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We introduce a cryptographic primitive named threshold trapdoor functions (TTDFs), from which we give generic constructions of threshold and revocation encryptions under adaptive corruption model. Then, we show TTDF can be instantiated…
Gradient boosted decision trees (GBDTs) are widely used in machine learning, and the output of current GBDT implementations is a single variable. When there are multiple outputs, GBDT constructs multiple trees corresponding to the output…
GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an…
Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential…
Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain…
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 challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau…
Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model.…
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known…
Symmetry-protected topological (SPT) phases are short-range entangled phases of matter with a non-local order parameter which are preserved under a local symmetry group. Here, by using unsupervised learning algorithm, namely the diffusion…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…
In the modern era, large volumes of data are being produced continuously, especially in domain-specific fields such as medical records and clinical files, defence logs and HTML-based web traffic. Data with such volume and complexity needs…
Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy…
Recently, there has been progress in supervised funetuning pretrained GPT-2 to build end-to-end task-oriented dialog (TOD) systems. However, online reinforcement learning of a GPT-2 based dialog system (DS), together with a end-to-end user…