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The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand,…
Reconstructing components of a genomic mixture from data obtained by means of DNA sequencing is a challenging problem encountered in a variety of applications including single individual haplotyping and studies of viral communities.…
Amphiphilic molecules spontaneously form self-assembled structures of various shapes depending on their molecular structures, the temperature, and other physical conditions. The functionalities of these structures are dictated by their…
Forest automata (FA) have recently been proposed as a tool for shape analysis of complex heap structures. FA encode sets of tree decompositions of heap graphs in the form of tuples of tree automata. In order to allow for representing…
Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…
We develop an approach for unsupervised learning of associations between co-occurring perceptual events using a large graph. We applied this approach to successfully solve the image captcha of China's railroad system. The approach is based…
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…
We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…
As an essential prerequisite task in image-based plant phenotyping, leaf segmentation has garnered increasing attention in recent years. While self-supervised learning is emerging as an effective alternative to various computer vision…
Given a graph $Y$ on $n$ vertices and a desired level of fault-tolerance $k$, an objective in fault-tolerant system design is to construct a supergraph $X$ on $n + k$ vertices such that the removal of any $k$ nodes from $X$ leaves a graph…
Large Language Models (LLMs) have transformed natural language processing, yet their internal mechanisms remain largely opaque. Recently, mechanistic interpretability has attracted significant attention from the research community as a…
Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…
Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed…
Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must…
The finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. However we prove that, in the most general case, the problem is undecidable. We study the case of automaton…
We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
This paper describes the system used in submission from SHANGHAITECH team to the IWPT 2021 Shared Task. Our system is a graph-based parser with the technique of Automated Concatenation of Embeddings (ACE). Because recent work found that…
We introduce a novel self-attention mechanism, which we call CSA (Chromatic Self-Attention), which extends the notion of attention scores to attention _filters_, independently modulating the feature channels. We showcase CSA in a…
Recent advancements in microbiology have motivated the study of the production of nanostructures with applications such as biomedical computing and molecular robotics. One way to construct these structures is to construct branched DNA…