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The notion of $\alpha$-equivalence between $\lambda$-terms is commonly used to identify terms that are considered equal. However, due to the primitive treatment of free variables, this notion falls short when comparing subterms occurring…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
This paper aims to provide an unsupervised modelling approach that allows for a more flexible representation of text embeddings. It jointly encodes the words and the paragraphs as individual matrices of arbitrary column dimension with unit…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
A program is characterized by its input model, and a formal input model can be of use in diverse areas including vulnerability analysis, reverse engineering, fuzzing and software testing, clone detection and refactoring. Unfortunately,…
The primary goal in this thesis is to identify better syntactic constraint or bias, that is language independent but also efficiently exploitable during sentence processing. We focus on a particular syntactic construction called…
Deep language models learning a hierarchical representation proved to be a powerful tool for natural language processing, text mining and information retrieval. However, representations that perform well for retrieval must capture semantic…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Spotting user-defined/flexible keywords represented in text frequently uses an expensive text encoder for joint analysis with an audio encoder in an embedding space, which can suffer from heterogeneous modality representation (i.e., large…
Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…
Scaling large language models has driven remarkable advancements across various domains, yet the continual increase in model size presents significant challenges for real-world deployment. The Mixture of Experts (MoE) architecture offers a…
The development of high-quality text embeddings is increasingly drifting toward an exclusionary future, defined by three critical barriers: prohibitive computational costs, a narrow linguistic focus that neglects most of the world's…
One primary focus in multimodal feature extraction is to find the representations of individual modalities that are maximally correlated. As a well-known measure of dependence, the Hirschfeld-Gebelein-R\'{e}nyi (HGR) maximal correlation…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
Subword tokenization requires balancing computational efficiency and vocabulary coverage, which often leads to suboptimal performance on languages and scripts not prioritized during training. We propose to augment pretrained language models…
Containment problems for polytopes and spectrahedra appear in various applications, such as linear and semidefinite programming, combinatorics, convexity and stability analysis of differential equations. This paper explores the theoretical…
Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…
Open-vocabulary 3D affordance detection requires localizing interaction regions on point clouds given novel affordance descriptions. Recent methods extend multimodal large language models (MLLMs) with special output tokens that are decoded…
Accurate classification of multi-modal financial documents, containing text, tables, charts, and images, is crucial but challenging. Traditional text-based approaches often fail to capture the complex multi-modal nature of these documents.…
Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi [GP18]) offer a general model for deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional…