论文检索

Applications/Climate

Mélisande Teng, Amna Elmustafa, Benjamin Akera, Yoshua Bengio, Hager Radi, Hugo Larochelle, David Rolnick

Biodiversity is declining at an unprecedented rate, impacting ecosystem services necessary to ensure food, water, and human health and well-being. Understanding the distribution of species and their habitats is crucial for conservation policy planning. However, traditional methods in ecology for species distribution models (SDMs) generally focus either on narrow sets of species or narrow geographical areas and there remain significant knowledge gaps about the distribution of species. A major reason for this is the limited availability of data traditionally used, due to the prohibitive amount of effort and expertise required for traditional field monitoring. The wide availability of remote sensing data and the growing adoption of citizen science tools to collect species observations data at low cost offer an opportunity for improving biodiversity monitoring and enabling the modelling of complex ecosystems. We introduce a novel task for mapping bird species to their habitats by predicting species encounter rates from satellite images, and present SatBird, a satellite dataset of locations in the USA with labels derived from presence-absence observation data from the citizen science database eBird, considering summer (breeding) and winter seasons. We also provide a dataset in Kenya representing low-data regimes. We additionally provide environmental data and species range maps for each location. We benchmark a set of baselines on our dataset, including SOTA models for remote sensing tasks. SatBird opens up possibilities for scalably modelling properties of ecosystems worldwide.

Applications/Climate

Andrea Nascetti, Ritu Yadav, Kirill Brodt, Qixun Qu, Hongwei Fan, Yuri Shendryk, Isha Shah, Christine Chung

Above Ground Biomass is an important variable as forests play a crucial role in mitigating climate change as they act as an efficient, natural and cost-effective carbon sink. Traditional field and airborne LiDAR measurements have been proven to provide reliable estimations of forest biomass. Nevertheless, the use of these techniques at a large scale can be challenging and expensive. Satellite data have been widely used as a valuable tool in estimating biomass on a global scale. However, the full potential of dense multi-modal satellite time series data, in combination with modern deep learning approaches, has yet to be fully explored. The aim of the "BioMassters" data challenge and benchmark dataset is to investigate the potential of multi-modal satellite data (Sentinel-1 SAR and Sentinel-2 MSI) to estimate forest biomass at a large scale using the Finnish Forest Centre's open forest and nature airborne LiDAR data as a reference. The performance of the top three baseline models shows the potential of deep learning to produce accurate and higher-resolution biomass maps. Our benchmark dataset is publically available at https://huggingface.co/datasets/nascetti-a/BioMassters (doi:10.57967/hf/1009) and the implementation of the top three winning models are available at https://github.com/drivendataorg/the-biomassters.

Applications/Neuroscience, Cognitive Science

Kushin Mukherjee, Holly Huey, Xuanchen Lu, Yael Vinker, Rio Aguina-Kang, Ariel Shamir, Judith Fan

Sketching is a powerful tool for creating abstract images that are sparse but meaningful. Sketch understanding poses fundamental challenges for general-purpose vision algorithms because it requires robustness to the sparsity of sketches relative to natural visual inputs and because it demands tolerance for semantic ambiguity, as sketches can reliably evoke multiple meanings. While current vision algorithms have achieved high performance on a variety of visual tasks, it remains unclear to what extent they understand sketches in a human-like way. Here we introduce $\texttt{SEVA}$, a new benchmark dataset containing approximately 90K human-generated sketches of 128 object concepts produced under different time constraints, and thus systematically varying in sparsity. We evaluated a suite of state-of-the-art vision algorithms on their ability to correctly identify the target concept depicted in these sketches and to generate responses that are strongly aligned with human response patterns on the same sketch recognition task. We found that vision algorithms that better predicted human sketch recognition performance also better approximated human uncertainty about sketch meaning, but there remains a sizable gap between model and human response patterns. To explore the potential of models that emulate human visual abstraction in generative tasks, we conducted further evaluations of a recently developed sketch generation algorithm (Vinker et al., 2022) capable of generating sketches that vary in sparsity. We hope that public release of this dataset and evaluation protocol will catalyze progress towards algorithms with enhanced capacities for human-like visual abstraction.

Applications/Computer Vision

Qihang Yu, Ju He, Xueqing Deng, Xiaohui Shen, Liang-Chieh Chen

Open-vocabulary segmentation is a challenging task requiring segmenting and recognizing objects from an open set of categories in diverse environments. One way to address this challenge is to leverage multi-modal models, such as CLIP, to provide image and text features in a shared embedding space, which effectively bridges the gap between closed-vocabulary and open-vocabulary recognition.Hence, existing methods often adopt a two-stage framework to tackle the problem, where the inputs first go through a mask generator and then through the CLIP model along with the predicted masks. This process involves extracting features from raw images multiple times, which can be ineffective and inefficient. By contrast, we propose to build everything into a single-stage framework using a _shared **F**rozen **C**onvolutional **CLIP** backbone_, which not only significantly simplifies the current two-stage pipeline, but also remarkably yields a better accuracy-cost trade-off. The resulting single-stage system, called FC-CLIP, benefits from the following observations: the _frozen_ CLIP backbone maintains the ability of open-vocabulary classification and can also serve as a strong mask generator, and the _convolutional_ CLIP generalizes well to a larger input resolution than the one used during contrastive image-text pretraining. Surprisingly, FC-CLIP advances state-of-the-art results on various benchmarks, while running practically fast. Specifically, when training on COCO panoptic data only and testing in a zero-shot manner, FC-CLIP achieve 26.8 PQ, 16.8 AP, and 34.1 mIoU on ADE20K, 18.2 PQ, 27.9 mIoU on Mapillary Vistas, 44.0 PQ, 26.8 AP, 56.2 mIoU on Cityscapes, outperforming the prior art under the same setting by +4.2 PQ, +2.4 AP, +4.2 mIoU on ADE20K, +4.0 PQ on Mapillary Vistas and +20.1 PQ on Cityscapes, respectively. Additionally, the training and testing time of FC-CLIP is 7.5x and 6.6x significantly faster than the same prior art, while using 5.9x fewer total model parameters. Meanwhile, FC-CLIP also sets a new state-of-the-art performance across various open-vocabulary semantic segmentation datasets. Code and models are available at https://github.com/bytedance/fc-clip

Reinforcement Learning/Batch Offline

Zexu Sun, Bowei He, Jinxin Liu, Xu Chen, Chen Ma, Shuai Zhang

In offline imitation learning (IL), an agent aims to learn an optimal expert behavior policy without additional online environment interactions. However, in many real-world scenarios, such as robotics manipulation, the offline dataset is collected from suboptimal behaviors without rewards. Due to the scarce expert data, the agents usually suffer from simply memorizing poor trajectories and are vulnerable to the variations in the environments, lacking the capability of generalizing to new environments.To automatically generate high-quality expert data and improve the generalization ability of the agent, we propose a framework named \underline{O}ffline \underline{I}mitation \underline{L}earning with \underline{C}ounterfactual data \underline{A}ugmentation (OILCA) by doing counterfactual inference. In particular, we leverage identifiable variational autoencoder to generate \textit{counterfactual} samples for expert data augmentation. We theoretically analyze the influence of the generated expert data and the improvement of generalization. Moreover, we conduct extensive experiments to demonstrate that our approach significantly outperforms various baselines on both \textsc{DeepMind Control Suite} benchmark for in-distribution performance and \textsc{CausalWorld} benchmark for out-of-distribution generalization.

Applications/Computer Vision

Yushan Zhang, Johan Edstedt, Bastian Wandt, Per-Erik Forssen, Maria Magnusson, Michael Felsberg

We tackle the task of scene flow estimation from point clouds. Given a source and a target point cloud, the objective is to estimate a translation from each point in the source point cloud to the target, resulting in a 3D motion vector field. Previous dominant scene flow estimation methods require complicated coarse-to-fine or recurrent architectures as a multi-stage refinement. In contrast, we propose a significantly simpler single-scale one-shot global matching to address the problem. Our key finding is that reliable feature similarity between point pairs is essential and sufficient to estimate accurate scene flow. We thus propose to decompose the feature extraction step via a hybrid local-global-cross transformer architecture which is crucial to accurate and robust feature representations. Extensive experiments show that the proposed Global Matching Scene Flow (GMSF) sets a new state-of-the-art on multiple scene flow estimation benchmarks. On FlyingThings3D, with the presence of occlusion points, GMSF reduces the outlier percentage from the previous best performance of 27.4% to 5.6%. On KITTI Scene Flow, without any fine-tuning, our proposed method shows state-of-the-art performance. On the Waymo-Open dataset, the proposed method outperforms previous methods by a large margin. The code is available at https://github.com/ZhangYushan3/GMSF.

Deep Learning/Graph Neural Networks

Tianyu Liu, Yuge Wang, Rex Ying, Hongyu Zhao

Discovering genes with similar functions across diverse biomedical contexts poses a significant challenge in gene representation learning due to data heterogeneity. In this study, we resolve this problem by introducing a novel model called Multimodal Similarity Learning Graph Neural Network, which combines Multimodal Machine Learning and Deep Graph Neural Networks to learn gene representations from single-cell sequencing and spatial transcriptomic data. Leveraging 82 training datasets from 10 tissues, three sequencing techniques, and three species, we create informative graph structures for model training and gene representations generation, while incorporating regularization with weighted similarity learning and contrastive learning to learn cross-data gene-gene relationships. This novel design ensures that we can offer gene representations containing functional similarity across different contexts in a joint space. Comprehensive benchmarking analysis shows our model's capacity to effectively capture gene function similarity across multiple modalities, outperforming state-of-the-art methods in gene representation learning by up to $\textbf{100.4}$%. Moreover, we employ bioinformatics tools in conjunction with gene representations to uncover pathway enrichment, regulation causal networks, and functions of disease-associated genes. Therefore, our model efficiently produces unified gene representations for the analysis of gene functions, tissue functions, diseases, and species evolution.

Deep Learning/Generative Models and Autoencoders

Evangelos Ntavelis, Aliaksandr Siarohin, Kyle Olszewski, Chaoyang Wang, Luc V Gool, Sergey Tulyakov

Diffusion-based methods have shown impressive visual results in the text-to-image domain. They first learn a latent space using an autoencoder, then run a denoising process on the bottleneck to generate new samples. However, learning an autoencoder requires substantial data in the target domain. Such data is scarce for 3D generation, prohibiting the learning of large-scale diffusion models for 3D synthesis. We present a novel approach to the generation of static and articulated 3D assets that has a 3D autodecoder at its core. The 3D autodecoder framework embeds properties learned from the target dataset in the latent space, which can then be decoded into a volumetric representation for rendering view-consistent appearance and geometry. We then identify the appropriate intermediate volumetric latent space, and introduce robust normalization and de-normalization operations to learn a 3D diffusion from 2D images or monocular videos of rigid or articulated objects. Our approach is flexible enough to use either existing camera supervision or no camera information at all -- instead efficiently learning it during training. Our evaluations demonstrate that our generation results outperform state-of-the-art alternatives on various benchmark datasets and metrics, including multi-view image datasets of synthetic objects, real in-the-wild videos of moving people, and a large-scale, real video dataset of static objects.

Applications/Computer Vision

Xiuye Gu, Yin Cui, Jonathan Huang, Abdullah Rashwan, Xuan Yang, Xingyi Zhou, Golnaz Ghiasi, Weicheng Kuo, Huizhong Chen, Liang-Chieh Chen 等

Observing the close relationship among panoptic, semantic and instance segmentation tasks, we propose to train a universal multi-dataset multi-task segmentation model: DaTaSeg. We use a shared representation (mask proposals with class predictions) for all tasks. To tackle task discrepancy, we adopt different merge operations and post-processing for different tasks. We also leverage weak-supervision, allowing our segmentation model to benefit from cheaper bounding box annotations. To share knowledge across datasets, we use text embeddings from the same semantic embedding space as classifiers and share all network parameters among datasets. We train DaTaSeg on ADE semantic, COCO panoptic, and Objects365 detection datasets. DaTaSeg improves performance on all datasets, especially small-scale datasets, achieving 54.0 mIoU on ADE semantic and 53.5 PQ on COCO panoptic. DaTaSeg also enables weakly-supervised knowledge transfer on ADE panoptic and Objects365 instance segmentation. Experiments show DaTaSeg scales with the number of training datasets and enables open-vocabulary segmentation through direct transfer. In addition, we annotate an Objects365 instance segmentation set of 1,000 images and release it as a public evaluation benchmark on https://laoreja.github.io/dataseg.

Applications/Computer Vision

Minghua Liu, Ruoxi Shi, Kaiming Kuang, Yinhao Zhu, Xuanlin Li, Shizhong Han, Hong Cai, Fatih Porikli, Hao Su

We introduce OpenShape, a method for learning multi-modal joint representations of text, image, and point clouds. We adopt the commonly used multi-modal contrastive learning framework for representation alignment, but with a specific focus on scaling up 3D representations to enable open-world 3D shape understanding. To achieve this, we scale up training data by ensembling multiple 3D datasets and propose several strategies to automatically filter and enrich noisy text descriptions. We also explore and compare strategies for scaling 3D backbone networks and introduce a novel hard negative mining module for more efficient training. We evaluate OpenShape on zero-shot 3D classification benchmarks and demonstrate its superior capabilities for open-world recognition. Specifically, OpenShape achieves a zero-shot accuracy of 46.8% on the 1,156-category Objaverse-LVIS benchmark, compared to less than 10% for existing methods. OpenShape also achieves an accuracy of 85.3% on ModelNet40, outperforming previous zero-shot baseline methods by 20% and performing on par with some fully-supervised methods. Furthermore, we show that our learned embeddings encode a wide range of visual and semantic concepts (e.g., subcategories, color, shape, style) and facilitate fine-grained text-3D and image-3D interactions. Due to their alignment with CLIP embeddings, our learned shape representations can also be integrated with off-the-shelf CLIP-based models for various applications, such as point cloud captioning and point cloud-conditioned image generation.

Optimization/Learning for Optimization

Garrett Bingham, Risto Miikkulainen

Carefully designed activation functions can improve the performance of neural networks in many machine learning tasks. However, it is difficult for humans to construct optimal activation functions, and current activation function search algorithms are prohibitively expensive. This paper aims to improve the state of the art through three steps: First, the benchmark datasets Act-Bench-CNN, Act-Bench-ResNet, and Act-Bench-ViT were created by training convolutional, residual, and vision transformer architectures from scratch with 2,913 systematically generated activation functions. Second, a characterization of the benchmark space was developed, leading to a new surrogate-based method for optimization. More specifically, the spectrum of the Fisher information matrix associated with the model's predictive distribution at initialization and the activation function's output distribution were found to be highly predictive of performance. Third, the surrogate was used to discover improved activation functions in several real-world tasks, with a surprising finding: a sigmoidal design that outperformed all other activation functions was discovered, challenging the status quo of always using rectifier nonlinearities in deep learning. Each of these steps is a contribution in its own right; together they serve as a practical and theoretical foundation for further research on activation function optimization.

Deep Learning/Sequential Models, Time series

Vinitra Swamy, Malika Satayeva, Jibril Frej, Thierry Bossy, Thijs Vogels, Martin Jaggi, Tanja Käser, Mary-Anne Hartley

Predicting multiple real-world tasks in a single model often requires a particularly diverse feature space. Multimodal (MM) models aim to extract the synergistic predictive potential of multiple data types to create a shared feature space with aligned semantic meaning across inputs of drastically varying sizes (i.e. images, text, sound). Most current MM architectures fuse these representations in parallel, which not only limits their interpretability but also creates a dependency on modality availability. We present MultiModN, a multimodal, modular network that fuses latent representations in a sequence of any number, combination, or type of modality while providing granular real-time predictive feedback on any number or combination of predictive tasks. MultiModN's composable pipeline is interpretable-by-design, as well as innately multi-task and robust to the fundamental issue of biased missingness. We perform four experiments on several benchmark MM datasets across 10 real-world tasks (predicting medical diagnoses, academic performance, and weather), and show that MultiModN's sequential MM fusion does not compromise performance compared with a baseline of parallel fusion. By simulating the challenging bias of missing not-at-random (MNAR), this work shows that, contrary to MultiModN, parallel fusion baselines erroneously learn MNAR and suffer catastrophic failure when faced with different patterns of MNAR at inference. To the best of our knowledge, this is the first inherently MNAR-resistant approach to MM modeling. In conclusion, MultiModN provides granular insights, robustness, and flexibility without compromising performance.

Deep Learning/Everything Else

Rui Yang, Lin Song, Yanwei Li, Sijie Zhao, Yixiao Ge, Xiu Li, Ying Shan

This paper aims to efficiently enable Large Language Models (LLMs) to use multi-modal tools.The advanced proprietary LLMs, such as ChatGPT and GPT-4, have shown great potential for tool usage through sophisticated prompt engineering.Nevertheless, these models typically rely on prohibitive computational costs and publicly inaccessible data.To address these challenges, we propose the GPT4Tools based on self-instruct to enable open-source LLMs, such as LLaMA and OPT, to use tools.It generates an instruction-following dataset by prompting an advanced teacher with various multi-modal contexts.By using the Low-Rank Adaptation (LoRA) optimization, our approach facilitates the open-source LLMs to solve a range of visual problems, including visual comprehension and image generation.Moreover, we provide a benchmark to evaluate the ability of LLMs to use tools, which is performed in both zero-shot and fine-tuning ways.Extensive experiments demonstrate the effectiveness of our method on various language models, which not only significantly improves the accuracy of invoking seen tools, but also enables the zero-shot capacity for unseen tools.

Social Aspects/Trustworthy Machine Learning

Ruixiang (Ryan) Tang, Jiayi Yuan, Yiming Li, Zirui Liu, Rui Chen, Xia Hu

In the field of natural language processing, the prevalent approach involves fine-tuning pretrained language models (PLMs) using local samples. Recent research has exposed the susceptibility of PLMs to backdoor attacks, wherein the adversaries can embed malicious prediction behaviors by manipulating a few training samples. In this study, our objective is to develop a backdoor-resistant tuning procedure that yields a backdoor-free model, no matter whether the fine-tuning dataset contains poisoned samples. To this end, we propose and integrate an \emph{honeypot module} into the original PLM, specifically designed to absorb backdoor information exclusively. Our design is motivated by the observation that lower-layer representations in PLMs carry sufficient backdoor features while carrying minimal information about the original tasks. Consequently, we can impose penalties on the information acquired by the honeypot module to inhibit backdoor creation during the fine-tuning process of the stem network. Comprehensive experiments conducted on benchmark datasets substantiate the effectiveness and robustness of our defensive strategy. Notably, these results indicate a substantial reduction in the attack success rate ranging from 10\% to 40\% when compared to prior state-of-the-art methods.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Zicheng Liu, Siyuan Li, Ge Wang, Lirong Wu, Cheng Tan, Stan Z. Li

Mixup is an efficient data augmentation approach that improves the generalization of neural networks by smoothing the decision boundary with mixed data. Recently, dynamic mixup methods have improved previous \textit{static} policies effectively (e.g., linear interpolation) by maximizing target-related salient regions in mixed samples, but excessive additional time costs are not acceptable. These additional computational overheads mainly come from optimizing the mixed samples according to the mixed labels. However, we found that the extra optimizing step may be redundant because label-mismatched mixed samples are informative hard mixed samples for deep models to localize discriminative features. In this paper, we thus are not trying to propose a more complicated dynamic mixup policy but rather an efficient mixup objective function with decoupled regularizer, named decoupled mixup (DM). The primary effect is that DM can adaptively utilize those hard mixed samples to mine discriminative features without losing the original smoothness of mixup. As a result, DM enables static mixup methods to achieve comparable or even exceed the performance of dynamic methods without any extra computation. This also leads to an interesting objective design problem for mixup training that we need to focus on both smoothing the decision boundaries and identifying discriminative features. Extensive experiments on supervised and semi-supervised learning benchmarks across seven datasets validate the effectiveness of DM.

Deep Learning/Theory

Mariia Seleznova, Dana Weitzner, Raja Giryes, Gitta Kutyniok, Hung-Hsu Chou

This work bridges two important concepts: the Neural Tangent Kernel (NTK), which captures the evolution of deep neural networks (DNNs) during training, and the Neural Collapse (NC) phenomenon, which refers to the emergence of symmetry and structure in the last-layer features of well-trained classification DNNs. We adopt the natural assumption that the empirical NTK develops a block structure aligned with the class labels, i.e., samples within the same class have stronger correlations than samples from different classes. Under this assumption, we derive the dynamics of DNNs trained with mean squared (MSE) loss and break them into interpretable phases. Moreover, we identify an invariant that captures the essence of the dynamics, and use it to prove the emergence of NC in DNNs with block-structured NTK. We provide large-scale numerical experiments on three common DNN architectures and three benchmark datasets to support our theory.

Deep Learning/Theory

Benjamin Edelman, Surbhi Goel, Sham Kakade, Eran Malach, Cyril Zhang

In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of computational-statistical gaps. We begin by considering offline sparse parity learning, a supervised classification problem which admits a statistical query lower bound for gradient-based training of a multilayer perceptron. This lower bound can be interpreted as a *multi-resource tradeoff frontier*: successful learning can only occur if one is sufficiently rich (large model), knowledgeable (large dataset), patient (many training iterations), or lucky (many random guesses). We show, theoretically and experimentally, that sparse initialization and increasing network width yield significant improvements in sample efficiency in this setting. Here, width plays the role of parallel search: it amplifies the probability of finding "lottery ticket" neurons, which learn sparse features more sample-efficiently. Finally, we show that the synthetic sparse parity task can be useful as a proxy for real problems requiring axis-aligned feature learning. We demonstrate improved sample efficiency on tabular classification benchmarks by using wide, sparsely-initialized MLP models; these networks sometimes outperform tuned random forests.

Jun Xia, Lecheng Zhang, Xiao Zhu, Yue Liu, Zhangyang Gao, Bozhen Hu, Cheng Tan, Jiangbin Zheng, Siyuan Li, Stan Z. Li

Molecular Property Prediction (MPP) is a crucial task in the AI-driven Drug Discovery (AIDD) pipeline, which has recently gained considerable attention thanks to advancements in deep learning. However, recent research has revealed that deep models struggle to beat traditional non-deep ones on MPP. In this study, we benchmark 12 representative models (3 non-deep models and 9 deep models) on 15 molecule datasets. Through the most comprehensive study to date, we make the following key observations: \textbf{(\romannumeral 1)} Deep models are generally unable to outperform non-deep ones; \textbf{(\romannumeral 2)} The failure of deep models on MPP cannot be solely attributed to the small size of molecular datasets; \textbf{(\romannumeral 3)} In particular, some traditional models including XGB and RF that use molecular fingerprints as inputs tend to perform better than other competitors. Furthermore, we conduct extensive empirical investigations into the unique patterns of molecule data and inductive biases of various models underlying these phenomena. These findings stimulate us to develop a simple-yet-effective feature mapping method for molecule data prior to feeding them into deep models. Empirically, deep models equipped with this mapping method can beat non-deep ones in most MoleculeNet datasets. Notably, the effectiveness is further corroborated by extensive experiments on cutting-edge dataset related to COVID-19 and activity cliff datasets.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Jing Li, Quanxue Gao, QIANQIAN WANG, Ming Yang, Wei Xia

Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have attracted much attention due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present orthogonal non-negative tensor factorization (Orth-NTF) and develop a novel multi-view clustering based on Orth-NTF with one-side orthogonal constraint. Our model directly performs Orth-NTF on the 3rd-order tensor which is composed of anchor graphs of views. Thus, our model directly considers the between-view relationship. Moreover, we use the tensor Schatten $p$-norm regularization as a rank approximation of the 3rd-order tensor which characterizes the cluster structure of multi-view data and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point. Extensive experiments on various benchmark datasets indicate that our proposed method is able to achieve satisfactory clustering performance.

Deep Learning/Algorithms

Qinsi Wang, Jinghan Ke, Zhi Liang, Sihai Zhang

Neural Architecture Search (NAS) has emerged as a favoured method for unearthing effective neural architectures. Recent development of large models has intensified the demand for faster search speeds and more accurate search results. However, designing large models by NAS is challenging due to the dramatical increase of search space and the associated huge performance evaluation cost. Consider a typical modular search space widely used in NAS, in which a neural architecture consists of $m$ block nodes and a block node has $n$ alternative blocks. Facing the space containing $n^m$ candidate networks, existing NAS methods attempt to find the best one by searching and evaluating candidate networks directly.Different from the general strategy that takes architecture search as a whole problem, we propose a novel divide-and-conquer strategy by making use of the modular nature of the search space.Here, we introduce MathNAS, a general NAS framework based on mathematical programming. In MathNAS, the performances of all possible building blocks in the search space are calculated first, and then the performance of a network is directly predicted based on the performances of its building blocks.Although estimating block performances involves network training, just as what happens for network performance evaluation in existing NAS methods, predicting network performance is completely training-free and thus extremely fast. In contrast to the $n^m$ candidate networks to evaluate in existing NAS methods, which requires training and a formidable computational burden, there are only $m*n$ possible blocks to handle in MathNAS.Therefore, our approach effectively reduces the complexity of network performance evaluation. The superiority of MathNAS is validated on multiple large-scale CV and NLP benchmark datasets. Notably on ImageNet-1k, MathNAS achieves 82.5\% top-1 accuracy, 1.2\% and 0.96\% higher than Swin-T and LeViT-256, respectively. In addition, when deployed on mobile device, MathNAS achieves real-time search and dynamic network switching within 1s (0.4s on TX2 GPU), surpassing baseline dynamic networks in on-device performance.