Related papers: Exponential Automatic Amortized Resource Analysis
Amortized analysis is a program cost analysis technique for data structures in which the cost of operations is specified in aggregate, under the assumption of continued sequential use. Typically, amortized analyses are presented…
Amortised analysis is a technique for proving a combined time bound for a batch of operations on a data structure, even if some of those operations are expensive. But the traditional method of amortised analysis yields incorrect time bounds…
Programs with dynamic allocation are able to create and use an unbounded number of fresh resources, such as references, objects, files, etc. We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling such…
We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist's method of amortised analysis, and is potential-based. The type system makes use of logarithmic…
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…
It is known that in some cases a Random Access Machine (RAM) benefits from having an additional input that is an arbitrary number, satisfying only the criterion of being sufficiently large. This is known as the ARAM model. We introduce a…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
Rust has become a popular system programming language that strikes a balance between memory safety and performance. Rust's type system ensures the safety of low-level memory controls; however, a well-typed Rust program is not guaranteed to…
While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet…
The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time…
Automatic data augmentation (AutoDA) plays an important role in enhancing the generalization of neural networks. However, mainstream AutoDA methods often encounter two challenges: either the search process is excessively time-consuming,…
We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…
Fine-tuning has become a popular approach to adapting large foundational models to specific tasks. As the size of models and datasets grows, parameter-efficient fine-tuning techniques are increasingly important. One of the most widely used…
This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes…
Low-Rank Adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning (PEFT) technique for foundation models. Recent work has highlighted an inherent asymmetry in the initialization of LoRA's low-rank factors, which has…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…
Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…
How is the limited capacity of working memory efficiently used to support human linguistic behaviors? In this paper, we propose Strategic Resource Allocation (SRA) as an efficiency principle for memory encoding in sentence processing. The…
In many areas of science, complex phenomena are modeled by stochastic parametric simulators, often featuring high-dimensional parameter spaces and intractable likelihoods. In this context, performing Bayesian inference can be challenging.…
We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the…