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Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference procedure. For instance, the ordinary least squares (OLS) estimator in an adaptive linear regression model can exhibit non-normal asymptotic behavior, posing challenges for accurate inference and interpretation. In this paper, we propose a general method for constructing debiased estimator which remedies this issue. It makes use of the idea of adaptive linear estimating equations, and we establish theoretical guarantees of asymptotic normality, supplemented by discussions on achieving near-optimal asymptotic variance. A salient feature of our estimator is that in the context of multi-armed bandits, our estimator retains the non-asymptotic performance of the least square estimator while obtaining asymptotic normality property. Consequently, this work helps connect two fruitful paradigms of adaptive inference: a) non-asymptotic inference using concentration inequalities and b) asymptotic inference via asymptotic normality.

Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren plateaux make these approaches less appealing. To improve the optimization the Quantum Natural Gradient (QNG) method [Quantum 4, 269 (2020)] was introduced - a method that uses information about the local geometry of the quantum state-space. While the QNG-based optimization is promising, in each step it requires more quantum resources, since to compute the QNG one requires $O(m^2)$ quantum state preparations, where $m$ is the number of parameters in the parameterized circuit. In this work we propose two methods that reduce the resources/state preparations required for QNG, while keeping the advantages and performance of the QNG-based optimization. Specifically, we first introduce the Random Natural Gradient (RNG) that uses random measurements and the classical Fisher information matrix (as opposed to the quantum Fisher information used in QNG). The essential quantum resources reduce to linear $O(m)$ and thus offer a quadratic "speed-up", while in our numerical simulations it matches QNG in terms of accuracy. We give some theoretical arguments for RNG and then benchmark the method with the QNG on both classical and quantum problems. Secondly, inspired by stochastic-coordinate methods, we propose a novel approximation to the QNG which we call Stochastic-Coordinate Quantum Natural Gradient that optimizes only a small (randomly sampled) fraction of the total parameters at each iteration. This method also performs equally well in our benchmarks, while it uses fewer resources than the QNG.

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and symmetrize it to be equivariant to the given group by employing a small equivariant network that parameterizes the probabilistic distribution underlying the symmetrization. The distribution is end-to-end trained with the base model which can maximize performance while reducing sample complexity of symmetrization. We show that this approach ensures not only equivariance to given group but also universal approximation capability in expectation. We implement our method on various base models, including patch-based transformers that can be initialized from pretrained vision transformers, and test them for a wide range of symmetry groups including permutation and Euclidean groups and their combinations. Empirical tests show competitive results against tailored equivariant architectures, suggesting the potential for learning equivariant functions for diverse groups using a non-equivariant universal base architecture. We further show evidence of enhanced learning in symmetric modalities, like graphs, when pretrained from non-symmetric modalities, like vision. Code is available at //github.com/jw9730/lps.

Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete diffusion models. Specifically, we first prove that the continuous probability flow is the Monge optimal transport map under certain conditions, and also present an equivalent evidence for discrete cases. In view of these findings, we are then able to define the discrete probability flow in line with the principles of optimal transport. Finally, drawing upon our newly established definitions, we propose a novel sampling method that surpasses previous discrete diffusion models in its ability to generate more certain outcomes. Extensive experiments on the synthetic toy dataset and the CIFAR-10 dataset have validated the effectiveness of our proposed discrete probability flow. Code is released at: //github.com/PangzeCheung/Discrete-Probability-Flow.

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the posterior distribution can be used for providing ensemble predictions and quantifying prediction uncertainty. It is well-known that deep learning models with lower sharpness have better generalization ability. However, existing posterior inferences are not aware of sharpness/flatness in terms of formulation, possibly leading to high sharpness for the models sampled from them. In this paper, we develop theories, the Bayesian setting, and the variational inference approach for the sharpness-aware posterior. Specifically, the models sampled from our sharpness-aware posterior, and the optimal approximate posterior estimating this sharpness-aware posterior, have better flatness, hence possibly possessing higher generalization ability. We conduct experiments by leveraging the sharpness-aware posterior with state-of-the-art Bayesian Neural Networks, showing that the flat-seeking counterparts outperform their baselines in all metrics of interest.

Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we provide a systematic study of the effects of the regularization strength on the performance of linear classifiers that are trained to solve binary classification problems by minimizing a regularized least-squares objective. We consider the over-parametrized regime and assume that the classes are generated from a Gaussian Mixture Model (GMM) where a fraction $c<\frac{1}{2}$ of the training data is mislabeled. Under these assumptions, we rigorously analyze the classification errors resulting from the application of ridge, $\ell_1$, and $\ell_\infty$ regression. In particular, we demonstrate that ridge regression invariably improves the classification error. We prove that $\ell_1$ regularization induces sparsity and observe that in many cases one can sparsify the solution by up to two orders of magnitude without any considerable loss of performance, even though the GMM has no underlying sparsity structure. For $\ell_\infty$ regularization we show that, for large enough regularization strength, the optimal weights concentrate around two values of opposite sign. We observe that in many cases the corresponding "compression" of each weight to a single bit leads to very little loss in performance. These latter observations can have significant practical ramifications.

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multiantenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs.

The framework of approximate differential privacy is considered, and augmented by introducing the notion of "the total variation of a (privacy-preserving) mechanism" (denoted by $\eta$-TV). With this refinement, an exact composition result is derived, and shown to be significantly tighter than the optimal bounds for differential privacy (which do not consider the total variation). Furthermore, it is shown that $(\varepsilon,\delta)$-DP with $\eta$-TV is closed under subsampling. The induced total variation of commonly used mechanisms are computed. Moreover, the notion of total variation of a mechanism is extended to the local privacy setting and privacy-utility tradeoffs are investigated. In particular, total variation distance and KL divergence are considered as utility functions and upper bounds are derived. Finally, the results are compared and connected to the (purely) locally differentially private setting.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.