong Xiao, Junchi Yan

Estimating the properties of quantum systems such as quantum phase has been critical in addressing the essential quantum many-body problems in physics and chemistry. Deep learning models have been recently introduced to property estimation, surpassing conventional statistical approaches. However, these methods are tailored to the specific task and quantum data at hand. It remains an open and attractive question for devising a more universal task-agnostic pretraining model for quantum property estimation. In this paper, we propose LLM4QPE, a large language model style quantum task-agnostic pretraining and finetuning paradigm that 1) performs unsupervised pretraining on diverse quantum systems with different physical conditions; 2) uses the pretrained model for supervised finetuning and delivers high performance with limited training data, on downstream tasks. It mitigates the cost for quantum data collection and speeds up convergence. Extensive experiments show the promising efficacy of LLM4QPE in various tasks including classifying quantum phases of matter on Rydberg atom model and predicting two-body correlation function on anisotropic Heisenberg model.

Deep Learning · Other Representation Learning

Hao Xiong, Yehui Tang, Yunlin He, Wei Tan, Junchi Yan

Network embedding (NE) is a prominent technique for network analysis where the nodes are represented as vectorized embeddings in a continuous space. Existing works tend to resort to the low-dimensional embedding space for efficiency and less risk of over-fitting. In this paper, we explore a new NE paradigm whose embedding dimension goes exponentially high w.r.t. the number of parameters, yet being very efficient and effective. Specifically, the node embeddings are represented as product states that lie in a super high-dimensional (e.g. $2^{32}$-dim) quantum Hilbert space, with a carefully designed optimization approach to guarantee the robustness to work in different scenarios. In the experiments, we show diverse virtues of our methods, including but not limited to: the overwhelming performance on downstream tasks against conventional low-dimensional NE baselines with the similar amount of computing resources, the super high efficiency for a fixed low embedding dimension (e.g. 512) with less than 1/200 memory usage, the robustness when equipped with different objectives and sampling strategies as a fundamental tool for future NE research. As a relatively unexplored topic in literature, the high-dimensional NE paradigm is demonstrated effective both experimentally and theoretically.

Theory · Learning Theory

Mohammadreza Mousavi Kalan, Samory Kpotufe

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might \emph{transfer} information to the target outlier detection task. Despite the recent empirical success of transfer learning in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target in outlier detection remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification---which formalizes \emph{supervised outlier detection}, i.e., unbalanced classification---with the added assumption that we have access to both source and (some or no) target outlier data. Our main results are then as follows:We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer.We then show that, in principle, these information-theoretic limits are achievable by \emph{adaptive} procedures, i.e., procedures with no a priori information on the discrepancy between source and target distributions.

Optimization · Non-Convex

Aaron Zweig, Joan Bruna

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging.In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

Theory · Learning Theory

Axel Laborieux, Friedemann Zenke

Equilibrium propagation (EP) is a compelling alternative to the back propagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to yield unbiased gradient estimates.Both requirements are challenging to implement in physical systems.Yet, whether and how weight asymmetry contributes to bias is unknown because, in practice, its contribution may be masked by a finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias.For complex-differentiable non-symmetric networks, we show that bias due to finite nudge can be avoided by estimating exact derivatives via a Cauchy integral.In contrast, weight asymmetry induces residual bias through poor alignment of EP's neuronal error vectors compared to BP resulting in low task performance.To mitigate the latter issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32$\times$32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

Optimization

Lizhang Chen, Bo Liu, Kaizhao Liang, Qiang Liu

Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It achieves results comparable to AdamW but with greater memory efficiency. As what we can expect from the result of the random search, Lion blends a number of elements from existing algorithms, including signed momentum, decoupled weight decay, Polayk and Nesterov momentum, but doesn't fit into any existing category of theoretically grounded optimizers. Thus, even though Lion appears to perform well as a general-purpose optimizer for a wide range of tasks, its theoretical basis remains uncertain. This absence of theoretical clarity limits opportunities to further enhance and expand Lion's efficacy. This work aims to demystify Lion. Using both continuous-time and discrete-time analysis, we demonstrate that Lion is a novel and theoretically grounded approach for minimizing a general loss function $f(x)$ while enforcing a bound constraint $||x||_\infty \leq 1/\lambda$. Lion achieves this through the incorporation of decoupled weight decay, where $\lambda$ represents the weight decay coefficient. Our analysis is facilitated by the development of a new Lyapunov function for the Lion updates. It applies to a wide range of Lion-$\phi$ algorithms, where the $sign(\cdot)$ operator in Lion is replaced by the subgradient of a convex function $\phi$, leading to the solution of the general composite optimization problem $\min_x f(x) + \phi^*(x)$. Our findings provide valuable insights into the dynamics of Lion and pave the way for further enhancements and extensions of Lion-related algorithms.

Mitchell Wortsman, Peter Liu, Lechao Xiao, Katie Everett, Alexander Alemi, Ben Adlam, John Co-Reyes, Izzeddin Gur, Abhishek Kumar, Roman Novak 等

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the MuParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model characteristics such as activation and gradient norms.

Deep Learning · Self-Supervised Learning

Guodong Wang, Yunhong Wang, Xiuguo Bao, Di Huang

One-class classification (OCC) involves predicting whether a new data is normal or anomalous based solely on the data from a single class during training. Various attempts have been made to learn suitable representations for OCC within a self-supervised framework. Notably, discriminative methods that use geometric visual transformations, such as rotation, to generate pseudo-anomaly samples have exhibited impressive detection performance. Although rotation is commonly viewed as a distribution-shifting transformation and is widely used in the literature, the cause of its effectiveness remains a mystery. In this study, we are the first to make a surprising observation: there exists a strong linear relationship (Pearson's Correlation, $r > 0.9$) between the accuracy of rotation prediction and the performance of OCC. This suggests that a classifier that effectively distinguishes different rotations is more likely to excel in OCC, and vice versa. The root cause of this phenomenon can be attributed to the transformation bias in the dataset, where representations learned from transformations already present in the dataset tend to be less effective, making it essential to accurately estimate the transformation distribution before utilizing pretext tasks involving these transformations for reliable self-supervised representation learning. To the end, we propose a novel two-stage method to estimate the transformation distribution within the dataset. In the first stage, we learn general representations through standard contrastive pre-training. In the second stage, we select potentially semantics-preserving samples from the entire augmented dataset, which includes all rotations, by employing density matching with the provided reference distribution. By sorting samples based on semantics-preserving versus shifting transformations, we achieve improved performance on OCC benchmarks.

Deep Learning · Graph Neural Networks

Nan Chen, Zemin Liu, Bryan Hooi, Bingsheng He, Rizal Fathony, Jun Hu, Jia Chen

Graph Anomaly Detection (GAD) has surfaced as a significant field of research, predominantly due to its substantial influence in production environments. Although existing approaches for node anomaly detection have shown effectiveness, they have yet to fully address two major challenges: operating in settings with limited supervision and managing class imbalance effectively. In response to these challenges, we propose a novel model, ConsisGAD, which is tailored for GAD in scenarios characterized by limited supervision and is anchored in the principles of consistency training. Under limited supervision, ConsisGAD effectively leverages the abundance of unlabeled data for consistency training by incorporating a novel learnable data augmentation mechanism, thereby introducing controlled noise into the dataset. Moreover, ConsisGAD takes advantage of the variance in homophily distribution between normal and anomalous nodes to craft a simplified GNN backbone, enhancing its capability to distinguish effectively between these two classes. Comprehensive experiments on several benchmark datasets validate the superior performance of ConsisGAD in comparison to state-of-the-art baselines. Our code is available at https://github.com/Xtra-Computing/ConsisGAD.

Deep Learning · Large Language Models

Shanda Li, Chong You, Guru Guruganesh, Joshua Ainslie, Santiago Ontanon, Manzil Zaheer, Sumit Sanghai, Yiming Yang, Sanjiv Kumar, Srinadh Bhojanapalli

Preventing the performance decay of Transformers on inputs longer than those used for training has been an important challenge in extending the context length of these models. Though the Transformer architecture has fundamentally no limits on the input sequence lengths it can process, the choice of position encoding used during training can limit the performance of these models on longer inputs. We propose a novel functional relative position encoding with progressive interpolation, FIRE, to improve Transformer generalization to longer contexts. We theoretically prove that this can represent some of the popular relative position encodings, such as T5's RPE, Alibi, and Kerple. We next empirically show that FIRE models have better generalization to longer contexts on both zero-shot language modeling and long text benchmarks.

Theory · Learning Theory

Shi Fu, Fengxiang He, Xinmei Tian, Dacheng Tao

This paper presents the first theoretical guarantee for Bayesian bilevel optimization (BBO) that we term for the prevalent bilevel framework combining Bayesian optimization at the outer level to tune hyperparameters, and the inner-level stochastic gradient descent (SGD) for training the model. We prove sublinear regret bounds suggesting simultaneous convergence of the inner-level model parameters and outer-level hyperparameters to optimal configurations for generalization capability. A pivotal, technical novelty in the proofs is modeling the excess risk of the SGD-trained parameters as evaluation noise during Bayesian optimization. Our theory implies the inner unit horizon, defined as the number of SGD iterations, shapes the convergence behavior of BBO. This suggests practical guidance on configuring the inner unit horizon to enhance training efficiency and model performance.

Applications · Computer Vision

Yuanwen Yue, Sabarinath Mahadevan, Jonas Schult, Francis Engelmann, Bastian Leibe, Konrad Schindler, Theodora Kontogianni

During interactive segmentation, a model and a user work together to delineate objects of interest in a 3D point cloud. In an iterative process, the model assigns each data point to an object (or the background), while the user corrects errors in the resulting segmentation and feeds them back into the model. The current best practice formulates the problem as binary classification and segments objects one at a time. The model expects the user to provide positive clicks to indicate regions wrongly assigned to the background and negative clicks on regions wrongly assigned to the object. Sequentially visiting objects is wasteful since it disregards synergies between objects: a positive click for a given object can, by definition, serve as a negative click for nearby objects. Moreover, a direct competition between adjacent objects can speed up the identification of their common boundary. We introduce AGILE3D, an efficient, attention-based model that (1) supports simultaneous segmentation of multiple 3D objects, (2) yields more accurate segmentation masks with fewer user clicks, and (3) offers faster inference. Our core idea is to encode user clicks as spatial-temporal queries and enable explicit interactions between click queries as well as between them and the 3D scene through a click attention module. Every time new clicks are added, we only need to run a lightweight decoder that produces updated segmentation masks. In experiments with four different 3D point cloud datasets, AGILE3D sets a new state-of-the-art. Moreover, we also verify its practicality in real-world setups with real user studies. Project page: https://ywyue.github.io/AGILE3D.

Applications · Computer Vision

Junsong Chen, Jincheng YU, Chongjian GE, Lewei Yao, Enze Xie, Zhongdao Wang, James Kwok, Ping Luo, Huchuan Lu, Zhenguo Li

The most advanced text-to-image (T2I) models require significant training costs (e.g., millions of GPU hours), seriously hindering the fundamental innovation for the AIGC community while increasing CO2 emissions. This paper introduces PixArt-$\alpha$, a Transformer-based T2I diffusion model whose image generation quality is competitive with state-of-the-art image generators (e.g., Imagen, SDXL, and even Midjourney), reaching near-commercial application standards. Additionally, it supports high-resolution image synthesis up to 1024px resolution with low training cost, as shown in Figure 1 and 2. To achieve this goal, three core designs are proposed: (1) Training strategy decomposition: We devise three distinct training steps that separately optimize pixel dependency, text-image alignment, and image aesthetic quality; (2) Efficient T2I Transformer: We incorporate cross-attention modules into Diffusion Transformer (DiT) to inject text conditions and streamline the computation-intensive class-condition branch; (3) High-informative data: We emphasize the significance of concept density in text-image pairs and leverage a large Vision-Language model to auto-label dense pseudo-captions to assist text-image alignment learning. As a result, PixArt-$\alpha$'s training speed markedly surpasses existing large-scale T2I models, e.g., PixArt-$\alpha$ only takes 10.8% of Stable Diffusion v1.5's training time (~675 vs. ~6,250 A100 GPU days), saving nearly \\$300,000 (\\$26,000 vs. \\$320,000) and reducing 90% CO2 emissions. Moreover, compared with a larger SOTA model, RAPHAEL, our training cost is merely 1%. Extensive experiments demonstrate that PixArt-$\alpha$ excels in image quality, artistry, and semantic control. We hope PixArt-$\alpha$ will provide new insights to the AIGC community and startups to accelerate building their own high-quality yet low-cost generative models from scratch.