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Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

David Holzmüller, Viktor Zaverkin, Johannes Kästner, Ingo Steinwart

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

Theory · Learning Theory

Frank Cole, Yulong Lu

While score-based generative models (SGMs) have achieved remarkable successes in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a measure of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep network approximation rate for the true score function associated to the forward process, which is interesting in its own right.

Probabilistic Methods · Gaussian Processes

Jihao Andreas Lin, Shreyas Padhy, Javier Antorán, Austin Tripp, Alexander Terenin, Csaba Szepesvari, José Miguel Hernández Lobato, David Janz

As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving this linear system, and show that when done right---by which we mean using specific insights from the optimisation and kernel communities---stochastic gradient descent is highly effective. To that end, we introduce a particularly simple stochastic dual descent algorithm, explain its design in an intuitive manner and illustrate the design choices through a series of ablation studies. Further experiments demonstrate that our new method is highly competitive. In particular, our evaluations on the UCI regression tasks and on Bayesian optimisation set our approach apart from preconditioned conjugate gradients and variational Gaussian process approximations. Moreover, our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.

Deep Learning · Generative Models and Autoencoders

Assaf Shocher, Amil Dravid, Yossi Gandelsman, Inbar Mosseri, Michael Rubinstein, Alexei Efros

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely $f(f(z))=f(z)$. The proposed model $f$ is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely $f(x)=x$. We define the target manifold as the set of all instances that $f$ maps to themselves.(2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, $f(f(z))=f(z)$ which encourages the range of $f(z)$ to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Miscellaneous Aspects of Machine Learning · Representation Learning

Zhongqi Yue, Jiankun Wang, Qianru Sun, Lei Ji, Eric Chang, Hanwang Zhang

Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes. We build a theoretical framework that connects the diffusion time-steps and the hidden attributes, which serves as an effective inductive bias for unsupervised learning. Specifically, the forward diffusion process incrementally adds Gaussian noise to samples at each time-step, which essentially collapses different samples into similar ones by losing attributes, e.g., fine-grained attributes such as texture are lost with less noise added (i.e., early time-steps), while coarse-grained ones such as shape are lost by adding more noise (i.e., late time-steps). To disentangle the modular attributes, at each time-step t, we learn a t-specific feature to compensate for the newly lost attribute, and the set of all {1,...,t}-specific features, corresponding to the cumulative set of lost attributes, are trained to make up for the reconstruction error of a pre-trained DM at time-step t. On CelebA, FFHQ, and Bedroom datasets, the learned feature significantly improves attribute classification and enables faithful counterfactual generation, e.g., interpolating only one specified attribute between two images, validating the disentanglement quality. Codes are in https://github.com/yue-zhongqi/diti.

Probabilistic Methods · Gaussian Processes

Quoc Phong Nguyen, Bryan Kian Hsiang Low, Patrick Jaillet

Research on optimizing the risk measure of a blackbox function using Gaussian processes, especially Bayesian optimization (BO) of risk measures, has become increasingly important due to the inevitable presence of uncontrollable variables in real-world applications. Nevertheless, existing works on BO of risk measures start the optimization from scratch for every new task without considering the results of prior tasks. In contrast, its vanilla BO counterpart has received a thorough investigation on utilizing prior tasks to speed up the current task through the body of works on meta-BO which, however, have not considered risk measures. To bridge this gap, this paper presents the first algorithm for meta-BO of risk measures (i.e., value-at-risk (VaR) and the conditional VaR), namely meta-VBO, by introducing a novel adjustment to the upper confidence bound acquisition function. Our proposed algorithm exhibits two desirable properties: (i) invariance to scaling and vertical shifting of the blackbox function and (ii) robustness to prior harmful tasks. We provide a theoretical performance guarantee for our algorithm and empirically demonstrate its performance using several synthetic function benchmarks and real-world objective functions.

Applications · Computer Vision

LI Yang, RUIZHENG WU, Jiyong Li, YINGCONG CHEN

Learning surfaces from neural radiance field (NeRF) became a rising topic in Multi-View Stereo (MVS). Recent Signed Distance Function (SDF)-based methods demonstrated their ability to reconstruct exact 3D shapes of Lambertian scenes. However, their results on reflective scenes are unsatisfactory due to the entanglement of specular radiance and complicated geometry. To address the challenges, we propose a Gaussian-based representation of normals in SDF fields. Supervised by polarization priors, this representation guides the learning of geometry behind the specular reflection and capture more details than existing methods. Moreover, we propose a reweighting strategy in optimization process to alleviate the noise issue of polarization priors. To validate the effectiveness of our design, we capture polarimetric information and ground truth meshes in additional reflective scenes with various geometry. We also evaluated our framework on PANDORA dataset. Both qualitative and quantitative comparisons prove our method outperforms existing neural 3D reconstruction methods in reflective scenes by a large margin.

Miscellaneous Aspects of Machine Learning · Representation Learning

Aming Wu, Cheng Deng

To promote the safe deployment of object detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) is recently proposed, aiming to detect unknown objects during training without reliance on any auxiliary OOD data. To alleviate the impact of lacking OOD data, for this task, one feasible solution is to exploit the known in-distribution (ID) data to synthesize proper OOD information for supervision, which strengthens detectors' discrimination. From the frequency perspective, since the phase generally reflects the content of the input, in this paper, we explore leveraging the phase of ID features to generate expected OOD features involving different content. And a method of Modulated Phase Diffusion (MPD) is proposed, containing a shared forward and two different reverse processes. Specifically, after calculating the phase of the extracted features, to prevent the rapid loss of content in the phase, the forward process gradually performs Gaussian Average on the phase instead of adding noise. The averaged phase and original amplitude are combined to obtain the features taken as the input of the reverse process. Next, one OOD branch is defined to synthesize virtual OOD features by continually enlarging the content discrepancy between the OOD features and original ones. Meanwhile, another modulated branch is designed to generate augmented features owning a similar phase as the original features by scaling and shifting the OOD branch. Both original and augmented features are used for training, enhancing the discrimination. Experimental results on OOD-OD, incremental object detection, and open-set object detection demonstrate the superiorities of our method. The source code will be released at https://github.com/AmingWu/MPD.

Probabilistic Methods · Gaussian Processes

Yijue Dai, Wenzhong Yan, Feng Yin

Integrating information while recognizing dependence from multiple data sources and enhancing the predictive performance of the multi-output regression are challenging tasks. Multioutput Gaussian Process (MOGP) methods offer outstanding solutions with tractable predictions and uncertainty quantification. However, their practical applications are hindered by high computational complexity and storage demand. Additionally, there exist model mismatches in existing MOGP models when dealing with non-Gaussian data. To improve the model representation ability in terms of flexibility, optimality, and scalability, this paper introduces a novel multi-output regression framework, termed Graphical MOGP (GMOGP), which is empowered by: (i) Generating flexible Gaussian process priors consolidated from dentified parents, (ii) providing dependent processes with attention-based graphical representations, and (iii) achieving Pareto optimal solutions of kernel hyperparameters via a distributed learning framework. Numerical results confirm that the proposed GMOGP significantly outperforms state-of-the-art MOGP alternatives in predictive performance, as well as in time and memory efficiency, across various synthetic and real datasets.

Probabilistic Methods · Bayesian Models and Methods

Yongsheng Mei, Mahdi Imani, Tian Lan

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum *a posteriori* inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nyström approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

Social Aspects · Trustworthy Machine Learning

Jiayuan Ye, Anastasia Borovykh, Soufiane Hayou, Reza Shokri

We introduce an analytical framework to quantify the changes in a machine learning algorithm's output distribution following the inclusion of a few data points in its training set, a notion we define as leave-one-out distinguishability (LOOD). This is key to measuring data **memorization** and information **leakage** as well as the **influence** of training data points in machine learning. We illustrate how our method broadens and refines existing empirical measures of memorization and privacy risks associated with training data. We use Gaussian processes to model the randomness of machine learning algorithms, and validate LOOD with extensive empirical analysis of leakage using membership inference attacks. Our analytical framework enables us to investigate the causes of leakage and where the leakage is high. For example, we analyze the influence of activation functions, on data memorization. Additionally, our method allows us to identify queries that disclose the most information about the training data in the leave-one-out setting. We illustrate how optimal queries can be used for accurate **reconstruction** of training data.

Reinforcement Learning · Deep RL

Zhenwen Dai, Federico Tomasi, Sina Ghiassian

In-context learning is a promising approach for online policy learning of offline reinforcement learning (RL) methods, which can be achieved at inference time without gradient optimization. However, this method is hindered by significant computational costs resulting from the gathering of large training trajectory sets and the need to train large Transformer models. We address this challenge by introducing an In-context Exploration-Exploitation (ICEE) algorithm, designed to optimize the efficiency of in-context policy learning. Unlike existing models, ICEE performs an exploration-exploitation trade-off at inference time within a Transformer model, without the need for explicit Bayesian inference. Consequently, ICEE can solve Bayesian optimization problems as efficiently as Gaussian process biased methods do, but in significantly less time. Through experiments in grid world environments, we demonstrate that ICEE can learn to solve new RL tasks using only tens of episodes, marking a substantial improvement over the hundreds of episodes needed by the previous in-context learning method.

Reinforcement Learning · Deep RL

Haque Ishfaq, Qingfeng Lan, Pan Xu, A. Rupam Mahmood, Doina Precup, anima anandkumar, Kamyar Azizzadenesheli

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of $\tilde{O}(d^{3/2}H^{3/2}\sqrt{T})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $T$ is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

Applications · Computer Vision

Zahra Babaiee, Peyman Kiasari, Daniela Rus, Radu Grosu

Recent advances in depthwise-separable convolutional neural networks (DS-CNNs) have led to novel architectures, that surpass the performance of classical CNNs, by a considerable scalability and accuracy margin. This paper reveals another striking property of DS-CNN architectures: discernible and explainable patterns emerge in their trained depthwise convolutional kernels in all layers. Through an extensive analysis of millions of trained filters, with different sizes and from various models, we employed unsupervised clustering with autoencoders, to categorize these filters. Astonishingly, the patterns converged into a few main clusters, each resembling the difference of Gaussian (DoG) functions, and their first and second-order derivatives. Notably, we classify over 95\% and 90\% of the filters from state-of-the-art ConvNeXtV2 and ConvNeXt models, respectively. This finding is not merely a technological curiosity; it echoes the foundational models neuroscientists have long proposed for the vision systems of mammals. Our results thus deepen our understanding of the emergent properties of trained DS-CNNs and provide a bridge between artificial and biological visual processing systems. More broadly, they pave the way for more interpretable and biologically-inspired neural network designs in the future.

Yuanfeng Ji, Zhe Chen, Enze Xie, Lanqing Hong, Xihui Liu, Zhaoqiang Liu, Tong Lu, Zhenguo Li, Ping Luo

We propose a simple, efficient, yet powerful framework for dense visual predictions based on the conditional diffusion pipeline. Our approach follows a "noise-to-map" generative paradigm for prediction by progressively removing noise from a random Gaussian distribution, guided by the image. The method, called DDP, efficiently extends the denoising diffusion process into the modern perception pipeline. Without task-specific design and architecture customization, DDP is easy to generalize to most dense prediction tasks, e.g., semantic segmentation and depth estimation. In addition, DDP shows attractive properties such as dynamic inference and uncertainty awareness, in contrast to previous single-step discriminative methods. We show top results on three representative tasks with six diverse benchmarks, without tricks, DDP achieves state-of-the-art or competitive performance on each task compared to the specialist counterparts. For example, semantic segmentation (83.9 mIoU on Cityscapes), BEV map segmentation (70.6 mIoU on nuScenes), and depth estimation (0.05 REL on KITTI). We hope that our approach will serve as a solid baseline and facilitate future research.

Shouwei Ruan, Yinpeng Dong, Hang Su, Jianteng Peng, Ning Chen, Xingxing Wei

Visual recognition models are not invariant to viewpoint changes in the 3D world, as different viewing directions can dramatically affect the predictions given the same object. Although many efforts have been devoted to making neural networks invariant to 2D image translations and rotations, viewpoint invariance is rarely investigated. As most models process images in the perspective view, it is challenging to impose invariance to 3D viewpoint changes based only on 2D inputs. Motivated by the success of adversarial training in promoting model robustness, we propose Viewpoint-Invariant Adversarial Training (VIAT) to improve viewpoint robustness of common image classifiers. By regarding viewpoint transformation as an attack, VIAT is formulated as a minimax optimization problem, where the inner maximization characterizes diverse adversarial viewpoints by learning a Gaussian mixture distribution based on a new attack GMVFool, while the outer minimization trains a viewpoint-invariant classifier by minimizing the expected loss over the worst-case adversarial viewpoint distributions. To further improve the generalization performance, a distribution sharing strategy is introduced leveraging the transferability of adversarial viewpoints across objects. Experiments validate the effectiveness of VIAT in improving the viewpoint robustness of various image classifiers based on the diversity of adversarial viewpoints generated by GMVFool.

Chen Henry Wu, Fernando De la Torre

Diffusion models generate images by iterative denoising. Recent work has shown that by making the denoising process deterministic, one can encode real images into latent codes of the same size, which can be used for image editing. This paper explores the possibility of defining a latent space even when the denoising process remains stochastic. Recall that, in stochastic diffusion models, Gaussian noises are added in each denoising step, and we can concatenate all the noises to form a latent code. This results in a latent space of much higher dimensionality than the original image. We demonstrate that this latent space of stochastic diffusion models can be used in the same way as that of deterministic diffusion models in two applications. First, we propose CycleDiffusion, a method for zero-shot and unpaired image editing using stochastic diffusion models, which improves the performance over its deterministic counterpart. Second, we demonstrate unified, plug-and-play guidance in the latent spaces of deterministic and stochastic diffusion models.

Aming Wu, Da Chen, Cheng Deng

To promote the safe application of detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) is recently proposed, whose goal is to detect unseen OOD objects without accessing any auxiliary OOD data. For this task, the challenge mainly lies in how to only leverage the known in-distribution (ID) data to detect OOD objects accurately without affecting the detection of ID objects, which can be framed as the diffusion problem for deep feature synthesis. Accordingly, such challenge could be addressed by the forward and reverse processes in the diffusion model. In this paper, we propose a new approach of Deep Feature Deblurring Diffusion (DFDD), consisting of forward blurring and reverse deblurring processes. Specifically, the forward process gradually performs Gaussian Blur on the extracted features, which is instrumental in retaining sufficient input-relevant information. By this way, the forward process could synthesize virtual OOD features that are close to the classification boundary between ID and OOD objects, which improves the performance of detecting OOD objects. During the reverse process, based on the blurred features, a dedicated deblurring model is designed to continually recover the lost details in the forward process. Both the deblurred features and original features are taken as the input for training, strengthening the discrimination ability. In the experiments, our method is evaluated on OOD-OD, open-set object detection, and incremental object detection. The significant performance gains over baselines demonstrate the superiorities of our method. The source code will be made available at: https://github.com/AmingWu/DFDD-OOD.

Mengwei Ren, Mauricio Delbracio, Hossein Talebi, Guido Gerig, Peyman Milanfar

Diffusion Probabilistic Models (DPMs) have recently been employed for image deblurring, formulated as an image-conditioned generation process that maps Gaussian noise to the high-quality image, conditioned on the blurry input. Image-conditioned DPMs (icDPMs) have shown more realistic results than regression-based methods when trained on pairwise in-domain data. However, their robustness in restoring images is unclear when presented with out-of-domain images as they do not impose specific degradation models or intermediate constraints. To this end, we introduce a simple yet effective multiscale structure guidance as an implicit bias that informs the icDPM about the coarse structure of the sharp image at the intermediate layers. This guided formulation leads to a significant improvement of the deblurring results, particularly on unseen domain. The guidance is extracted from the latent space of a regression network trained to predict the clean-sharp target at multiple lower resolutions, thus maintaining the most salient sharp structures. With both the blurry input and multiscale guidance, the icDPM model can better understand the blur and recover the clean image. We evaluate a single-dataset trained model on diverse datasets and demonstrate more robust deblurring results with fewer artifacts on unseen data. Our method outperforms existing baselines, achieving state-of-the-art perceptual quality while keeping competitive distortion metrics.

Liang Xu, Ziyang Song, Dongliang Wang, Jing Su, Zhicheng Fang, Chenjing Ding, Weihao Gan, Yichao Yan, Xin Jin, Xiaokang Yang 等

We present a GAN-based Transformer for general action-conditioned 3D human motion generation, including not only single-person actions but also multi-person interactive actions. Our approach consists of a powerful Action-conditioned motion TransFormer (ActFormer) under a GAN training scheme, equipped with a Gaussian Process latent prior. Such a design combines the strong spatio-temporal representation capacity of Transformer, superiority in generative modeling of GAN, and inherent temporal correlations from the latent prior. Furthermore, ActFormer can be naturally extended to multi-person motions by alternately modeling temporal correlations and human interactions with Transformer encoders. To further facilitate research on multi-person motion generation, we introduce a new synthetic dataset of complex multi-person combat behaviors. Extensive experiments on NTU-13, NTU RGB+D 120, BABEL and the proposed combat dataset show that our method can adapt to various human motion representations and achieve superior performance over the state-of-the-art methods on both single-person and multi-person motion generation tasks, demonstrating a promising step towards a general human motion generator.