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Quantum resistance is vital for emerging cryptographic systems as quantum technologies continue to advance towards large-scale, fault-tolerant quantum computers. Resistance may be offered by quantum key distribution (QKD), which provides information-theoretic security using quantum states of photons, but may be limited by transmission loss at long distances. An alternative approach uses classical means and is conjectured to be resistant to quantum attacks, so-called post-quantum cryptography (PQC), but it is yet to be rigorously proven, and its current implementations are computationally expensive. To overcome the security and performance challenges present in each, here we develop hybrid protocols by which QKD and PQC inter-operate within a joint quantum-classical network. In particular, we consider different hybrid designs that may offer enhanced speed and/or security over the individual performance of either approach. Furthermore, we present a method for analyzing the security of hybrid protocols in key distribution networks. Our hybrid approach paves the way for joint quantum-classical communication networks, which leverage the advantages of both QKD and PQC and can be tailored to the requirements of various practical networks.

Generalization outside the scope of one's training data requires leveraging prior knowledge about the effects that transfer, and the effects that don't, between different data sources. Bayesian transfer learning is a principled paradigm for specifying this knowledge, and refining it on the basis of data from the source (training) and target (prediction) tasks. We address the challenging transfer learning setting where the learner (i) cannot fine-tune in the target task, and (ii) does not know which source data points correspond to the same task (i.e., the data sources are unknown). We propose a proxy-informed robust method for probabilistic transfer learning (PROMPT), which provides a posterior predictive estimate tailored to the structure of the target task, without requiring the learner have access to any outcome information from the target task. Instead, PROMPT relies on the availability of proxy information. PROMPT uses the same proxy information for two purposes: (i) estimation of effects specific to the target task, and (ii) construction of a robust reweighting of the source data for estimation of effects that transfer between tasks. We provide theoretical results on the effect of this reweighting on the risk of negative transfer, and demonstrate application of PROMPT in two synthetic settings.

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions, such Markov processes admit time reversals that turn out to be PDMPs as well. We apply this observation to three PDMPs considered in the literature: the Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. For these three particular instances, we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump. Based on these results, we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally, we provide bounds in the total variation distance between the data distribution and the resulting distribution of our model in the case where the base distribution is the standard $d$-dimensional Gaussian distribution. Promising numerical simulations support further investigations into this class of models.

For the distributions of finitely many binary random variables, we study the interaction of restrictions of the supports with conditional independence constraints. We prove a generalization of the Hammersley-Clifford theorem for distributions whose support is a natural distributive lattice: that is, any distribution which has natural lattice support and satisfies the pairwise Markov statements of a graph must factor according to the graph. We also show a connection to the Hibi ideals of lattices.

We propose to condition a generative model by a given image classifier uncertainty in order to analyze and explain its behavior. Preliminary experiments on synthetic data and a corrupted version of MNIST dataset illustrate the idea.

Training Data Detection (TDD) is a task aimed at determining whether a specific data instance is used to train a machine learning model. In the computer security literature, TDD is also referred to as Membership Inference Attack (MIA). Given its potential to assess the risks of training data breaches, ensure copyright authentication, and verify model unlearning, TDD has garnered significant attention in recent years, leading to the development of numerous methods. Despite these advancements, there is no comprehensive benchmark to thoroughly evaluate the effectiveness of TDD methods. In this work, we introduce TDDBench, which consists of 13 datasets spanning three data modalities: image, tabular, and text. We benchmark 21 different TDD methods across four detection paradigms and evaluate their performance from five perspectives: average detection performance, best detection performance, memory consumption, and computational efficiency in both time and memory. With TDDBench, researchers can identify bottlenecks and areas for improvement in TDD algorithms, while practitioners can make informed trade-offs between effectiveness and efficiency when selecting TDD algorithms for specific use cases. Our large-scale benchmarking also reveals the generally unsatisfactory performance of TDD algorithms across different datasets. To enhance accessibility and reproducibility, we open-source TDDBench for the research community.

Point processes are widely used statistical models for uncovering the temporal patterns in dependent event data. In many applications, the event time cannot be observed exactly, calling for the incorporation of time uncertainty into the modeling of point process data. In this work, we introduce a framework to model time-uncertain point processes possibly on a network. We start by deriving the formulation in the continuous-time setting under a few assumptions motivated by application scenarios. After imposing a time grid, we obtain a discrete-time model that facilitates inference and can be computed by first-order optimization methods such as Gradient Descent or Variation inequality (VI) using batch-based Stochastic Gradient Descent (SGD). The parameter recovery guarantee is proved for VI inference at an $O(1/k)$ convergence rate using $k$ SGD steps. Our framework handles non-stationary processes by modeling the inference kernel as a matrix (or tensor on a network) and it covers the stationary process, such as the classical Hawkes process, as a special case. We experimentally show that the proposed approach outperforms previous General Linear model (GLM) baselines on simulated and real data and reveals meaningful causal relations on a Sepsis-associated Derangements dataset.

The spectral decomposition of graph adjacency matrices is an essential ingredient in the design of graph signal processing (GSP) techniques. When the adjacency matrix has multi-dimensional eigenspaces, it is desirable to base GSP constructions on a particular eigenbasis that better reflects the graph's symmetries. In this paper, we provide an explicit and detailed representation-theoretic account for the spectral decomposition of the adjacency matrix of a weighted Cayley graph. Our method applies to all weighted Cayley graphs, regardless of whether they are quasi-Abelian, and offers detailed descriptions of eigenvalues and eigenvectors derived from the coefficient functions of the representations of the underlying group. Next, we turn our attention to constructing frames on Cayley graphs. Frames are overcomplete spanning sets that ensure stable and potentially redundant systems for signal reconstruction. We use our proposed eigenbases to build frames that are suitable for developing signal processing on Cayley graphs. These are the Frobenius--Schur frames and Cayley frames, for which we provide a characterization and a practical recipe for their construction.

Large language models (LLMs) excel in tasks requiring processing and interpretation of input text. Abstract screening is a labour-intensive component of systematic review involving repetitive application of inclusion and exclusion criteria on a large volume of studies identified by a literature search. Here, LLMs (GPT-3.5 Turbo, GPT-4 Turbo, GPT-4o, Llama 3 70B, Gemini 1.5 Pro, and Claude Sonnet 3.5) were trialled on systematic reviews in a full issue of the Cochrane Library to evaluate their accuracy in zero-shot binary classification for abstract screening. Trials over a subset of 800 records identified optimal prompting strategies and demonstrated superior performance of LLMs to human researchers in terms of sensitivity (LLMmax = 1.000, humanmax = 0.775), precision (LLMmax = 0.927, humanmax = 0.911), and balanced accuracy (LLMmax = 0.904, humanmax = 0.865). The best performing LLM-prompt combinations were trialled across every replicated search result (n = 119,691), and exhibited consistent sensitivity (range 0.756-1.000) but diminished precision (range 0.004-0.096). 66 LLM-human and LLM-LLM ensembles exhibited perfect sensitivity with a maximal precision of 0.458, with less observed performance drop in larger trials. Significant variation in performance was observed between reviews, highlighting the importance of domain-specific validation before deployment. LLMs may reduce the human labour cost of systematic review with maintained or improved accuracy and sensitivity. Systematic review is the foundation of evidence-based medicine, and LLMs can contribute to increasing the efficiency and quality of this mode of research.