Related papers: Uncountable realtime probabilistic classes
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing…
We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an…
Altenbernd, Thomas and W\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller ones,…
Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture…
An infinite bit sequence is called recursively random if no computable strategy betting along the sequence has unbounded capital. It is well-known that the property of recursive randomness is closed under computable permutations. We…
When a planner must decide whether it has enough evidence to make a decision based on probability, it faces the sample size problem. Current planners using probabilities need not deal with this problem because they do not generate their…
Bidirectional long short-term memory (bi-LSTM) networks have recently proven successful for various NLP sequence modeling tasks, but little is known about their reliance to input representations, target languages, data set size, and label…
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…
In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\in\mathbb{N}_1$ accepting a language $L_d$ that is different from any…
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…
Prior research has demonstrated noticeable performance gains through the use of probabilistic tokenizations, an approach that involves employing multiple tokenizations of the same input string during the training phase of a language model.…
Large Language Models (LLMs) are known to produce very high-quality tests and responses to our queries. But how much can we trust this generated text? In this paper, we study the problem of uncertainty quantification in LLMs. We propose a…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Large language models (LLMs) have wide applications in the field of natural language processing(NLP), such as GPT-4 and Llama. However, with the exponential growth of model parameter sizes, LLMs bring significant resource overheads. Low-bit…
We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the run-time we are able to retrieve the most…