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In randomized experiments, the classic stable unit treatment value assumption (SUTVA) states that the outcome for one experimental unit does not depend on the treatment assigned to other units. However, the SUTVA assumption is often violated in applications such as online marketplaces and social networks where units interfere with each other. We consider the estimation of the average treatment effect in a network interference model using a mixed randomization design that combines two commonly used experimental methods: Bernoulli randomized design, where treatment is independently assigned for each individual unit, and cluster-based design, where treatment is assigned at an aggregate level. Essentially, a mixed randomization experiment runs these two designs simultaneously, allowing it to better measure the effect of network interference. We propose an unbiased estimator for the average treatment effect under the mixed design and show the variance of the estimator is bounded by $O({d^2}n^{-1}p^{-1})$ where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the probability of treatment. We also establish a lower bound of $\Omega(d^{1.5}n^{-1}p^{-1})$ for the variance of any mixed design. For a family of sparse networks characterized by a growth constant $\kappa \leq d$, we improve the upper bound to $O({\kappa^7 d}n^{-1}p^{-1})$. Furthermore, when interference weights on the edges of the network are unknown, we propose a weight-invariant design that achieves a variance bound of $O({d^3}n^{-1}p^{-1})$.

Since its invention HyperLogLog has become the standard algorithm for approximate distinct counting. Due to its space efficiency and suitability for distributed systems, it is widely used and also implemented in numerous databases. This work presents UltraLogLog, which shares the same practical properties as HyperLogLog. It is commutative, idempotent, mergeable, and has a fast guaranteed constant-time insert operation. At the same time, it requires 28% less space to encode the same amount of distinct count information, which can be extracted using the maximum likelihood method. Alternatively, a simpler and faster estimator is proposed, which still achieves a space reduction of 24%, but at an estimation speed comparable to that of HyperLogLog. In a non-distributed setting where martingale estimation can be used, UltraLogLog is able to reduce space by 17%. Moreover, its smaller entropy and its 8-bit registers lead to better compaction when using standard compression algorithms. All this is verified by experimental results that are in perfect agreement with the theoretical analysis which also outlines potential for even more space-efficient data structures. A production-ready Java implementation of UltraLogLog has been released as part of the open-source Hash4j library.

We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method has no free parameters and requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including off-diagonal expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ansatze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ansatze we can accurately recover vertical excitation energies and oscillator strengths on molecules as large as benzene. Beyond the examples on molecules presented here, we expect this technique will be of great interest for applications of variational quantum Monte Carlo to atomic, nuclear and condensed matter physics.

A vast number of systems across the world use algorithmic decision making (ADM) to (partially) automate decisions that have previously been made by humans. When designed well, these systems promise more objective decisions while saving large amounts of resources and freeing up human time. However, when ADM systems are not designed well, they can lead to unfair decisions which discriminate against societal groups. The downstream effects of ADMs critically depend on the decisions made during the systems' design and implementation, as biases in data can be mitigated or reinforced along the modeling pipeline. Many of these design decisions are made implicitly, without knowing exactly how they will influence the final system. It is therefore important to make explicit the decisions made during the design of ADM systems and understand how these decisions affect the fairness of the resulting system. To study this issue, we draw on insights from the field of psychology and introduce the method of multiverse analysis for algorithmic fairness. In our proposed method, we turn implicit design decisions into explicit ones and demonstrate their fairness implications. By combining decisions, we create a grid of all possible "universes" of decision combinations. For each of these universes, we compute metrics of fairness and performance. Using the resulting dataset, one can see how and which decisions impact fairness. We demonstrate how multiverse analyses can be used to better understand variability and robustness of algorithmic fairness using an exemplary case study of predicting public health coverage of vulnerable populations for potential interventions. Our results illustrate how decisions during the design of a machine learning system can have surprising effects on its fairness and how to detect these effects using multiverse analysis.

Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, an important tool for simulating quantum circuits in the tractable regime. We first show that although DDs were suggested to succinctly represent important quantum states, they actually require exponential space for certain stabilizer states. To remedy this, we introduce a more powerful decision diagram variant, called Local Invertible Map-DD (LIMDD). We prove that the set of quantum states represented by poly-sized LIMDDs strictly contains the union of stabilizer states and other decision diagram variants. Finally, there exist circuits which LIMDDs can efficiently simulate, while their output states cannot be succinctly represented by two state-of-the-art simulation paradigms: the stabilizer decomposition techniques for Clifford + $T$ circuits and Matrix-Product States. By uniting two successful approaches, LIMDDs thus pave the way for fundamentally more powerful solutions for simulation and analysis of quantum computing.

Nowadays, the increasing complexity of Advanced Driver Assistance Systems (ADAS) and Automated Driving (AD) means that the industry must move towards a scenario-based approach to validation rather than relying on established technology-based methods. This new focus also requires the validation process to take into account Safety of the Intended Functionality (SOTIF), as many scenarios may trigger hazardous vehicle behaviour. Thus, this work demonstrates how the integration of the SOTIF process within an existing validation tool suite can be achieved. The necessary adaptations are explained with accompanying examples to aid comprehension of the approach.

Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is an important task for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as $O(3^N)$ for $N$-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma and others [PhysRevA.74.052302] established that the complexity could be drastically reduced when looking at fidelity lower bounds for states that exhibit symmetries, such as Dicke States and GHZ States. For larger states, these bounds still need to be tight enough to provide reasonable estimations on NISQ devices. For the first time and more than 15 years after the theoretical introduction, we report meaningful lower bounds for the state preparation fidelity of all Dicke States up to $N=10$, and all GHZ states up to $N=20$ on Quantinuum H1 ion-trap systems using efficient implementations of recently proposed scalable circuits for these states. Our achieved lower bounds match or exceed previously reported exact fidelities on superconducting systems for much smaller states. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.

The Fisher-Kolmogorov equation is a diffusion-reaction PDE that is used to model the accumulation of prionic proteins, which are responsible for many different neurological disorders. Likely, the most important and studied misfolded protein in literature is the Amyloid-$\beta$, responsible for the onset of Alzheimer disease. Starting from medical images we construct a reduced-order model based on a graph brain connectome. The reaction coefficient of the proteins is modelled as a stochastic random field, taking into account all the many different underlying physical processes, which can hardly be measured. Its probability distribution is inferred by means of the Monte Carlo Markov Chain method applied to clinical data. The resulting model is patient-specific and can be employed for predicting the disease's future development. Forward uncertainty quantification techniques (Monte Carlo and sparse grid stochastic collocation) are applied with the aim of quantifying the impact of the variability of the reaction coefficient on the progression of protein accumulation within the next 20 years.

The aim of Machine Unlearning (MU) is to provide theoretical guarantees on the removal of the contribution of a given data point from a training procedure. Federated Unlearning (FU) consists in extending MU to unlearn a given client's contribution from a federated training routine. Current FU approaches are generally not scalable, and do not come with sound theoretical quantification of the effectiveness of unlearning. In this work we present Informed Federated Unlearning (IFU), a novel efficient and quantifiable FU approach. Upon unlearning request from a given client, IFU identifies the optimal FL iteration from which FL has to be reinitialized, with unlearning guarantees obtained through a randomized perturbation mechanism. The theory of IFU is also extended to account for sequential unlearning requests. Experimental results on different tasks and dataset show that IFU leads to more efficient unlearning procedures as compared to basic re-training and state-of-the-art FU approaches.

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs the applicability of this approach to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differential equation (ODE) on the network parameters and the solution propagated forward in time; however, we demonstrate that current methods based on this approach suffer from two key issues. First, following the ODE produces an uncontrolled growth in the conditioning of the problem, ultimately leading to unacceptably large numerical errors. Second, as the ODE methods scale cubically with the number of model parameters, they are restricted to small neural networks, significantly limiting their ability to represent intricate PDE initial conditions and solutions. Building on these insights, we develop Neural IVP, an ODE based IVP solver which prevents the network from getting ill-conditioned and runs in time linear in the number of parameters, enabling us to evolve the dynamics of challenging PDEs with neural networks.