Related papers: Categorical Semantics for Time Travel
Diffusion models have quickly become the go-to paradigm for generative modelling of perceptual signals (such as images and sound) through iterative refinement. Their success hinges on the fact that the underlying physical phenomena are…
The category Set_* of sets and partial functions is well-known to be traced monoidal, meaning that a partial function S+U -/-> T+U can be coherently transformed into a partial function S -/-> T. This transformation is generally described in…
We report an extension of a Keras Model, called CTCModel, to perform the Connectionist Temporal Classification (CTC) in a transparent way. Combined with Recurrent Neural Networks, the Connectionist Temporal Classification is the reference…
Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give…
A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether…
Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…
Connectionist temporal classification (CTC) has matured as an alignment free to sequence transduction and shows competitive for end-to-end speech recognition. In the CTC topology, the blank symbol occupies more than half of the state…
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
Examples are given of the creation of closed timelike curves by choices of coordinate identifications. Following G\"odel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of…
Time Series data are broadly studied in various domains of transportation systems. Traffic data area challenging example of spatio-temporal data, as it is multi-variate time series with high correlations in spatial and temporal…
We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which this is based. The framework has no need for coin…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
Understanding the semantic shifts of multimodal information is only possible with models that capture cross-modal interactions over time. Under this paradigm, a new embedding is needed that structures visual-textual interactions according…
Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…
We show that a large class of 2-adic Schr\"odinger equations is the scaling limit of certain continuous-time quantum Markov chains (CTQMCs). Practically, a discretization of such an equation gives a CTQMC. As a practical result, we…
The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to…
Boundary time crystals (BTCs) are prominent examples of continuous time crystals in collective spin systems governed by Lindbladian evolution. To date, their analysis has mostly relied on semiclassical and numerical approaches. Here, we…
We study an exact model of string theory propagating in a space-time containing regions with closed time-like curves (CTCs) separated from a finite cosmological region bounded by a Big Bang and a Big Crunch. The model is an non-trivial…