Graph Neural Networks (GNNs) are a popular technique for modelling graph-structured data and computing node-level representations via aggregation of information from the neighborhood of each node. However, this aggregation implies an increased risk of revealing sensitive information, as a node can participate in the inference for multiple nodes. This implies that standard privacy-preserving machine learning techniques, such as differentially private stochastic gradient descent (DP-SGD) - which are designed for situations where each data point participates in the inference for one point only - either do not apply, or lead to inaccurate models. In this work, we formally define the problem of learning GNN parameters with node-level privacy, and provide an algorithmic solution with a strong differential privacy guarantee. We employ a careful sensitivity analysis and provide a non-trivial extension of the privacy-by-amplification technique to the GNN setting. An empirical evaluation on standard benchmark datasets demonstrates that our method is indeed able to learn accurate privacy-preserving GNNs which outperform both private and non-private methods that completely ignore graph information.

In distributed learning, a central server trains a model according to updates provided by nodes holding local data samples. In the presence of one or more malicious servers sending incorrect information (a Byzantine adversary), standard algorithms for model training such as stochastic gradient descent (SGD) fail to converge. In this paper, we present a simplified convergence theory for the generic Byzantine Resilient SGD method originally proposed by Blanchard et al. [NeurIPS 2017]. Compared to the existing analysis, we shown convergence to a stationary point in expectation under standard assumptions on the (possibly nonconvex) objective function and flexible assumptions on the stochastic gradients.

The study of hand-object interaction requires generating viable grasp poses for high-dimensional multi-finger models, often relying on analytic grasp synthesis which tends to produce brittle and unnatural results. This paper presents Grasp'D, an approach for grasp synthesis with a differentiable contact simulation from both known models as well as visual inputs. We use gradient-based methods as an alternative to sampling-based grasp synthesis, which fails without simplifying assumptions, such as pre-specified contact locations and eigengrasps. Such assumptions limit grasp discovery and, in particular, exclude high-contact power grasps. In contrast, our simulation-based approach allows for stable, efficient, physically realistic, high-contact grasp synthesis, even for gripper morphologies with high-degrees of freedom. We identify and address challenges in making grasp simulation amenable to gradient-based optimization, such as non-smooth object surface geometry, contact sparsity, and a rugged optimization landscape. Grasp'D compares favorably to analytic grasp synthesis on human and robotic hand models, and resultant grasps achieve over 4x denser contact, leading to significantly higher grasp stability. Video and code available at https://graspd-eccv22.github.io/.

In this paper, we consider to improve the stochastic variance reduce gradient (SVRG) method via incorporating the curvature information of the objective function. We propose to reduce the variance of stochastic gradients using the computationally efficient Barzilai-Borwein (BB) method by incorporating it into the SVRG. We also incorporate a BB-step size as its variant. We prove its linear convergence theorem that works not only for the proposed method but also for the other existing variants of SVRG with second-order information. We conduct the numerical experiments on the benchmark datasets and show that the proposed method with constant step size performs better than the existing variance reduced methods for some test problems.

Practical results have shown that deep learning optimizers using small constant learning rates, hyperparameters close to one, and large batch sizes can find the model parameters of deep neural networks that minimize the loss functions. We first show theoretical evidence that the momentum method (Momentum) and adaptive moment estimation (Adam) perform well in the sense that the upper bound of the theoretical performance measure is small with a small constant learning rate, hyperparameters close to one, and a large batch size. Next, we show that there exists a batch size called the critical batch size minimizing the stochastic first-order oracle (SFO) complexity, which is the stochastic gradient computation cost, and that SFO complexity increases once the batch size exceeds the critical batch size. Finally, we provide numerical results that support our theoretical results. That is, the numerical results indicate that Adam using a small constant learning rate, hyperparameters close to one, and the critical batch size minimizing SFO complexity has faster convergence than Momentum and stochastic gradient descent (SGD).

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal stochastic gradient algorithm based on variance reduction called ProxSVRG+. We provide a clean and tight analysis of ProxSVRG+, which shows that it outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, hence solves an open problem proposed in Reddi et al. (2016b). Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG (Reddi et al., 2016b) and extends to the online setting by avoiding full gradient computations. Then, we further propose an optimal algorithm, called SSRGD, based on SARAH (Nguyen et al., 2017) and show that SSRGD further improves the gradient complexity of ProxSVRG+ and achieves the optimal upper bound, matching the known lower bound of (Fang et al., 2018; Li et al., 2021). Moreover, we show that both ProxSVRG+ and SSRGD enjoy automatic adaptation with local structure of the objective function such as the Polyak-\L{}ojasiewicz (PL) condition for nonconvex functions in the finite-sum case, i.e., we prove that both of them can automatically switch to faster global linear convergence without any restart performed in prior work ProxSVRG (Reddi et al., 2016b). Finally, we focus on the more challenging problem of finding an $(\epsilon, \delta)$-local minimum instead of just finding an $\epsilon$-approximate (first-order) stationary point (which may be some bad unstable saddle points). We show that SSRGD can find an $(\epsilon, \delta)$-local minimum by simply adding some random perturbations. Our algorithm is almost as simple as its counterpart for finding stationary points, and achieves similar optimal rates.

With rising powerful, low-cost embedded devices, the edge computing has become an increasingly popular choice. In this paper, we propose a new incremental local stochastic gradient descent (SGD) tailored on the Raspberry Pi to deal with large ImageNet ILSVRC 2010 dataset having 1,261,405 images with 1,000 classes. The local SGD splits the data block into $k$ partitions using $k$means algorithm and then it learns in the parallel way SGD models in each data partition to classify the data locally. The incremental local SGD sequentially loads small data blocks of the training dataset to learn local SGD models. The numerical test results on Imagenet dataset show that our incremental local SGD algorithm with the Raspberry Pi 4 is faster and more accurate than the state-of-the-art linear SVM run on a PC Intel(R) Core i7-4790 CPU, 3.6 GHz, 4 cores.

Now let's dive in to cost function It calculates the measure between the original value and your predicted value generated from your model. Cost functions may differ according to your selection, your manager's selection, or the project necessity. Imagine that you got a Data set about house prices. You have built the model and made a prediction afterward. The actual price of the house is: $155.000

Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often oscillate indefinitely. To reduce this discrepancy between theory and practice, this paper focuses on the generalization of neural networks whose training dynamics do not necessarily converge to fixed points. Our main contribution is to propose a notion of statistical algorithmic stability (SAS) that extends classical algorithmic stability to non-convergent algorithms and to study its connection to generalization. This ergodic-theoretic approach leads to new insights when compared to the traditional optimization and learning theory perspectives. We prove that the stability of the time-asymptotic behavior of a learning algorithm relates to its generalization and empirically demonstrate how loss dynamics can provide clues to generalization performance. Our findings provide evidence that networks that "train stably generalize better" even when the training continues indefinitely and the weights do not converge.

In this article, I will not explain to you all of the (exciting!) Instead, I will provide you with some implementations and pictures that should make it possible to understand the gist of the paper. I also gave my best to create an implementation of the optimizers mentioned in the paper, but use the code with care because I'm also not an expert in this regard. In order to understand what Anti-PGD (Anti-Perturbed Gradient Descent) is about, let us shortly recap how GD and the derived algorithms such as SGD and PGD work. Let us assume that we want to minimize a function f with a gradient denoted as f(θ).