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Exploring the impact of post-training rounding in regression models

Jan Kalina (2024)

Applications of Mathematics

Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows for the perturbation of parameters through an additive error with values within a specified interval. This...

Extending regular expressions with homomorphic replacement

Henning Bordihn, Jürgen Dassow, Markus Holzer (2010)

RAIRO - Theoretical Informatics and Applications

We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns,...

Factoring and testing primes in small space

Viliam Geffert, Dana Pardubská (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We discuss how much space is sufficient to decide whether a unary given number n is a prime. We show that O(log log n) space is sufficient for a deterministic Turing machine, if it is equipped with an additional pebble movable along the input tape, and also for an alternating machine, if the space restriction applies only to its accepting computation subtrees. In other words, the language is a prime is in pebble–DSPACE(log log n) and also in accept–ASPACE(log log n). Moreover, if the given n is...

Feedback, trace and fixed-point semantics

P. Katis, Nicoletta Sabadini, Robert F. C. Walters (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce a notion of category with feedback-with-delay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we obtain a description of the free compact closed category on a symmetric monoidal category. We thus obtain a categorical analogue of the classical localization of a ring with respect to a multiplicative subset....

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