Related papers: dxo: A System for Relational Algebra and Different…

The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…

Preference optimization methods such as DPO align large language models (LLMs) using paired comparisons, but their effectiveness can be highly sensitive to the quality and difficulty of preference pairs. A common heuristic treats…

Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…

Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…

The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but…

The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, the Sigma formulas express relations that are witnessed in a…

We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…

A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…

We derive and investigate two DPO variants that explicitly model the possibility of declaring a tie in pair-wise comparisons. We replace the Bradley-Terry model in DPO with two well-known modeling extensions, by Rao and Kupper and by…

Direct Preference Optimization (DPO), which aligns models with human preferences through win/lose data pairs, has achieved remarkable success in language and image generation. However, applying DPO to video diffusion models faces critical…

We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorithm and of Osada's generalized rho algorithm as special cases.…

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and…

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…

Recent advances in large language models (LLMs) have shown that reasoning ability can be significantly enhanced through Reinforcement Learning with Verifiable Rewards (RLVR). Group Relative Policy Optimization (GRPO) has emerged as the de…

This paper discusses relational operations in the first-order logical environment {FOLE}. Here we demonstrate how FOLE expresses the relational operations of database theory in a clear and implementable representation. An analysis of the…

Aligning large language models with human preferences has emerged as a critical focus in language modeling research. Yet, integrating preference learning into Text-to-Image (T2I) generative models is still relatively uncharted territory.…

Inference scaling further accelerates Large Language Models (LLMs) toward Artificial General Intelligence (AGI), with large-scale Reinforcement Learning (RL) to unleash long Chain-of-Thought reasoning. Most contemporary reasoning approaches…

Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…