Related papers: The Voynich Codex Decoded: Statistical Symbolism a…
In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any…
We explore the capabilities of LVLMs and LLMs in deciphering rare scripts not encoded in Unicode. We introduce a novel approach to construct a multimodal dataset of linguistic puzzles involving such scripts, utilizing a tokenization method…
Reconstructing visual stimuli from human brain activity (e.g., fMRI) bridges neuroscience and computer vision by decoding neural representations. However, existing methods often overlook critical brain structure-function relationships,…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
We consider a symbolic coding for geodesics on the family of Veech surfaces (translation surfaces rich with affine symmetries) recently discovered by Bouw and Moeller. These surfaces, as noticed by Hooper, can be realized by cutting and…
Efficient inference in large language models (LLMs) has become a critical focus as their scale and complexity grow. Traditional autoregressive decoding, while effective, suffers from computational inefficiencies due to its sequential token…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of…
Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain the blocks of so called geometric…
Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable…
Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but…
In this letter, we propose a Voronoi shaping method with reduced encoding complexity. The method works for integer shaping and coding lattices satisfying the chain $\Lambda_s \subseteq \textbf{K}\mathbb{Z}^n \subseteq \Lambda_c$, with…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
Visual reasoning tasks such as visual question answering (VQA) require an interplay of visual perception with reasoning about the question semantics grounded in perception. However, recent advances in this area are still primarily driven by…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
We describe an implementation of a hybrid statistical/symbolic approach to repairing parser failures in a speech-to-speech translation system. We describe a module which takes as input a fragmented parse and returns a repaired meaning…
We present a novel metric for the evaluation of the morphological plausibility of subword segmentation. Unlike the typically used morpheme boundary or retrieval F-score, which requires gold segmentation data that is either unavailable or of…
Understanding the high-level conceptual structure of quantum algorithms from their low-level circuit representations is a critical task for verification, debugging, and education. While traditional numerical simulators can calculate output…
Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…