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In this paper, we consider the problem of learning functions over sets, i.e., functions that are invariant to permutations of input set items. Recent approaches of pooling individual element embeddings can necessitate extremely large…
Pretraining plays a pivotal role in acquiring generalized knowledge from large-scale data, achieving remarkable successes as evidenced by large models in CV and NLP. However, progress in the graph domain remains limited due to fundamental…
Mathematicians still use Naive Set Theory when generating sets without danger of producing any contradiction. Therefore their working method can be considered as a consistent inference system with an experience of over 100 years. My…
Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape (Mohan et al. 2022) are similar, but work with different underlying algebraic operations. In this paper, we exploit…
Few-shot algorithms aim at learning new tasks provided only a handful of training examples. In this work we investigate few-shot learning in the setting where the data points are sequences of tokens and propose an efficient learning…
Until recently, the question of the effective inductive bias of deep models on tabular data has remained unanswered. This paper investigates the hypothesis that arithmetic feature interaction is necessary for deep tabular learning. To test…
In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be…
In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
We investigate the capabilities of transformer models on relational reasoning tasks. In these tasks, models are trained on a set of strings encoding abstract relations, and are then tested out-of-distribution on data that contains symbols…
As pre-trained text-to-image diffusion models have become a useful tool for image synthesis, people want to specify the results in various ways. This paper tackles training-free appearance transfer, which produces an image with the…
Transformers often struggle with length generalization, meaning they fail to generalize to sequences longer than those encountered during training. While arithmetic tasks are commonly used to study length generalization, certain tasks are…
The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
The Transformer architecture is shown to provide a powerful framework as an end-to-end model for building expression trees from online handwritten gestures corresponding to glyph strokes. In particular, the attention mechanism was…
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…
SHAP is a popular method for measuring variable importance in machine learning models. In this paper, we study the algorithm used to estimate SHAP scores and outline its connection to the functional ANOVA decomposition. We use this…
We use deep learning to model interactions across two or more sets of objects, such as user-movie ratings, protein-drug bindings, or ternary user-item-tag interactions. The canonical representation of such interactions is a matrix (or a…