Related papers: Rank-decreasing transductions
Extractive compression is a challenging natural language processing problem. This work contributes by formulating neural extractive compression as a parse tree transduction problem, rather than a sequence transduction task. Motivated by…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
Recent progress in language modeling has expanded the range of tasks that can be approached through natural language interfaces, including problems that require structured reasoning. However, it remains unclear how effectively…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
The lattice cohomology of a plumbed 3--manifold $M$ associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of $M$, and in the comparison of the topological properties with…
Our theoretical understanding of deep learning has not kept pace with its empirical success. While network architecture is known to be critical, we do not yet understand its effect on learned representations and network behavior, or how…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Architectural obfuscation - e.g., permuting hidden-state tensors, linearly transforming embedding tables, or remapping tokens - has recently gained traction as a lightweight substitute for heavyweight cryptography in privacy-preserving…
The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing…
We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Pruning is a standard technique for removing unnecessary structure from a neural network to reduce its storage footprint, computational demands, or energy consumption. Pruning can reduce the parameter-counts of many state-of-the-art neural…
We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
We explore whether it is possible to build lighter parsers, that are statistically equivalent to their corresponding standard version, for a wide set of languages showing different structures and morphologies. As testbed, we use the…
We study higher-dimensional analogues of graph-theoretic trees within the class of pure n-simplicial complexes. Focusing on the case m = n-1 in Dewdney's (m, n)-tree framework, we introduce refined notions of path and circuit sequences that…
We study locally closed transformation monoids which contain the automorphism group of the random graph. We show that such a transformation monoid is locally generated by the permutations in the monoid, or contains a constant operation, or…