相关论文: Reversed Indexes $\approx$ Values in Wavelet Trees
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense,…
In a dynamic retrieval system, documents must be ingested as they arrive, and be immediately findable by queries. Our purpose in this paper is to describe an index structure and processing regime that accommodates that requirement for…
Reversible computation has been recognised as a potential solution to the technological bottleneck in the future of computing machinery. Rolf Landauer determined the lower limit for power dissipation in computation and noted that…
A string-like compact data structure for unlabelled rooted trees is given using 2n bits.
Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…
Recent retrieval-augmented models enhance basic methods by building a hierarchical structure over retrieved text chunks through recursive embedding, clustering, and summarization. The most relevant information is then retrieved from both…
The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
Implicit neural representations (INRs) have emerged as a compact and parametric alternative to discrete array-based data representations, encoding information directly in neural network weights to enable resolution-independent…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
We consider the statistical problem of recovering a hidden "ground truth" binary labeling for the vertices of a graph up to low Hamming error from noisy edge and vertex measurements. We present new algorithms and a sharp finite-sample…
Wavelets have emerged as a cutting edge technology in a number of fields. Concrete results of their application in Image and Signal processing suggest that wavelets can be effectively applied to Natural Language Processing (NLP) tasks that…
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…
Convex clustering refers, for given $\left\{x_1, \dots, x_n\right\} \subset \mathbb{R}^p$, to the minimization of \begin{eqnarray*} u(\gamma) & = & \underset{u_1, \dots, u_n }{\arg\min}\;\sum_{i=1}^{n}{\lVert x_i - u_i \rVert^2} + \gamma…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…