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The equivalence of a systematic convolutional encoder as linear state-space control system is first realized and presented through an example. Then, utilizing this structure, a new optimal state-sequence estimator is derived, in the spirit…
Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a…
The statistical properties of letters frequencies in European literature texts are investigated. The determination of logarithmic dependence of letters sequence for one-language and two-language texts are examined. The pare of languages is…
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…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after…
We revisit hierarchical bracketing encodings from a practical perspective in the context of dependency graph parsing. The approach encodes graphs as sequences, enabling linear-time parsing with $n$ tagging actions, and still representing…
Decoding approaches are widely used in neuroscience and machine learning to compare stimulus representations across neural systems, such as different brain regions, organisms, and deep learning models. Popular methods include decoding…
We produce a new basis for the Schur and Weyl modules associated to a row-convex shape, D. The basis is indexed by new class of "straight" tableaux which we introduce by weakening the usual requirements for standard tableaux. Spanning is…
Existing literature on source coding with side information (SCSI) mostly uses the state-of-the-art channel codes namely LDPC codes, turbo codes, and their variants and assume classical unique decoding. In this paper, we present an algebraic…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
Large Language Models (LLMs) often struggle with complex mathematical reasoning, where prose-based generation leads to unverified and arithmetically unsound solutions. Current prompting strategies like Chain of Thought still operate within…
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…
Stochastic sampling strategies are widely adopted in large language models (LLMs) to balance output coherence and diversity. These heuristics are often inherited in Multimodal LLMs (MLLMs) without task-specific justification. However, we…
Speculative decoding has emerged as an effective approach for accelerating autoregressive inference by parallelizing token generation through a draft-then-verify paradigm. However, existing methods rely on static drafting lengths and rigid…
Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…
Encoding and decoding models are widely used in systems, cognitive, and computational neuroscience to make sense of brain-activity data. However, the interpretation of their results requires care. Decoding models can help reveal whether…
Code has emerged as a precise and executable medium for reasoning and action in the agent era. Yet, progress has largely focused on language-centric tasks such as program synthesis and debugging, leaving visual-centric coding underexplored.…