We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by {\em orders of magnitude}.

The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the particular noise structure of SGD to its \emph{linear stability} (Wu et al., 2018). Specifically, we consider training over-parameterized models with square loss. We prove that if a global minimum $\theta^*$ is linearly stable for SGD, then it must satisfy $\|H(\theta^*)\|_F\leq O(\sqrt{B}/\eta)$, where $\|H(\theta^*)\|_F, B,\eta$ denote the Frobenius norm of Hessian at $\theta^*$, batch size, and learning rate, respectively. Otherwise, SGD will escape from that minimum \emph{exponentially} fast. Hence, for minima accessible to SGD, the sharpness---as measured by the Frobenius norm of the Hessian---is bounded \emph{independently} of the model size and sample size. The key to obtaining these results is exploiting the particular structure of SGD noise: The noise concentrates in sharp directions of local landscape and the magnitude is proportional to loss value. This alignment property of SGD noise provably holds for linear networks and random feature models (RFMs), and is empirically verified for nonlinear networks. Moreover, the validity and practical relevance of our theoretical findings are also justified by extensive experiments on CIFAR-10 dataset.

Incorporating the natural document-sentence-word structure into hierarchical Bayesian modeling, we propose convolutional Poisson gamma dynamical systems (PGDS) that introduce not only word-level probabilistic convolutions, but also sentence-level stochastic temporal transitions. With word-level convolutions capturing phrase-level topics and sentence-level transitions capturing how the topic usages evolve over consecutive sentences, we aggregate the topic proportions of all sentences of a document as its feature representation. To consider not only forward but also backward sentence-level information transmissions, we further develop a bidirectional convolutional PGDS to incorporate the full contextual information to represent each sentence. For efficient inference, we construct a convolutional-recurrent inference network, which provides both sentence-level and document-level representations, and introduce a hybrid Bayesian inference scheme combining stochastic-gradient MCMC and amortized variational inference. Experimental results on a variety of document corpora demonstrate that the proposed models can extract expressive multi-level latent representations, including interpretable phrase-level topics and sentence-level temporal transitions as well as discriminative document-level features, achieving state-of-the-art document categorization performance while being memory and computation efficient.

To enable large-scale machine learning in bandwidth-hungry environments such as wireless networks, significant progress has been made recently in designing communication-efficient federated learning algorithms with the aid of communication compression. On the other end, privacy preserving, especially at the client level, is another important desideratum that has not been addressed simultaneously in the presence of advanced communication compression techniques yet. In this paper, we propose a unified framework that enhances the communication efficiency of private federated learning with communication compression. Exploiting both general compression operators and local differential privacy, we first examine a simple algorithm that applies compression directly to differentially-private stochastic gradient descent, and identify its limitations. We then propose a unified framework SoteriaFL for private federated learning, which accommodates a general family of local gradient estimators including popular stochastic variance-reduced gradient methods and the state-of-the-art shifted compression scheme. We provide a comprehensive characterization of its performance trade-offs in terms of privacy, utility, and communication complexity, where SoteriaFL is shown to achieve better communication complexity without sacrificing privacy nor utility than other private federated learning algorithms without communication compression.

As the model size grows rapidly, fine-tuning the large pre-trained language model has become increasingly difficult due to its extensive memory usage. Previous works usually focus on reducing the number of trainable parameters in the network. While the model parameters do contribute to memory usage, the primary memory bottleneck during training arises from storing feature maps, also known as activations, as they are crucial for gradient calculation. Notably, machine learning models are typically trained using stochastic gradient descent.We argue that in stochastic optimization, models can handle noisy gradients as long as the gradient estimator is unbiased with reasonable variance.Following this motivation, we propose a new family of unbiased estimators called \sas, for matrix production with reduced variance, which only requires storing the sub-sampled activations for calculating the gradient.Our work provides both theoretical and experimental evidence that, in the context of tuning transformers, our proposed estimators exhibit lower variance compared to existing ones.By replacing the linear operation with our approximated one in transformers, we can achieve up to 2.7X peak memory reduction with almost no accuracy drop and enables up to $6.4\times$ larger batch size.Under the same hardware, \sas enables better down-streaming task performance by applying larger models and/or faster training speed with larger batch sizes.The code is available at https://anonymous.4open.science/r/WTACRS-A5C5/.

This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network using stochastic gradient descent. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method of Rolland et al. [2022], assuming a sufficiently good estimation of the score function. Finally, we analyze the upper bound of score-matching estimation within the score-based generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.

A central issue in machine learning is how to train models on sensitive user data. Industry has widely adopted a simple algorithm: Stochastic Gradient Descent with noise (a.k.a.

We study online change point detection problems under the constraint of local differential privacy (LDP) where, in particular, the statistician does not have access to the raw data. As a concrete problem, we study a multivariate nonparametric regression problem. At each time point $t$, the raw data are assumed to be of the form $(X_t, Y_t)$, where $X_t$ is a $d$-dimensional feature vector and $Y_t$ is a response variable. Our primary aim is to detect changes in the regression function $m_t(x)=\mathbb{E}(Y_t |X_t=x)$ as soon as the change occurs. We provide algorithms which respect the LDP constraint, which control the false alarm probability, and which detect changes with a minimal (minimax rate-optimal) delay. To quantify the cost of privacy, we also present the optimal rate in the benchmark, non-private setting. These non-private results are also new to the literature and thus are interesting \emph{per se}. In addition, we study the univariate mean online change point detection problem, under privacy constraints. This serves as the blueprint of studying more complicated private change point detection problems.

In this paper, we study one challenging issue in multi-view data clustering. To be specific, for two data matrices $\mathbf{X}^{(1)}$ and $\mathbf{X}^{(2)}$ corresponding to two views, we do not assume that $\mathbf{X}^{(1)}$ and $\mathbf{X}^{(2)}$ are fully aligned in row-wise. Instead, we assume that only a small portion of the matrices has established the correspondence in advance. Such a partially view-aligned problem (PVP) could lead to the intensive labor of capturing or establishing the aligned multi-view data, which has less been touched so far to the best of our knowledge. To solve this practical and challenging problem, we propose a novel multi-view clustering method termed partially view-aligned clustering (PVC). To be specific, PVC proposes to use a differentiable surrogate of the non-differentiable Hungarian algorithm and recasts it as a pluggable module. As a result, the category-level correspondence of the unaligned data could be established in a latent space learned by a neural network, while learning a common space across different views using the ``aligned'' data. Extensive experimental results show promising results of our method in clustering partially view-aligned data.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely Geometric Expansion for all-order Tensor Factorization (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.