Related papers: A Log-Sensitive Encoding of Turing Machines in the…

Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…

Magnetic tapes are often considered as an outdated storage technology, yet they are still used to store huge amounts of data. Their main interests are a large capacity and a low price per gigabyte, which come at the cost of a much larger…

Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a…

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework.…

This paper introduces a highly efficient greedy decoding algorithm for Transducer-based speech recognition models. We redesign the standard nested-loop design for RNN-T decoding, swapping loops over frames and labels: the outer loop…

Although Transformers-based architectures excel at processing textual information, their naive adaptation for tabular data often involves flattening the table structure. This simplification can lead to the loss of essential…

Multiparty computation approaches to secure neural network inference commonly rely on garbled circuits for securely executing nonlinear activation functions. However, garbled circuits require excessive communication between server and…

We present two rewriting systems that define labelled explicit substitution lambda-calculi. Our work is motivated by the close correspondence between Levy's labelled lambda-calculus and paths in proof-nets, which played an important role in…

For any fixed $k$, a remarkably simple single-tape Turing machine can simulate $k$ independent counters in real time. Informally, a counter is a storage unit that maintains a single integer (initially 0), incrementing it, decrementing it,…

Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…

Class imbalance, which is also called long-tailed distribution, is a common problem in classification tasks based on machine learning. If it happens, the minority data will be overwhelmed by the majority, which presents quite a challenge…

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…

We show that for all functions $t(n) \geq n$, every multitape Turing machine running in time $t$ can be simulated in space only $O(\sqrt{t \log t})$. This is a substantial improvement over Hopcroft, Paul, and Valiant's simulation of time…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

Tabular data have been playing a mostly important role in diverse real-world fields, such as healthcare, engineering, finance, etc. The recent success of deep learning has fostered many deep networks (e.g., Transformer, ResNet) based…

We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…

A tapered floating point encoding is proposed which uses the redundant signed radix 2 system and is based on the canonical recoding. By making use of ternary technology, the encoding has a dynamic range exceeding that of the…

Turbo code is a great achievement in the field of communication system. It can be created by connecting a turbo encoder and a decoder serially. A Turbo encoder is build with parallel concatenation of two simple convolutional codes. By…

Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…

Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…