Related papers: The Sketch of a Polymorphic Symphony
Experimental science is enabled by the combination of synthesis, imaging, and functional characterization. Synthesis of a new material is typically followed by a set of characterization methods aiming to provide feedback for optimization or…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
Shared memory programming models usually provide worksharing and task constructs. The former relies on the efficient fork-join execution model to exploit structured parallelism; while the latter relies on fine-grained synchronization among…
We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
We present a methodology for training foundational transformer models capable of processing collider data with diverse kinematic signatures. Our universal foundation model is designed for simultaneous analysis of all processes involving…
We present Primal, a deterministic feature mapping framework that harnesses the number-theoretic independence of prime square roots to construct robust, tunable vector representations. Diverging from standard stochastic projections (e.g.,…
We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non…
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…
Destination-passing style programming introduces destinations, which represent the address of a write-once memory cell. These destinations can be passed as function parameters, allowing the caller to control memory management: the callee…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
Ability to use definitions occurring in the code directly in equational reasoning is one of the key strengths of functional programming. This is impossible in the case of Haskell type class methods unless a particular instance type is…
Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…
In this document, we propose a description, via a Haskell implementation, of a generalization of the notion of regular expression allowing us to group the definitions and the methods of (tree or word) automata constructions over one generic…