The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have nowadays gained particular attention. In this paper, we study two variants of this kind, namely, the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. We prove their convergence to the objective distribution in terms of KL-divergence under the sole assumptions of smoothness and Log-Sobolev inequality which are weaker conditions than those used in prior works for these algorithms. With the batch size and the inner loop length set to $\sqrt{n}$, the gradient complexity to achieve an $\epsilon$-precision is $\tilde{O}((n+dn^{1/2}\epsilon^{-1})\gamma^2 L^2\alpha^{-2})$, which is an improvement from any previous analyses. We also show some essential applications of our result to non-convex optimization.

Online learning (OL) from data streams is an emerging area of research that encompasses numerous challenges from stream processing, machine learning, and networking. Recent extensions of stream-processing platforms, such as Apache Kafka and Flink, already provide basic extensions for the training of neural networks in a stream-processing pipeline. However, these extensions are not scalable and flexible enough for many real-world use-cases, since they do not integrate the neural-network libraries as a first-class citizen into their architectures. In this paper, we present TensAIR, which provides an end-to-end dataflow engine for OL from data streams via a protocol to which we refer as asynchronous iterative routing. TensAIR supports the common dataflow operators, such as Map, Reduce, Join, and has been augmented by the data-parallel OL functions train and predict. These belong to the new Model operator, in which an initial TensorFlow model (either freshly initialized or pre-trained) is replicated among multiple decentralized worker nodes. Our decentralized architecture allows TensAIR to efficiently shard incoming data batches across the distributed model replicas, which in turn trigger the model updates via asynchronous stochastic gradient descent. We empirically demonstrate that TensAIR achieves a nearly linear scale-out in terms of (1) the number of worker nodes deployed in the network, and (2) the throughput at which the data batches arrive at the dataflow operators. We exemplify the versatility of TensAIR by investigating both sparse (Word2Vec) and dense (CIFAR-10) use-cases, for which we are able to demonstrate very significant performance improvements in comparison to Kafka, Flink, and Horovod. We also demonstrate the magnitude of these improvements by depicting the possibility of real-time concept drift adaptation of a sentiment analysis model trained over a Twitter stream.

This paper studies the decentralized nonconvex optimization problem $\min_{x\in{\mathbb R}^d} f(x)\triangleq \frac{1}{m}\sum_{i=1}^m f_i(x)$, where $f_i(x)\triangleq \frac{1}{n}\sum_{j=1}^n f_{i,j}(x)$ is the local function on the $i$-th agent of the network. We propose a novel stochastic algorithm called DEcentralized probAbilistic Recursive gradiEnt deScenT (\DEAREST), which integrates the techniques of variance reduction, gradient tracking and multi-consensus. We construct a Lyapunov function that simultaneously characterizes the function value, the gradient estimation error and the consensus error for the convergence analysis. Based on this measure, we provide a concise proof to show DEAREST requires at most ${\mathcal O}(mn+\sqrt{mn}L\varepsilon^{-2})$ incremental first-order oracle (IFO) calls and ${\mathcal O}({L\varepsilon^{-2}}/{\sqrt{1-\lambda_2(W)}}\,)$ communication rounds to find an $\varepsilon$-stationary point in expectation, where $L$ is the smoothness parameter and $\lambda_2(W)$ is the second-largest eigenvalue of the gossip matrix $W$. We can verify both of the IFO complexity and communication complexity match the lower bounds. To the best of our knowledge, DEAREST is the first optimal algorithm for decentralized nonconvex finite-sum optimization.

Data dimension reduction (DDR) is all about mapping data from high dimensions to low dimensions, various techniques of DDR are being used for image dimension reduction like Random Projections, Principal Component Analysis (PCA), the Variance approach, LSA-Transform, the Combined and Direct approaches, and the New Random Approach. Auto-encoders (AE) are used to learn end-to-end mapping. In this paper, we demonstrate that pre-processing not only speeds up the algorithms but also improves accuracy in both supervised and unsupervised learning. In pre-processing of DDR, first PCA based DDR is used for supervised learning, then we explore AE based DDR for unsupervised learning. In PCA based DDR, we first compare supervised learning algorithms accuracy and time before and after applying PCA. Similarly, in AE based DDR, we compare unsupervised learning algorithm accuracy and time before and after AE representation learning. Supervised learning algorithms including support-vector machines (SVM), Decision Tree with GINI index, Decision Tree with entropy and Stochastic Gradient Descent classifier (SGDC) and unsupervised learning algorithm including K-means clustering, are used for classification purpose. We used two datasets MNIST and FashionMNIST Our experiment shows that there is massive improvement in accuracy and time reduction after pre-processing in both supervised and unsupervised learning.

We study the overparametrization bounds required for the global convergence of stochastic gradient descent algorithm for a class of one hidden layer feed-forward neural networks, considering most of the activation functions used in practice, including ReLU. We improve the existing state-of-the-art results in terms of the required hidden layer width. We introduce a new proof technique combining nonlinear analysis with properties of random initializations of the network. First, we establish the global convergence of continuous solutions of the differential inclusion being a nonsmooth analogue of the gradient flow for the MSE loss. Second, we provide a technical result (working also for general approximators) relating solutions of the aforementioned differential inclusion to the (discrete) stochastic gradient descent sequences, hence establishing linear convergence towards zero loss for the stochastic gradient descent iterations.

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).

Using the below source code we will specify the optimizer as stochastic gradient descent and will mention the learning rate as 0.001. After that, we will compile the model with loss functions for both outputs. Note: We can mention different loss functions for different outputs. In the same way, we can also mention different metrics for different outputs. Using the below syntax we will train the model for 500 epochs.

Adversarial attacks can deceive neural networks by adding tiny perturbations to their input data. Ensemble defenses, which are trained to minimize attack transferability among sub-models, offer a promising research direction to improve robustness against such attacks while maintaining a high accuracy on natural inputs. We discover, however, that recent state-of-the-art (SOTA) adversarial attack strategies cannot reliably evaluate ensemble defenses, sizeably overestimating their robustness. This paper identifies the two factors that contribute to this behavior. First, these defenses form ensembles that are notably difficult for existing gradient-based method to attack, due to gradient obfuscation. Second, ensemble defenses diversify sub-model gradients, presenting a challenge to defeat all sub-models simultaneously, simply summing their contributions may counteract the overall attack objective; yet, we observe that ensemble may still be fooled despite most sub-models being correct. We therefore introduce MORA, a model-reweighing attack to steer adversarial example synthesis by reweighing the importance of sub-model gradients. MORA finds that recent ensemble defenses all exhibit varying degrees of overestimated robustness. Comparing it against recent SOTA white-box attacks, it can converge orders of magnitude faster while achieving higher attack success rates across all ensemble models examined with three different ensemble modes (i.e., ensembling by either softmax, voting or logits). In particular, most ensemble defenses exhibit near or exactly 0% robustness against MORA with $\ell^\infty$ perturbation within 0.02 on CIFAR-10, and 0.01 on CIFAR-100. We make MORA open source with reproducible results and pre-trained models; and provide a leaderboard of ensemble defenses under various attack strategies.

Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA) for solving the MaxCut problem. Specifically, we address two problems in the QAOA, how to initialise the algorithm, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as a warm-starting technique for QAOA. We demonstrate that merging GNNs with QAOA can outperform both approaches individually. Furthermore, we demonstrate how graph neural networks enables warm-start generalisation across not only graph instances, but also to increasing graph sizes, a feature not straightforwardly available to other warm-starting methods. For training the QAOA, we test several optimisers for the MaxCut problem up to 16 qubits and benchmark against vanilla gradient descent. These include quantum aware/agnostic and machine learning based/neural optimisers. Examples of the latter include reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the optimisation problems can be solved using QAOA in an end-to-end differentiable pipeline.

Gradient descent or its variants are popular in training neural networks. However, in deep Q-learning with neural network approximation, a type of reinforcement learning, gradient descent (also known as Residual Gradient (RG)) is barely used to solve Bellman residual minimization problem. On the contrary, Temporal Difference (TD), an incomplete gradient descent method prevails. In this work, we perform extensive experiments to show that TD outperforms RG, that is, when the training leads to a small Bellman residual error, the solution found by TD has a better policy and is more robust against the perturbation of neural network parameters. We further use experiments to reveal a key difference between reinforcement learning and supervised learning, that is, a small Bellman residual error can correspond to a bad policy in reinforcement learning while the test loss function in supervised learning is a standard index to indicate the performance. We also empirically examine that the missing term in TD is a key reason why RG performs badly. Our work shows that the performance of a deep Q-learning solution is closely related to the training dynamics and how an incomplete gradient descent method can find a good policy is interesting for future study.