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 cryptography. Our model is able to incorporate computational security, set-up assumptions and various attack models such as colluding or independently acting subsets of adversaries in a modular, flexible fashion. We conclude by using string diagrams to rederive the security of the one-time pad, correctness of Diffie-Hellman key exchange and no-go results concerning the limits of bipartite and tripartite cryptography, ruling out e.g., composable commitments and broadcasting. On the way, we exhibit two categorical constructions of resource theories that might be of independent interest: one capturing resources shared among multiple parties and one capturing resource conversions that succeed asymptotically.
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We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for different classes of prior distributions, including Gaussian process priors. We show that fractional posterior credible sets can provide reliable semiparametric uncertainty quantification, but have inflated size. To remedy this, we further propose a \textit{shifted-and-rescaled} fractional posterior set that is an efficient confidence set having optimal size under regularity conditions. As part of our proofs, we also refine existing contraction rate results for fractional posteriors by sharpening the dependence of the rate on the fractional exponent.
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input may strongly differ from the true underlying data. However, recent works suggest that this bias is low in the context of high-dimensional linear predictors when data is supposed to be missing completely at random (MCAR). This paper completes the picture for linear predictors by confirming the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension.To this aim, we consider a unique underlying random features model, which offers a rigorous framework for studying predictive performances, whilst the dimension of the observed features varies.Building on these theoretical results, we establish finite-sample bounds on stochastic gradient (SGD) predictors applied to zero-imputed data, a strategy particularly well suited for large-scale learning.If the MCAR assumption appears to be strong, we show that similar favorable behaviors occur for more complex missing data scenarios.
The goal of anomaly detection is to identify observations that are generated by a distribution that differs from the reference distribution that qualifies normal behavior. When examining a time series, the reference distribution may evolve over time. The anomaly detector must therefore be able to adapt to such changes. In the online context, it is particularly difficult to adapt to abrupt and unpredictable changes. Our solution to this problem is based on the detection of breakpoints in order to adapt in real time to the new reference behavior of the series and to increase the accuracy of the anomaly detection. This solution also provides a control of the False Discovery Rate by extending methods developed for stationary series.
We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics, machine learning and physics-informed machine learning. A straightforward solution is to replace the exact objective with a Monte Carlo estimate before employing standard first-order methods like gradient descent, which yields the classical stochastic gradient descent method. But replacing the true objective with an estimate ensues a ``generalisation error''. Rigorous bounds for this error typically require strong compactness and Lipschitz continuity assumptions while providing a very slow decay with sample size. We propose a different optimisation strategy relying on a natural gradient descent in which the true gradient is approximated in local linearisations of the model class via (quasi-)projections based on optimal sampling methods. Under classical assumptions on the loss and the nonlinear model class, we prove that this scheme converges almost surely monotonically to a stationary point of the true objective and we provide convergence rates.
Municipalities are vulnerable to cyberattacks with devastating consequences, but they lack key information to evaluate their own risk and compare their security posture to peers. Using data from 83 municipalities collected via a cryptographically secure computation platform about their security posture, incidents, security control failures, and losses, we build data-driven cyber risk models and cyber security benchmarks for municipalities. We produce benchmarks of the security posture in a sector, the frequency of cyber incidents, forecasted annual losses for organizations based on their defensive posture, and a weighting of cyber controls based on their individual failure rates and associated losses. Combined, these four items can help guide cyber policymaking by quantifying the cyber risk in a sector, identifying gaps that need to be addressed, prioritizing policy interventions, and tracking progress of those interventions over time. In the case of the municipalities, these newly derived risk measures highlight the need for continuous measured improvement of cybersecurity readiness, show clear areas of weakness and strength, and provide governments with some early targets for policy focus such as security education, incident response, and focusing efforts first on municipalities at the lowest security levels that have the highest risk reduction per security dollar invested.
Using dominating sets to separate vertices of graphs is a well-studied problem in the larger domain of identification problems. In such problems, the objective is typically to separate any two vertices of a graph by their unique neighbourhoods in a suitably chosen dominating set of the graph. Such a dominating and separating set is often referred to as a \emph{code} in the literature. Depending on the types of dominating and separating sets used, various problems arise under various names in the literature. In this paper, we introduce a new problem in the same realm of identification problems whereby the code, called the \emph{open-separating dominating code}, or the \emph{OSD-code} for short, is a dominating set and uses open neighbourhoods for separating vertices. The paper studies the fundamental properties concerning the existence, hardness and minimality of OSD-codes. Due to the emergence of a close and yet difficult to establish relation of the OSD-codes with another well-studied code in the literature called the open locating dominating codes, or OLD-codes for short, we compare the two on various graph classes. Finally, we also provide an equivalent reformulation of the problem of finding OSD-codes of a graph as a covering problem in a suitable hypergraph and discuss the polyhedra associated with OSD-codes, again in relation to OLD-codes of some graph classes already studied in this context.
This article presents a new polynomial parameterized sigmoid called SIGTRON, which is an extended asymmetric sigmoid with Perceptron, and its companion convex model called SIGTRON-imbalanced classification (SIC) model that employs a virtual SIGTRON-induced convex loss function. In contrast to the conventional $\pi$-weighted cost-sensitive learning model, the SIC model does not have an external $\pi$-weight on the loss function but has internal parameters in the virtual SIGTRON-induced loss function. As a consequence, when the given training dataset is close to the well-balanced condition, we show that the proposed SIC model is more adaptive to variations of the dataset, such as the inconsistency of the scale-class-imbalance ratio between the training and test datasets. This adaptation is achieved by creating a skewed hyperplane equation. Additionally, we present a quasi-Newton optimization(L-BFGS) framework for the virtual convex loss by developing an interval-based bisection line search. Empirically, we have observed that the proposed approach outperforms $\pi$-weighted convex focal loss and balanced classifier LIBLINEAR(logistic regression, SVM, and L2SVM) in terms of test classification accuracy with $51$ two-class and $67$ multi-class datasets. In binary classification problems, where the scale-class-imbalance ratio of the training dataset is not significant but the inconsistency exists, a group of SIC models with the best test accuracy for each dataset (TOP$1$) outperforms LIBSVM(C-SVC with RBF kernel), a well-known kernel-based classifier.
Automatic Speech Recognition (ASR) systems are used in the financial domain to enhance the caller experience by enabling natural language understanding and facilitating efficient and intuitive interactions. Increasing use of ASR systems requires that such systems exhibit very low error rates. The predominant ASR models to collect numeric data are large, general-purpose commercial models -- Google Speech-to-text (STT), or Amazon Transcribe -- or open source (OpenAI's Whisper). Such ASR models are trained on hundreds of thousands of hours of audio data and require considerable resources to run. Despite recent progress large speech recognition models, we highlight the potential of smaller, specialized "micro" models. Such light models can be trained perform well on number recognition specific tasks, competing with general models like Whisper or Google STT while using less than 80 minutes of training time and occupying at least an order of less memory resources. Also, unlike larger speech recognition models, micro-models are trained on carefully selected and curated datasets, which makes them highly accurate, agile, and easy to retrain, while using low compute resources. We present our work on creating micro models for multi-digit number recognition that handle diverse speaking styles reflecting real-world pronunciation patterns. Our work contributes to domain-specific ASR models, improving digit recognition accuracy, and privacy of data. An added advantage, their low resource consumption allows them to be hosted on-premise, keeping private data local instead uploading to an external cloud. Our results indicate that our micro-model makes less errors than the best-of-breed commercial or open-source ASRs in recognizing digits (1.8% error rate of our best micro-model versus 5.8% error rate of Whisper), and has a low memory footprint (0.66 GB VRAM for our model versus 11 GB VRAM for Whisper).
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs, polytopes, lattice paths, Hopf algebras, etc. In this paper, we first revisit the structure of the respective equivalence classes: weak rectangulations that preserve rectangle-segment adjacencies, and strong rectangulations that preserve rectangle-rectangle adjacencies. We thoroughly investigate posets defined by adjacency in rectangulations of both kinds, and unify and simplify known bijections between rectangulations and permutation classes. This yields a uniform treatment of mappings between permutations and rectangulations that unifies the results from earlier contributions, and emphasizes parallelism and differences between the weak and the strong cases. Then, we consider the special case of guillotine rectangulations, and prove that they can be characterized - under all known mappings between permutations and rectangulations - by avoidance of two mesh patterns that correspond to "windmills" in rectangulations. This yields new permutation classes in bijection with weak guillotine rectangulations, and the first known permutation class in bijection with strong guillotine rectangulations. Finally, we address enumerative issues and prove asymptotic bounds for several families of strong rectangulations.
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage designs where sample sizes are reassessed for a specific conditional power and the goal is to minimize the expected sample size. The previous theory can easily lead to a non-monotonous conditional error function which is highly undesirable for logical reasons and can harm type I error rate control for composite null hypotheses. The here presented method extends the existing theory by introducing intermediate monotonising steps that can easily be implemented.
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