Differentially private synthetic data enables the sharing and analysis of sensitive datasets while providing rigorous privacy guarantees for individual contributors. A central challenge is to achieve strong utility guarantees for meaningful downstream analysis. Many existing methods ensure uniform accuracy over broad query classes, such as all Lipschitz functions, but this level of generality often leads to suboptimal rates for statistics of practical interest. Since many common data analysis queries exhibit smoothness beyond what worst-case Lipschitz bounds capture, we ask whether exploiting this additional structure can yield improved utility. We study the problem of generating $(\varepsilon,\delta)$-differentially private synthetic data from a dataset of size $n$ supported on the hypercube $[-1,1]^d$, with utility guarantees uniformly for all smooth queries having bounded derivatives up to order $k$. We propose a polynomial-time algorithm that achieves a minimax error rate of $O_{k,d}(n^{-\min {1, \frac{k}{d}}})$, up to a $\log(n)$ factor. This characterization uncovers a phase transition at $k=d$. Our results generalize the Chebyshev moment matching framework of (Musco et al., 2025; Wang et al., 2016) and strictly improve the error rates for $k$-smooth queries established in (Wang et al., 2016). Moreover, we establish the first minimax lower bound for the utility of $(\varepsilon,\delta)$-differentially private synthetic data with respect to $k$-smooth queries, extending the Wasserstein lower bound for $\varepsilon$-differential privacy in (Boedihardjo et al., 2024).

We introduce \emph{Wedge Sampling}, a new non-adaptive sampling scheme for low-rank tensor completion. We study recovery of an order-$k$ low-rank tensor of dimension $n\times\cdots\times n$ from a subset of its entries. Unlike the standard uniform entry model (i.e., i.i.d. samples from $[n]^k$), wedge sampling allocates observations to structured length-two patterns (wedges) in an associated bipartite sampling graph. By directly promoting these length-two connections, the sampling design strengthens the spectral signal that underlies efficient initialization, in regimes where uniform sampling is too sparse to generate enough informative correlations. Our main result shows that this change in sampling paradigm enables polynomial-time algorithms to achieve both weak and exact recovery with nearly linear sample complexity in $n$. The approach is also plug-and-play: wedge-sampling–based spectral initialization can be combined with existing refinement procedures (e.g., spectral or gradient-based methods) using only an additional $\tilde O(n)$ uniformly sampled entries, substantially improving over the $\tilde O(n^{k/2})$ sample complexity typically required under uniform entry sampling for efficient methods. Overall, our results suggest that the statistical-to-computational gap highlighted by Barak and Moitra [Mathematical Programming, 193(2):513–548, 2022] is, to a large extent, a consequence of the uniform entry sampling model for tensor completion, and alternative non-adaptive measurement designs that guarantee a strong initialization can overcome this barrier.

The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborov{á} (2014), is a Hermitian matrix designed for applying spectral clustering algorithms to sparse networks. Rather than employing a non-symmetric and high-dimensional non-backtracking operator, a spectral method based on the Bethe-Hessian matrix is conjectured to also reach the Kesten-Stigum detection threshold in the sparse stochastic block model (SBM). We provide the first rigorous analysis of the Bethe-Hessian spectral method in the SBM under both the bounded expected degree and the growing degree regimes. Specifically, we demonstrate that: (i) When the expected degree $d\geq 2$, the number of negative outliers of the Bethe-Hessian matrix can consistently estimate the number of blocks above the Kesten-Stigum threshold, thus confirming a conjecture from Saade, Krzakala, and Zdeborov{á} (2014) for $d\geq 2$. (ii) For sufficiently large $d$, its eigenvectors can be used to achieve weak recovery. (iii) As $d\to\infty$, we establish the concentration of the locations of its negative outlier eigenvalues, and weak consistency can be achieved via a spectral method based on the Bethe-Hessian matrix.

For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that use factorized gradient descent. Under certain statistical model assumptions, it is known that nuclear norm minimization recovers the ground truth as soon as the number of samples scales linearly with the number of degrees of freedom of the ground-truth. In contrast, while non-convex approaches are computationally less expensive, existing recovery guarantees assume that the number of samples scales at least quadratically with the rank $r$ of the ground-truth matrix. In this paper, we close this gap by showing that the non-convex approaches can be as efficient as nuclear norm minimization in terms of sample complexity. Namely, we consider the problem of reconstructing a positive semidefinite matrix from a few Gaussian measurements. We show that factorized gradient descent with spectral initialization converges to the ground truth with a linear rate as soon as the number of samples scales with $ \Omega (rd\kappa^2)$, where $d$ is the dimension, and $\kappa$ is the condition number of the ground truth matrix. This improves the previous rank-dependence in the sample complexity of non-convex matrix factorization from quadratic to linear. Our proof relies on a probabilistic decoupling argument, where we show that the gradient descent iterates are only weakly dependent on the individual entries of the measurement matrices. We expect that our proof technique will be of independent interest to other non-convex problems.

Recent advances in hierarchical policy learning highlight the advantages of decomposing systems into high-level and low-level agents, enabling efficient long-horizon reasoning and precise fine-grained control. However, the interface between these hierarchy levels remains underexplored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we propose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We propose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility. Additionally, we integrate domain symmetries into both levels and theoretically demonstrate the system's overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating significant improvements in both simulation and real-world settings.

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus thus far has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In the proportional regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of a linear kernel. In this work, we extend the study of kernel regression to the quadratic asymptotic regime, where $n \asymp d^2$. In this regime, we demonstrate that a broad class of inner-product kernels exhibits behavior similar to a quadratic kernel. Specifically, we establish an operator norm approximation bound for the difference between the original kernel random matrix and a quadratic kernel random matrix with additional correction terms compared to the Taylor expansion of the kernel functions. The approximation works for general data distributions under a Gaussian-moment-matching assumption with a covariance structure. This new approximation is utilized to obtain a limiting spectral distribution of the original kernel matrix and characterize the precise asymptotic training and test errors for KRR in the quadratic regime when $n/d^2$ converges to a non-zero constant. The generalization errors are obtained for (i) a random teacher model, (ii) a deterministic teacher model where the weights are perfectly aligned with the covariance of the data. Under the random teacher model setting, we also verify that the generalized cross-validation (GCV) estimator can consistently estimate the generalization error in the quadratic regime for anisotropic data. Our proof techniques combine moment methods, Wick's formula, orthogonal polynomials, and resolvent analysis of random matrices with correlated entries.

We consider the problem of low-rank rectangular matrix completion in the regime where the matrix $M$ of size $n\times m$ is “long", i.e., the aspect ratio $m/n$ diverges to infinity. Such matrices are of particular interest in the study of tensor completion, where they arise from the unfolding of a low-rank tensor. In the case where the sampling probability is $\frac{d}{\sqrt{mn}}$, we propose a new spectral algorithm for recovering the singular values and left singular vectors of the original matrix $M$ based on a variant of the standard non-backtracking operator of a suitably defined bipartite weighted random graph, which we call a \textit{non-backtracking wedge operator}. When $d$ is above a Kesten-Stigum-type sampling threshold, our algorithm recovers a correlated version of the singular value decomposition of $M$ with quantifiable error bounds. This is the first result in the regime of bounded $d$ for weak recovery and the first for weak consistency when $d\to\infty$ arbitrarily slowly without any polylog factors. As an application, for low-CP-rank orthogonal $k$-tensor completion, we efficiently achieve weak recovery with sample size $O(n^{k/2})$ and weak consistency with sample size $\omega(n^{k/2})$. A similar result is obtained for low-multilinear-rank tensor completion with $O(n^{k/2})$ many samples.

In this work, we propose MagicPose, a diffusion-based model for 2D human pose and facial expression retargeting. Specifically, given a reference image, we aim to generate a person’s new images by controlling the poses and facial expressions while keeping the identity unchanged. To this end, we propose a two-stage training strategy to disentangle human motions and appearance (e.g., facial expressions, skin tone, and dressing), consisting of (1) the pre-training of an appearance-control block and (2) learning appearance-disentangled pose control. Our novel design enables robust appearance control over generated human images, including body, facial attributes, and even background. By leveraging the prior knowledge of image diffusion models, MagicPose generalizes well to unseen human identities and complex poses without the need for additional fine-tuning. Moreover, the proposed model is easy to use and can be considered as a plug-in module/extension to Stable Diffusion. The project website is here. The code is available here.

We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime, where the width of the first layer is much larger than the sample size. Our analysis shows high-probability non-asymptotic concentration results for the training errors, cross-validations, and generalization errors of RFRR centered around their respective values for a kernel ridge regression (KRR). This KRR is derived from an expected kernel generated by a nonlinear random feature map. We then approximate the performance of the KRR by a polynomial kernel matrix obtained from the Hermite polynomial expansion of the activation function, whose degree only depends on the orthogonality among different data points. This polynomial kernel determines the asymptotic behavior of the RFRR and the KRR. Our results hold for a wide variety of activation functions and input data sets that exhibit nearly orthogonal properties. Based on these approximations, we obtain a lower bound for the generalization error of the RFRR for a nonlinear student-teacher model.

We present a highly effective algorithmic approach for generating $\varepsilon$-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset $\mathcal X$ in the hypercube $[0,1]^d$, our algorithm generates synthetic dataset $\mathcal Y$ such that the expected 1-Wasserstein distance between the empirical measure of $\mathcal X$ and $\mathcal Y$ is $O((\varepsilon n)^{-1/d})$ for $d\geq 2$, and is $O(\log^2(\varepsilon n)(\varepsilon n)^{-1})$ for $d=1$. The accuracy guarantee is optimal up to a constant factor for $d\geq 2$, and up to a logarithmic factor for $d=1$. Our algorithm has a fast running time of $O(\varepsilon d n)$ for all $d\geq 1$ and demonstrates improved accuracy compared to the method in Boedihardjo et al. (2022) for $d\geq 2$.

We present Corgi, a novel method for text-to-image generation. Corgi is based on our proposed shifted diffusion model, which achieves better image embedding generation from input text. Unlike the baseline diffusion model used in DALL-E 2, our method seamlessly encodes prior knowledge of the pre-trained CLIP model in its diffusion process by designing a new initialization distribution and a new transition step of the diffusion. Compared to the strong DALL-E 2 baseline, our method performs better in generating image embedding from the text in terms of both efficiency and effectiveness, resulting in better text-to-image generation. Extensive large-scale experiments are conducted and evaluated in terms of both quantitative measures and human evaluation, indicating a stronger generation ability of our method compared to existing ones. Furthermore, our model enables semi-supervised and language-free training for text-to-image generation, where only part or none of the images in the training dataset have an associated caption. Trained with only 1.7% of the images being captioned, our semi-supervised model obtains FID results comparable to DALL-E 2 on zero-shot text-to-image generation evaluated on MS-COCO. Corgi also achieves new state-of-the-art results across different datasets on downstream language-free text-to-image generation tasks, outperforming the previous method, Lafite, by a large margin.

Synthesizing high-fidelity talking head videos by fitting input audio sequences is a highly anticipated technique in many applications, such as digital humans, virtual video conferences, and human-computer interaction. Popular GAN-based methods aim to align speech audio with lip motions and head poses. However, existing methods are prone to training instability and even mode collapse, resulting in low-quality video generation. In this paper, we propose a novel audio-driven diffusion method for generating high-resolution realistic videos of talking heads with the help of the denoising diffusion model. Specifically, the face attribute disentanglement module is proposed to disentangle eye blinking and lip motion features, where the lip motion features are synchronized with audio features via the contrastive learning strategy, and the disentangled motion features are aligned well with the talking head. Furthermore, the denoising diffusion model takes the source image and the warped motion features as input to generate the high-resolution realistic talking head with diverse head poses. Extensive evaluations using multiple metrics demonstrate that our method outperforms the current techniques both qualitatively and quantitatively.

Existing cross-dataset deepfake detection approaches exploit mouth-related mismatches between the auditory and visual modalities in fake videos to enhance generalisation to unseen forgeries. However, such methods inevitably suffer performance degradation with limited or unaltered mouth motions, we argue that face forgery detection consistently benefits from using high-level cues across the whole face region. In this paper, we propose a two-phase audio-driven multi-modal transformer-based framework, termed AVForensics, to perform deepfake video content detection from an audio-visual matching view related to full face. In the first pre-training phase, we apply the novel uniform masking strategy to model global facial features and learn temporally dense video representations in a self-supervised cross-modal manner, by capturing the natural correspondence between the visual and auditory modalities regardless of large-scaled labelled data and heavy memory usage. Then we use these learned representations to fine-tune for the down-stream deepfake detection task in the second phase, which encourages the model to offer accurate predictions based on captured global facial movement features. Extensive experiments and visualizations on various public datasets demonstrate the superiority of our self-supervised pre-trained method for achieving generalisable and robust deepfake video detection.

Video moment retrieval aims to retrieve a target moment from an untrimmed video that semantically corresponds to the given language query. Existing methods commonly treat it as a regression task or a ranking task from the perspective of computer vision. Most of these works neglect comprehensive relations between video content and language context at a multi-granularity level and fail to efficiently model temporal relations among different video moments. In this paper, we formulate video moment retrieval into video reading comprehension by treating the input video as a text passage and language query as a question. To tackle the above impediments, we propose a Comprehensive Relation-aware Network (CRNet) to perceive comprehensive relations from extensive aspects. Specifically, we unite visual and textual features simultaneously at both clip-level and moment-level to thoroughly exploit inter-modality information, leading to a coarse-and-fine cross-modal interaction. Moreover, a background suppression module is introduced to restrain irrelevant background clips, meanwhile, a novel IoU attention mechanism and graph attention layer are efficiently devised to focus on the dependencies among highly-correlated video moments for the best choice selection. In-depth experiments on three public datasets TACoS, ActivityNet Captions, and Charades-STA demonstrate the superiority of our solution.

We consider the community detection problem in a sparse q-uniform hypergraph G, assuming that G is generated according to the Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based on the non-backtracking operator for hypergraphs works with high probability down to the generalized Kesten-Stigum detection threshold conjectured by Angelini et al. (2015). We characterize the spectrum of the non-backtracking operator for the sparse HSBM and provide an efficient dimension reduction procedure using the Ihara-Bass formula for hypergraphs. As a result, community detection for the sparse HSBM on n vertices can be reduced to an eigenvector problem of a 2n×2n non-normal matrix constructed from the adjacency matrix and the degree matrix of the hypergraph. To the best of our knowledge, this is the first provable and efficient spectral algorithm that achieves the conjectured threshold for HSBMs with r blocks generated according to a general symmetric probability tensor.

With the swift development of deep learning, hyper-realistic images generated by advanced facial manipulation techniques have posed a serious threat to the trustworthiness of digital media information. Most existing approaches formulate face forgery detection as a coarse-grained classification problem. They still significantly focus on low-level semantic cues which are sensitive to common corruptions such as video compression and generalise poorly to unseen forgeries. To address this issue, we propose a novel fine-grained feature learning framework for face forgery detection. To be specific, we adopt fine-grained frequency decomposition via a patch-wise manner to extract more sufficient information hidden in the frequency domain. We also propose the depth-wise separable attention module to select more informative features and captures the fine-grained cues from different input spaces. Moreover, to further explore the essential discrepancies, attention-guided feature augment module is introduced to fully exploit the multi-domain relations and incorporate frequency features into spatial clues. Extensive experiments and visualizations on public datasets fully demonstrate the effectiveness and robustness of our method against the state-of-the-art competitors.

Focusing on text-to-image (T2I) generation, we propose Text and Image Mutual-Translation Adversarial Networks (TIME), a lightweight but effective model that jointly learns a T2I generator G and an image captioning discriminator D under the Generative Adversarial Network framework. While previous methods tackle the T2I problem as a uni-directional task and use pre-trained language models to enforce the image--text consistency, TIME requires neither extra modules nor pre-training. We show that the performance of G can be boosted substantially by training it jointly with D as a language model. Specifically, we adopt Transformers to model the cross-modal connections between the image features and word embeddings, and design an annealing conditional hinge loss that dynamically balances the adversarial learning. In our experiments, TIME achieves state-of-the-art (SOTA) performance on the CUB dataset (Inception Score of 4.91 and Fréchet Inception Distance of 14.3 on CUB), and shows promising performance on MS-COCO dataset on image captioning and downstream vision-language tasks.

Imagining a colored realistic image from an arbitrary-drawn sketch is one of human capabilities that we eager machines to mimic. Unlike previous methods that either require the sketch-image pairs or utilize low-quantity detected edges as sketches, we study the exemplar-based sketch-to-image (s2i) synthesis task in a self-supervised learning manner, eliminating the necessity of the paired sketch data. To this end, we first propose an unsupervised method to efficiently synthesize line-sketches for general RGB-only datasets. With the synthetic paired-data, we then present a self-supervised Auto-Encoder (AE) to decouple the content/style features from sketches and RGB-images, and synthesize images both content-faithful to the sketches and style-consistent to the RGB-images. While prior works employ either the cycle-consistence loss or dedicated attentional modules to enforce the content/style fidelity, we show AE's superior performance with pure self-supervisions. To further improve the synthesis quality in high resolution, we also leverage an adversarial network to refine the details of synthetic images. Extensive experiments on $1024^2$ resolution demonstrate a new state-of-art-art performance of the proposed model on CelebA-HQ and Wiki-Art datasets. Moreover, with the proposed sketch generator, the model shows a promising performance on style mixing and style transfer, which the synthesized images are not only style-consistent but also semantically meaningful.

Exploring the potential of GANs for unsupervised disentanglement learning, this paper proposes a novel GAN-based disentanglement framework with One-Hot Sampling and Orthogonal Regularization (OOGAN). While previous works mostly attempt to tackle disentanglement learning through VAE and seek to implicitly minimize the Total Correlation (TC) objective with various sorts of approximation methods, we show that GANs have a natural advantage in disentangling with an alternating latent variable (noise) sampling method that is straightforward and robust. Furthermore, we provide a brand-new perspective on designing the structure of the generator and discriminator, demonstrating that a minor structural change and an orthogonal regularization on model weights entails an improved disentanglement. Instead of experimenting on simple toy datasets, we conduct experiments on higher-resolution images and show that OOGAN greatly pushes the boundary of unsupervised disentanglement.

We propose a sequential variational autoencoder to learn disentangled representations of sequential data (e.g., videos and audios) under self-supervision. Specifically, we exploit the benefits of some readily accessible supervision signals from input data itself or some off-the-shelf functional models and accordingly design auxiliary tasks for our model to utilize these signals. With the supervision of the signals, our model can easily disentangle the representation of an input sequence into static factors and dynamic factors (i.e., time-invariant and time-varying parts). Comprehensive experiments across videos and audios verify the effectiveness of our model on representation disentanglement and generation of sequential data, and demonstrate that, our model with self-supervision performs comparable to, if not better than, the fully-supervised model with ground truth labels, and outperforms state-of-the-art unsupervised models by a large margin.

Data augmentation is widely used to increase data variance in training deep neural networks. However, previous methods require either comprehensive domain knowledge or high computational cost. Can we learn data transformation automatically and efficiently with limited domain knowledge? Furthermore, can we leverage data transformation to improve not only network training but also network testing? In this work, we propose adaptive data transformation to achieve the two goals. The AdaTransform can increase data variance in training and decrease data variance in testing. Experiments on different tasks prove that it can improve generalization performance.

We investigate learning feature-to-feature translator networks by alternating back-propagation as a general-purpose solution to zero-shot learning (ZSL) problems. It is a generative model-based ZSL framework. In contrast to models based on generative adversarial networks (GAN) or variational autoencoders (VAE) that require auxiliary networks to assist the training, our model consists of a single conditional generator that maps class-level semantic features and Gaussian white noise vectors accounting for instance-level latent factors to visual features, and is trained by maximum likelihood estimation. The training process is a simple yet effective alternating back-propagation process that iterates the following two steps: (i) the inferential back-propagation to infer the latent noise vector of each observed example, and (ii) the learning back-propagation to update the model parameters. We show that, with slight modifications, our model is capable of learning from incomplete visual features for ZSL. We conduct extensive comparisons with existing generative ZSL methods on five benchmarks, demonstrating the superiority of our method in not only ZSL performance but also convergence speed and computational cost. Specifically, our model outperforms the existing state-of-the-art methods by a remarkable margin up to 3.1% and 4.0% in ZSL and generalized ZSL settings, respectively.

Zero-shot learning extends the conventional object classification to the unseen class recognition by introducing semantic representations of classes. Existing approaches predominantly focus on learning the proper mapping function for visual-semantic embedding, while neglecting the effect of learning discriminative visual features. In this paper, we study the significance of the discriminative region localization. We propose a semantic-guided multi-attention localization model, which automatically discovers the most discriminative parts of objects for zero-shot learning without any human annotations. Our model jointly learns cooperative global and local features from the whole object as well as the detected parts to categorize objects based on semantic descriptions. Moreover, with the joint supervision of embedding softmax loss and class-center triplet loss, the model is encouraged to learn features with high inter-class dispersion and intra-class compactness. Through comprehensive experiments on three widely used zero-shot learning benchmarks, we show the efficacy of the multi-attention localization and our proposed approach improves the state-of-the-art results by a considerable margin.

Most existing zero-shot learning methods consider the problem as a visual semantic embedding one. Given the demonstrated capability of Generative Adversarial Networks(GANs) to generate images, we instead leverage GANs to imagine unseen categories from text descriptions and hence recognize novel classes with no examples being seen. Specifically, we propose a simple yet effective generative model that takes as input noisy text descriptions about an unseen class (e.g. Wikipedia articles) and generates synthesized visual features for this class. With added pseudo data, zero-shot learning is naturally converted to a traditional classification problem. Additionally, to preserve the inter-class discrimination of the generated features, a visual pivot regularization is proposed as an explicit supervision. Unlike previous methods using complex engineered regularizers, our approach can suppress the noise well without additional regularization. Empirically, we show that our method consistently outperforms the state of the art on the largest available benchmarks on Text-based Zero-shot Learning.

In this paper, we study learning visual classifiers from unstructured text descriptions at part precision with no training images. We propose a learning framework that is able to connect text terms to its relevant parts and suppress connections to non-visual text terms without any part-text annotations. For instance, this learning process enables terms like beak to be sparsely linked to the visual representation of parts like head, while reduces the effect of non-visual terms like migrate on classifier prediction. Images are encoded by a part-based CNN that detect bird parts and learn part-specific representation. Part-based visual classifiers are predicted from text descriptions of unseen visual classifiers to facilitate classification without training images (also known as zero-shot recognition). We performed our experiments on CUBirds 2011 dataset and improves the state-of-the-art textbased zero-shot recognition results from 34.7% to 43.6%. We also created large scale benchmarks on North American Bird Images augmented with text descriptions, where we also show that our approach outperforms existing methods. Our code, data, and models are publically available link [1].

Due to the large volumes of data that need to be processed, efficient memory access and data transmission are crucial for high-performance implementations of convolutional neural networks (CNNs). Approximate memory is a promising technique to achieve efficient memory access and data transmission in CNN hardware implementations. To assess the feasibility of applying approximate memory techniques, we propose a framework for the data resilience evaluation (DRE) of CNNs and verify its effectiveness on a suite of prevalent CNNs. Simulation results show that a high degree of data resilience exists in these networks. By scaling the bit-width of the first five dominant data subsets, the data volume can be reduced by 80.38% on average with a 2.69% loss in relative prediction accuracy. For approximate memory with random errors, all the synaptic weights can be stored in the approximate part when the error rate is less than 10--4, while 3 MSBs must be protected if the error rate is fixed at 10--3. These results indicate a great potential for exploiting approximate memory techniques in CNN hardware design.

The exponentially increasing use of moving platforms for video capture introduces the urgent need to develop the general background subtraction algorithms with the capability to deal with the moving background. In this paper, we propose a multilayer-based framework for online background subtraction for videos captured by moving cameras. Unlike the previous treatments of the problem, the proposed method is not restricted to binary segmentation of background and foreground, but formulates it as a multi-label segmentation problem by modeling multiple foreground objects in different layers when they appear simultaneously in the scene. We assign an independent processing layer to each foreground object, as well as the background, where both motion and appearance models are estimated, and a probability map is inferred using a Bayesian filtering framework. Finally, Multi-label Graph-cut on Markov Random Field is employed to perform pixel-wise labeling. Extensive evaluation results show that the proposed method outperforms state-of-the-art methods on challenging video sequences.