Related papers: Efficient Construction of Reversible Transducers f…
We introduce Tangent Attention Fine-Tuning (TAFT), a method for fine-tuning linearized transformers obtained by computing a First-order Taylor Expansion around a pre-trained initialization. We show that the Jacobian-Vector Product resulting…
The theory of regular and aperiodic transformations of finite strings has recently received a lot of interest. These classes can be equivalently defined using logic (Monadic second-order logic and first-order logic), two-way machines…
Recent studies of the computational power of recurrent neural networks (RNNs) reveal a hierarchy of RNN architectures, given real-time and finite-precision assumptions. Here we study auto-regressive Transformers with linearised attention,…
We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…
Multi-dimensional discrete Fourier transforms (DFT) are typically decomposed into multiple 1D transforms. Hence, parallel implementations of any multi-dimensional DFT focus on parallelizing within or across the 1D DFT. Existing DFT packages…
Retrieval-augmented language models (LMs) have received much attention recently. However, typically the retriever is not trained jointly as a native component of the LM, but added post-hoc to an already-pretrained LM, which limits the…
Transformer, originally devised for natural language processing, has also attested significant success in computer vision. Thanks to its super expressive power, researchers are investigating ways to deploy transformers to reinforcement…
Desirably, the world relies on the devices being compact, as they could drive to the increased functionality of integrated circuits at the provided footstep, that is becoming more reliable. To reduce the scalability over the devices,…
Deterministic two-way transducers on finite words have been shown by Engelfriet and Hoogeboom to have the same expressive power as MSO-transductions. We introduce a notion of aperiodicity for these transducers and we show that aperiodic…
General-purpose pretrained sentence encoders such as BERT are not ideal for real-world conversational AI applications; they are computationally heavy, slow, and expensive to train. We propose ConveRT (Conversational Representations from…
The Transformer has quickly become the dominant architecture for various pattern recognition tasks due to its capacity for long-range representation. However, transformers are data-hungry models and need large datasets for training. In…
The Discrete Periodic Radon Transform (DPRT) has been extensively used in applications that involve image reconstructions from projections. This manuscript introduces a fast and scalable approach for computing the forward and inverse DPRT…
The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original…
We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language…
The question whether P equals NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata. Every nondeterministic…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…
The origin semantics for transducers was proposed in 2014, and led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for…