Word meaning may change over time as a reflection of changes in human society. Therefore, modeling time in word representation is necessary for some diachronic tasks. Most existing diachronic word representation approaches train the embeddings separately for each pre-grouped time-stamped corpus and align these embeddings, e.g., by orthogonal projections, vector initialization, temporal referencing, and compass. However, not only does word meaning change in a short time, word meaning may also be subject to evolution over long timespans, thus resulting in a unified continuous process. A recent approach called'DiffTime' models semantic evolution as functions parameterized by multiple-layer nonlinear neural networks over time. In this paper, we will carry on this line of work by learning explicit functions over time for each word. Our approach, called'Word2Fun', reduces the space complexity from O(TVD) to O(kVD) where kis a small constant (k T). In particular, a specific instance based on polynomial functions could provably approximate any function modeling word evolution with a given negligible error thanks to the Weierstrass Approximation Theorem. The effectiveness of the proposed approach is evaluated in diverse tasks including timeaware word clustering, temporal analogy, and semantic change detection.

Non-convex optimization is a difficult and crucial task.

Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. Inspired by the universal approximation property of classical neural networks, ensuring that every continuous function can be arbitrarily well approximated uniformly on a compact set of a Euclidean space, some recent works have established analogous results for QNNs, ranging from single-qubit to multi-qubit QNNs, and even hybrid classical-quantum models. In this paper, we study the approximation capabilities of QNNs for periodic functions with respect to the supremum norm. We use the Jackson inequality to approximate a given function by implementing its approximating trigonometric polynomial via a suitable QNN. In particular, we see that by restricting to the class of periodic functions, one can achieve a quadratic reduction of the number of parameters, producing better approximation results than in the literature. Moreover, the smoother the function, the fewer parameters are needed to construct a QNN to approximate the function.

But it is often the case that we want to find global optima.

Non-convex optimization is a difficult and crucial task.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The set in question in this paper is the set of function with bounded partial derivatives up to order K. The authors' technique mimics the work of Thaler et al (ICALP 2012) only the authors decompose the queries not into regular polynomials (Chebyshev polynomials in the case of Thaler et al), but rather to trigonometric polynomial in this case. The bulk of the work is indeed to show that the abovementioned set of queries can be well-approximated by trigonometric polynomials. Having established that, adding Laplace noise to each monomial suffices to guarantee differential privacy.