Related papers: Uniform Memory and Serialization for Lambda Calcul…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
State-machine replication, a fundamental approach to designing fault-tolerant services, requires commands to be executed in the same order by all replicas. Moreover, command execution must be deterministic: each replica must produce the…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
Reasoning is a core capability of large language models, yet how multi-step reasoning is learned and executed remains unclear. We study this question in a controlled cellular-automata (1dCA) framework that excludes memorisation by using…
An explicit lattice realization of a non-Abelian topological memory is presented. The correspondence between logical and physical states is seen directly by use of the stabilizer formalism. The resilience of the encoded states against…
Under a unified operational definition, we define LLM memory as a persistent state written during pretraining, finetuning, or inference that can later be addressed and that stably influences outputs. We propose a four-part taxonomy…
Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which…
A new model for general cyclical long memory is introduced, by means of random modulation of certain bivariate long memory time series. This construction essentially decouples the two key features of cyclical long memory: quasi-periodicity…
Replication is a key technique in the design of efficient and reliable distributed systems. As information grows, it becomes difficult or even impossible to store all information at every replica. A common approach to deal with this problem…
We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the…
A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal,…
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…
This paper is concerned with distributed limited memory prediction for continuous-time linear stochastic systems with multiple sensors. A distributed fusion with the weighted sum structure is applied to the optimal local limited memory…
Fundamental machine learning theory shows that different samples contribute unequally both in learning and testing processes. Contemporary studies on DNN imply that such sample difference is rooted on the distribution of intrinsic pattern…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
Analogue computers use continuous properties of physical system for modeling. In the paper is described possibility of modeling by analogue quantum computers for some model of data analysis. It is analogue associative memory and a formal…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
Algorithm performance in supervised learning is a combination of memorization, generalization, and luck. By estimating how much information an algorithm can memorize from a dataset, we can set a lower bound on the amount of performance due…
Various non-classical approaches of distributed information processing, such as neural networks, computation with Ising models, reservoir computing, vector symbolic architectures, and others, employ the principle of collective-state…
With the explosive growth of data, long-sequence modeling has become increasingly important in tasks such as natural language processing and bioinformatics. However, existing methods face inherent trade-offs between efficiency and memory.…