Related papers: The Quest for Optimal Sorting Networks: Efficient …
In this paper a new method for checking the subsumption relation for the optimal-size sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of…
We establish new depth upper bounds for sorting networks on 27 and 28 channels, improving the previous best bound of 14 to 13. Our 28-channel network is constructed with reflectional symmetry by combining high-quality prefixes of 16- and…
Sorting networks are oblivious sorting algorithms with many interesting theoretical properties and practical applications. One of the related classical challenges is the search of optimal networks respect to size (number of comparators) of…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
A complete set of filters $F_n$ for the optimal-depth $n$-input sorting network problem is such that if there exists an $n$-input sorting network of depth $d$ then there exists one of the form $C \oplus C'$ for some $C \in F_n$. Previous…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
The construction of large-scale, low-latency networks becomes difficult as the number of nodes increases. In general, the way to construct a theoretically optimal solution is unknown. However, it is known that some methods can construct…
In this paper we study several variations of the \emph{pancake flipping problem}, which is also well known as the problem of \emph{sorting by prefix reversals}. We consider the variations in the sorting process by adding with prefix…
Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…
This paper studies new properties of the front and back ends of a sorting network, and illustrates the utility of these in the search for new bounds on optimal sorting networks. Search focuses first on the "outsides" of the network and then…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…
Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling,…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Large language models (LLMs) have revolutionized natural language processing (NLP) by excelling at understanding and generating human-like text. However, their widespread deployment can be prohibitively expensive. SortedNet is a recent…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
Current GNN-oriented NAS methods focus on the search for different layer aggregate components with shallow and simple architectures, which are limited by the 'over-smooth' problem. To further explore the benefits from structural diversity…
Synthesis of distributed protocols is a hard, often undecidable, problem. Completion techniques provide partial remedy by turning the problem into a search problem. However, the space of candidate completions is still massive. In this…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…