Despite the impressive progress of multimodal generative models, video-to-audio generation still suffers from limited performance and limits the flexibility to prioritize sound synthesis for specific objects within the scene. Conversely, text-to-audio generation methods generate high-quality audio but pose challenges in ensuring comprehensive scene depiction and time-varying control. To tackle these challenges, we propose a novel video-and-text-to-audio generation method, called ReWaS, where video serves as a conditional control for a text-to-audio generation model. Especially, our method estimates the structural information of sound (namely, energy) from the video while receiving key content cues from a user prompt. We employ a well-performing text-to-audio model to consolidate the video control, which is much more efficient for training multimodal diffusion models with massive triplet-paired (audio-video-text) data. In addition, by separating the generative components of audio, it becomes a more flexible system that allows users to freely adjust the energy, surrounding environment, and primary sound source according to their preferences. Experimental results demonstrate that our method shows superiority in terms of quality, controllability, and training efficiency.

Vision-language models (VLMs) embed aligned image-text pairs into a joint space but often rely on deterministic embeddings, assuming a one-to-one correspondence between images and texts. This oversimplifies real-world relationships, which are inherently many-to-many, with multiple captions describing a single image and vice versa. We introduce Probabilistic Language-Image Pre-training (ProLIP), the first probabilistic VLM pre-trained on a billion-scale image-text dataset using only probabilistic objectives, achieving a strong zero-shot capability (e.g., 74.6% ImageNet zero-shot accuracy with ViT-B/16). ProLIP efficiently estimates uncertainty by an ``uncertainty token'' without extra parameters. We also introduce a novel inclusion loss that enforces distributional inclusion relationships between image-text pairs and between original and masked inputs. Experiments demonstrate that, by leveraging uncertainty estimates, ProLIP benefits downstream tasks and aligns with intuitive notions of uncertainty, e.g., shorter texts being more uncertain and more general inputs including specific ones. Utilizing text uncertainties, we further improve ImageNet accuracy from 74.6% to 75.8% (under a few-shot setting), supporting the practical advantages of our probabilistic approach. The code is available at https://github.com/naver-ai/prolip

Composed image retrieval (CIR) task takes a composed query of image and text, aiming to search relative images for both conditions. Conventional CIR approaches need a training dataset composed of triplets of query image, query text, and target image, which is very expensive to collect. Several recent works have worked on the zero-shot (ZS) CIR paradigm to tackle the issue without using pre-collected triplets. However, the existing ZS-CIR methods show limited backbone scalability and generalizability due to the lack of diversity of the input texts during training. We propose a novel CIR framework, only using language for its training. Our LinCIR (Language-only training for CIR) can be trained only with text datasets by a novel self-supervision named self-masking projection (SMP). We project the text latent embedding to the token embedding space and construct a new text by replacing the keyword tokens of the original text. Then, we let the new and original texts have the same latent embedding vector. With this simple strategy, LinCIR is surprisingly efficient and highly effective; LinCIR with CLIP ViT-G backbone is trained in 48 minutes and shows the best ZS-CIR performances on four different CIR benchmarks, CIRCO, GeneCIS, FashionIQ, and CIRR, even outperforming supervised method on FashionIQ. Code is available at github.com/navervision/lincir

Image-Text Matching (ITM) task, a fundamental vision-language (VL) task, suffers from the inherent ambiguity arising from multiplicity and imperfect annotations. Deterministic functions are not sufficiently powerful to capture ambiguity, prompting the exploration of probabilistic embeddings to tackle the challenge. However, the existing probabilistic ITM approach encounters two key shortcomings; the burden of heavy computations due to the Monte Carlo approximation, and the loss saturation issue in the face of abundant false negatives. To overcome the issues, this paper presents an improved Probabilistic Cross-Modal Embeddings (named PCME++) by introducing a new probabilistic distance with a closed-form solution. In addition, two optimization techniques are proposed to enhance PCME++ further: first, the incorporation of pseudo-positives to prevent the negative effect under massive false negatives; second, mixed sample data augmentation for probabilistic matching. Experimental results on MS-COCO Caption and two extended benchmarks, CxC and ECCV Caption, demonstrate the effectiveness of PCME++ compared to state-of-the-art ITM methods. The robustness of PCME++ is also evaluated under noisy image-text correspondences. In addition, the potential applicability of PCME++ in automatic prompt-filtering for zero-shot classification is shown. The code is available at https://github.com/naver-ai/pcmepp.

Forward- or reverse-mode automatic differentiation (AD) is a popular algorithm for computing the derivative of a function expressed by a program. AD always outputs the correct derivative if a program does not use any non-differentiable functions and control flows; however, it may return an arbitrary value otherwise. In this work, we investigate what AD computes for neural networks that may contain non-differentiable functions such as ReLU and maxpools. We first prove that AD always returns a generalized derivative called a Clarke subderivative for networks with pointwise activation functions, if the minibatch size is one and all non-differentiable neurons have distinct bias parameters. We show that the same conclusion does not hold otherwise, but does hold under some mild sufficient conditions. We also prove similar results for more general networks that can use maxpools and bias parameters shared across different neurons. We empirically check our sufficient conditions over popular network architectures and observe that AD almost always computes a Clarke subderivative in practical learning setups.

Jungbeom Lee, Sanghyuk Chun, Sangdoo Yun. Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2024.

The notion of algorithmic fairness has been actively explored from various aspects of fairness, such as counterfactual fairness (CF) and group fairness (GF). However, the exact relationship between CF and GF remains to be unclear, especially in image classification tasks; the reason is because we often cannot collect counterfactual samples regarding a sensitive attribute, essential for evaluating CF, from the existing images (e.g., a photo of the same person but with different secondary sex characteristics). In this paper, we construct new image datasets for evaluating CF by using a high-quality image editing method and carefully labeling with human annotators. Our datasets, CelebA-CF and LFW-CF, build upon the popular image GF benchmarks; hence, we can evaluate CF and GF simultaneously. We empirically observe that CF does not imply GF in image classification, whereas previous studies on tabular datasets observed the opposite. We theoretically show that it could be due to the existence of a latent attribute $G$ that is correlated with, but not caused by, the sensitive attribute (e.g., secondary sex characteristics are highly correlated with hair length). From this observation, we propose a simple baseline, Counterfactual Knowledge Distillation (CKD), to mitigate such correlation with the sensitive attributes. Extensive experimental results on CelebA-CF and LFW-CF demonstrate that CF-achieving models satisfy GF if we successfully reduce the reliance on $G$ (e.g., using CKD).

Automatic few-shot font generation aims to solve a well-defined, real-world problem because manual font designs are expensive and sensitive to the expertise of designers. Existing methods learn to disentangle style and content elements by developing a universal style representation for each font style. However, this approach limits the model in representing diverse local styles because it is unsuitable for complicated letter systems. For example, Chinese characters consist of a varying number of components (often called "radical") with a highly complex structure. In this paper, we propose a novel font generation method that learns localized styles, namely component-wise style representations, instead of universal styles. The proposed style representations enable synthesizing complex local details in text designs. However, learning component-wise styles solely from a few reference glyphs is infeasible when a target script has a large number of components, for example, over 200 for Chinese. To reduce the number of required reference glyphs, we represent component-wise styles by a product of component and style factors inspired by low-rank matrix factorization. Owing to the combination of strong representation and a compact factorization strategy, our method shows remarkably better few-shot font generation results (with only eight reference glyphs) than other state-of-the-art methods. Moreover, strong locality supervision was not utilized, such as the location of each component, skeleton, or strokes. The source code is available at https://github.com/clovaai/lffont.

We need billion-scale images to achieve more generalizable and ground-breaking vision models, as well as massive dataset storage to ship the images (e.g., the LAION-5B dataset needs 240TB storage space). However, it has become challenging to deal with unlimited dataset storage with limited storage infrastructure. A number of storage-efficient training methods have been proposed to tackle the problem, but they are rarely scalable or suffer from severe damage to performance. In this paper, we propose a storage-efficient training strategy for vision classifiers for large-scale datasets (e.g., ImageNet) that only uses 1024 tokens per instance without using the raw level pixels; our token storage only needs <1% of the original JPEG-compressed raw pixels. We also propose token augmentations and a Stem-adaptor module to make our approach able to use the same architecture as pixel-based approaches with only minimal modifications on the stem layer and the carefully tuned optimization settings. Our experimental results on ImageNet-1k show that our method significantly outperforms other storage-efficient training methods with a large gap. We further show the effectiveness of our method in other practical scenarios, storage-efficient pre-training, and continual learning. Code is available at https://github.com/naver-ai/seit.

Weakly-supervised object localization (WSOL) has gained popularity over the last years for its promise to train localization models with only image-level labels. Since the seminal WSOL work of class activation mapping (CAM), the field has focused on how to expand the attention regions to cover objects more broadly and localize them better. However, these strategies rely on full localization supervision for validating hyperparameters and model selection, which is in principle prohibited under the WSOL setup. In this paper, we argue that WSOL task is ill-posed with only image-level labels, and propose a new evaluation protocol where full supervision is limited to only a small held-out set not overlapping with the test set. We observe that, under our protocol, the five most recent WSOL methods have not made a major improvement over the CAM baseline. Moreover, we report that existing WSOL methods have not reached the few-shot learning baseline, where the full-supervision at validation time is used for model training instead. Based on our findings, we discuss some future directions for WSOL. Source code and dataset are available at https://github.com/clovaai/wsolevaluation https://github.com/clovaai/wsolevaluation.

Recently, fairness-aware learning have become increasingly crucial, but most of those methods operate by assuming the availability of fully annotated demographic group labels. We emphasize that such assumption is unrealistic for real-world applications since group label annotations are expensive and can conflict with privacy issues. In this paper, we consider a more practical scenario, dubbed as Algorithmic Group Fairness with the Partially annotated Group labels (Fair-PG). We observe that the existing methods to achieve group fairness perform even worse than the vanilla training, which simply uses full data only with target labels, under Fair-PG. To address this problem, we propose a simple Confidence-based Group Label assignment (CGL) strategy that is readily applicable to any fairness-aware learning method. CGL utilizes an auxiliary group classifier to assign pseudo group labels, where random labels are assigned to low confident samples. We first theoretically show that our method design is better than the vanilla pseudo-labeling strategy in terms of fairness criteria. Then, we empirically show on several benchmark datasets that by combining CGL and the state-of-the-art fairness-aware in-processing methods, the target accuracies and the fairness metrics can be jointly improved compared to the baselines. Furthermore, we convincingly show that CGL enables to naturally augment the given group-labeled dataset with external target label-only datasets so that both accuracy and fairness can be improved. Code is available at https://github.com/naver-ai/cgl_fairness.

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-theart performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when taskirrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.

We propose the first unified theoretical analysis of mixed sample data augmentation (MSDA), such as Mixup and CutMix. Our theoretical results show that regardless of the choice of the mixing strategy, MSDA behaves as a pixel-level regularization of the underlying training loss and a regularization of the first layer parameters. Similarly, our theoretical results support that the MSDA training strategy can improve adversarial robustness and generalization compared to the vanilla training strategy. Using the theoretical results, we provide a high-level understanding of how different design choices of MSDA work differently. For example, we show that the most popular MSDA methods, Mixup and CutMix, behave differently, e.g., CutMix regularizes the input gradients by pixel distances, while Mixup regularizes the input gradients regardless of pixel distances. Our theoretical results also show that the optimal MSDA strategy depends on tasks, datasets, or model parameters. From these observations, we propose generalized MSDAs, a Hybrid version of Mixup and CutMix (HMix) and Gaussian Mixup (GMix), simple extensions of Mixup and CutMix. Our implementation can leverage the advantages of Mixup and CutMix, while our implementation is very efficient, and the computation cost is almost neglectable as Mixup and CutMix. Our empirical study shows that our HMix and GMix outperform the previous state-of-the-art MSDA methods in CIFAR-100 and ImageNet classification tasks.

Automatic few-shot font generation is a practical and widely studied problem because manual designs are expensive and sensitive to the expertise of designers. Existing few-shot font generation methods aim to learn to disentangle the style and content element from a few reference glyphs, and mainly focus on a universal style representation for each font style. However, such approach limits the model in representing diverse local styles, and thus makes it unsuitable to the most complicated letter system, e.g., Chinese, whose characters consist of a varying number of components (often called ``radical'') with a highly complex structure. In this paper, we propose a novel font generation method by learning localized styles, namely component-wise style representations, instead of universal styles. The proposed style representations enable us to synthesize complex local details in text designs. However, learning component-wise styles solely from reference glyphs is infeasible in the few-shot font generation scenario, when a target script has a large number of components, e.g., over 200 for Chinese. To reduce the number of reference glyphs, we simplify component-wise styles by a product of component factor and style factor, inspired by low-rank matrix factorization. Thanks to the combination of strong representation and a compact factorization strategy, our method shows remarkably better few-shot font generation results (with only 8 reference glyph images) than other state-of-the-arts, without utilizing strong locality supervision, e.g., location of each component, skeleton, or strokes. The source code is available at https://github.com/clovaai/lffont.

Cross-modal retrieval methods build a common representation space for samples from multiple modalities, typically from the vision and the language domains. For images and their captions, the multiplicity of the correspondences makes the task particularly challenging. Given an image (respectively a caption), there are multiple captions (respectively images) that equally make sense. In this paper, we argue that deterministic functions are not sufficiently powerful to capture such one-to-many correspondences. Instead, we propose to use Probabilistic Cross-Modal Embedding (PCME), where samples from the different modalities are represented as probabilistic distributions in the common embedding space. Since common benchmarks such as COCO suffer from non-exhaustive annotations for cross-modal matches, we propose to additionally evaluate retrieval on the CUB dataset, a smaller yet clean database where all possible image-caption pairs are annotated. We extensively ablate PCME and demonstrate that it not only improves the retrieval performance over its deterministic counterpart but also provides uncertainty estimates that render the embeddings more interpretable. Code is available at https://github.com/naver-ai/pcme.

ImageNet has been the most popular image classification benchmark, but it is also the one with a significant level of label noise. Recent studies have shown that many samples contain multiple classes, despite being assumed to be a single-label benchmark. They have thus proposed to turn ImageNet evaluation into a multi-label task, with exhaustive multi-label annotations per image. However, they have not fixed the training set, presumably because of a formidable annotation cost. We argue that the mismatch between single-label annotations and effectively multi-label images is equally, if not more, problematic in the training setup, where random crops are applied. With the single-label annotations, a random crop of an image may contain an entirely different object from the ground truth, introducing noisy or even incorrect supervision during training. We thus re-label the ImageNet training set with multi-labels. We address the annotation cost barrier by letting a strong image classifier, trained on an extra source of data, generate the multi-labels. We utilize the pixel-wise multi-label predictions before the final pooling layer, in order to exploit the additional location-specific supervision signals. Training on the re-labeled samples results in improved model performances across the board. ResNet-50 attains the top-1 accuracy of 78.9% on ImageNet with our localized multi-labels, which can be further boosted to 80.2% with the CutMix regularization. We show that the models trained with localized multi-labels also outperforms the baselines on transfer learning to object detection and instance segmentation tasks, and various robustness benchmarks. The re-labeled ImageNet training set, pre-trained weights, and the source code are available at https://github.com/naverai/relabel_imagenet.

Vision Transformer (ViT) extends the application range of transformers from language processing to computer vision tasks as being an alternative architecture against the existing convolutional neural networks (CNN). Since the transformer-based architecture has been innovative for computer vision modeling, the design convention towards an effective architecture has been less studied yet. From the successful design principles of CNN, we investigate the role of spatial dimension conversion and its effectiveness on transformer-based architecture. We particularly attend to the dimension reduction principle of CNNs; as the depth increases, a conventional CNN increases channel dimension and decreases spatial dimensions. We empirically show that such a spatial dimension reduction is beneficial to a transformer architecture as well, and propose a novel Pooling-based Vision Transformer (PiT) upon the original ViT model. We show that PiT achieves the improved model capability and generalization performance against ViT. Throughout the extensive experiments, we further show PiT outperforms the baseline on several tasks such as image classification, object detection, and robustness evaluation. Source codes and ImageNet models are available at https://github.com/naver-ai/pit.

A few-shot font generation (FFG) method has to satisfy two objectives: the generated images should preserve the underlying global structure of the target character and present the diverse local reference style. Existing FFG methods aim to disentangle content and style either by extracting a universal representation style or extracting multiple component-wise style representations. However, previous methods either fail to capture diverse local styles or cannot be generalized to a character with unseen components, e.g., unseen language systems. To mitigate the issues, we propose a novel FFG method, named Multiple Localized Experts Few-shot Font Generation Network (MX-Font). MX-Font extracts multiple style features not explicitly conditioned on component labels, but automatically by multiple experts to represent different local concepts, e.g., left-side sub-glyph. Owing to the multiple experts, MX-Font can capture diverse local concepts and show the generalizability to unseen languages. During training, we utilize component labels as weak supervision to guide each expert to be specialized for different local concepts. We formulate the component assign problem to each expert as the graph matching problem, and solve it by the Hungarian algorithm. We also employ the independence loss and the content-style adversarial loss to impose the content-style disentanglement. In our experiments, MX-Font outperforms previous state-of-the-art FFG methods in the Chinese generation and cross-lingual, e.g., Chinese to Korean, generation. Source code is available at https://github.com/clovaai/mxfont.

Domain generalization (DG) methods aim to achieve generalizability to an unseen target domain by using only training data from the source domains. Although a variety of DG methods have been proposed, a recent study shows that under a fair evaluation protocol, called DomainBed, the simple empirical risk minimization (ERM) approach works comparable to or even outperforms previous methods. Unfortunately, simply solving ERM on a complex, non-convex loss function can easily lead to sub-optimal generalizability by seeking sharp minima. In this paper, we theoretically show that finding flat minima results in a smaller domain generalization gap. We also propose a simple yet effective method, named Stochastic Weight Averaging Densely (SWAD), to find flat minima. SWAD finds flatter minima and suffers less from overfitting than does the vanilla SWA by a dense and overfit-aware stochastic weight sampling strategy. SWAD shows state-of-the-art performances on five DG benchmarks, namely PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet, with consistent and large margins of +1.6% averagely on out-of-domain accuracy. We also compare SWAD with conventional generalization methods, such as data augmentation and consistency regularization methods, to verify that the remarkable performance improvements are originated from by seeking flat minima, not from better in-domain generalizability. Last but not least, SWAD is readily adaptable to existing DG methods without modification; the combination of SWAD and an existing DG method further improves DG performances. Source code is available at https://github.com/khanrc/swad.

Effective control and prediction of dynamical systems require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs), a recipe for learning SHS dynamics without a priori knowledge on the number, mode parameters, and inter-modal transition dynamics. NHAs provide a systematic inference method based on normalizing flows, neural differential equations, and self-supervision. We showcase NHAs on several tasks, including mode recovery and flow learning in systems with stochastic transitions, and end-to-end learning of hierarchical robot controllers.

Weakly-supervised object localization (WSOL) has gained popularity over the last years for its promise to train localization models with only image-level labels. Since the seminal WSOL work of class activation mapping (CAM), the field has focused on how to expand the attention regions to cover objects more broadly and localize them better. However, these strategies rely on full localization supervision to validate hyperparameters and for model selection, which is in principle prohibited under the WSOL setup. In this paper, we argue that WSOL task is ill-posed with only image-level labels, and propose a new evaluation protocol where full supervision is limited to only a small held-out set not overlapping with the test set. We observe that, under our protocol, the five most recent WSOL methods have not made a major improvement over the CAM baseline. Moreover, we report that existing WSOL methods have not reached the few-shot learning baseline, where the full-supervision at validation time is used for model training instead. Based on our findings, we discuss some future directions for WSOL.

We introduce a trainable front-end module for audio representation learning that exploits the inherent harmonic structure of audio signals. The proposed architecture, composed of a set of filters, compels the subsequent network to capture harmonic relations while preserving spectro-temporal locality. Since the harmonic structure is known to have a key role in human auditory perception, one can expect these harmonic filters to yield more efficient audio representations. Experimental results show that a simple convolutional neural network back-end with the proposed front-end outperforms state-of-the-art baseline methods in automatic music tagging, keyword spotting, and sound event tagging tasks.

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias shortcuts, resulting in improved generalisation. Source code is available at https://github.com/clovaai/rebias.

Recent style transfer models have provided promising artistic results. However, given a photograph as a reference style, existing methods are limited by spatial distortions or unrealistic artifacts, which should not happen in real photographs. We introduce a theoretically sound correction to the network architecture that remarkably enhances photorealism and faithfully transfers the style. The key ingredient of our method is wavelet transforms that naturally fits in deep networks. We propose a wavelet corrected transfer based on whitening and coloring transforms (WCT2) that allows features to preserve their structural information and statistical properties of VGG feature space during stylization. This is the first and the only end-to-end model that can stylize a 1024x1024 resolution image in 4.7 seconds, giving a pleasing and photorealistic quality without any post-processing. Last but not least, our model provides a stable video stylization without temporal constraints. Our code, generated images, pre-trained models and supplementary documents are all available at https://github.com/ClovaAI/WCT2.

Regional dropout strategies have been proposed to enhance performance of convolutional neural network classifiers. They have proved to be effective for guiding the model to attend on less discriminative parts of objects (e.g. leg as opposed to head of a person), thereby letting the network generalize better and have better object localization capabilities. On the other hand, current methods for regional dropout removes informative pixels on training images by overlaying a patch of either black pixels or random noise. Such removal is not desirable because it suffers from information loss causing inefficiency in training. We therefore propose the CutMix augmentation strategy: patches are cut and pasted among training images where the ground truth labels are also mixed proportionally to the area of the patches. By making efficient use of training pixels and retaining the regularization effect of regional dropout, CutMix consistently outperforms state-of-the-art augmentation strategies on CIFAR and ImageNet classification tasks, as well as on ImageNet weakly-supervised localization task. Moreover, unlike previous augmentation methods, our CutMix-trained ImageNet classifier, when used as a pretrained model, results in consistent performance gain in Pascal detection and MS-COCO image captioning benchmarks. We also show that CutMix can improve the model robustness against input corruptions and its out-of distribution detection performance.

In mobile application, the push notification is an important function to make users consume an item (eg. movie, novel). If a mobile application sends too many notifications to users without considering their preferences, it can cause them to turn off the notification or even deleting the mobile application. Thus, we develop a framework that selects a set of users who are likely to react to the push notification. To the best of our knowledge, we first apply recommendation techniques (i.e., collaborative filtering and content-based models) to the problem of discovering the target of push notification.