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We investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of the numerical simulators have inconsistent dimensions across the multilevel hierarchy. This requires the introduction of grid transfer operators borrowed from multigrid methods. Starting from a simple 1D illustration, we demonstrate numerically that the resulting MLMC estimator deteriorates the estimation of high-frequency components of the discretized expectation field compared to a Monte Carlo (MC) estimator. By adapting mathematical tools initially developed for multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. This analysis provides a spectral decomposition of the variance into contributions associated with each scale component of the discretized field. We then propose improved MLMC estimators using a filtering mechanism similar to the smoothing process of multigrid methods. The filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. These improvements are quantified for the specific class of simulators considered in our spectral analysis. The resulting filtered MLMC (F-MLMC) estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the proposed F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator.

It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of large number of neurons per hidden layer. In this work we prove an analogous result for Quantum Neural Networks (QNNs). Namely, we show that the outputs of certain models based on Haar random unitary or orthogonal deep QNNs converge to Gaussian processes in the limit of large Hilbert space dimension $d$. The derivation of this result is more nuanced than in the classical case due to the role played by the input states, the measurement observable, and the fact that the entries of unitary matrices are not independent. An important consequence of our analysis is that the ensuing Gaussian processes cannot be used to efficiently predict the outputs of the QNN via Bayesian statistics. Furthermore, our theorems imply that the concentration of measure phenomenon in Haar random QNNs is worse than previously thought, as we prove that expectation values and gradients concentrate as $\mathcal{O}\left(\frac{1}{e^d \sqrt{d}}\right)$. Finally, we discuss how our results improve our understanding of concentration in $t$-designs.

We present a framework for the efficient computation of optimal Bayesian decisions under intractable likelihoods, by learning a surrogate model for the expected utility (or its distribution) as a function of the action and data spaces. We leverage recent advances in simulation-based inference and Bayesian optimization to develop active learning schemes to choose where in parameter and action spaces to simulate. This allows us to learn the optimal action in as few simulations as possible. The resulting framework is extremely simulation efficient, typically requiring fewer model calls than the associated posterior inference task alone, and a factor of $100-1000$ more efficient than Monte-Carlo based methods. Our framework opens up new capabilities for performing Bayesian decision making, particularly in the previously challenging regime where likelihoods are intractable, and simulations expensive.

One of the main challenges of multimodal learning is the need to combine heterogeneous modalities (e.g., video, audio, text). For example, video and audio are obtained at much higher rates than text and are roughly aligned in time. They are often not synchronized with text, which comes as a global context, e.g., a title, or a description. Furthermore, video and audio inputs are of much larger volumes, and grow as the video length increases, which naturally requires more compute dedicated to these modalities and makes modeling of long-range dependencies harder. We here decouple the multimodal modeling, dividing it into separate, focused autoregressive models, processing the inputs according to the characteristics of the modalities. We propose a multimodal model, called Mirasol3B, consisting of an autoregressive component for the time-synchronized modalities (audio and video), and an autoregressive component for the context modalities which are not necessarily aligned in time but are still sequential. To address the long-sequences of the video-audio inputs, we propose to further partition the video and audio sequences in consecutive snippets and autoregressively process their representations. To that end, we propose a Combiner mechanism, which models the audio-video information jointly within a timeframe. The Combiner learns to extract audio and video features from raw spatio-temporal signals, and then learns to fuse these features producing compact but expressive representations per snippet. Our approach achieves the state-of-the-art on well established multimodal benchmarks, outperforming much larger models. It effectively addresses the high computational demand of media inputs by both learning compact representations, controlling the sequence length of the audio-video feature representations, and modeling their dependencies in time.

A Retrieval-Augmented Language Model (RALM) augments a generative language model by retrieving context-specific knowledge from an external database. This strategy facilitates impressive text generation quality even with smaller models, thus reducing orders of magnitude of computational demands. However, RALMs introduce unique system design challenges due to (a) the diverse workload characteristics between LM inference and retrieval and (b) the various system requirements and bottlenecks for different RALM configurations such as model sizes, database sizes, and retrieval frequencies. We propose Chameleon, a heterogeneous accelerator system that integrates both LM and retrieval accelerators in a disaggregated architecture. The heterogeneity ensures efficient acceleration of both LM inference and retrieval, while the accelerator disaggregation enables the system to independently scale both types of accelerators to fulfill diverse RALM requirements. Our Chameleon prototype implements retrieval accelerators on FPGAs and assigns LM inference to GPUs, with a CPU server orchestrating these accelerators over the network. Compared to CPU-based and CPU-GPU vector search systems, Chameleon achieves up to 23.72x speedup and 26.2x energy efficiency. Evaluated on various RALMs, Chameleon exhibits up to 2.16x reduction in latency and 3.18x speedup in throughput compared to the hybrid CPU-GPU architecture. These promising results pave the way for bringing accelerator heterogeneity and disaggregation into future RALM systems.

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis functions DeePC behavioral predictor and we identify necessary and sufficient conditions for equivalence with a corresponding basis functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.

A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly impacted by some decoherence channels and weakly coupled to the other subsystems. This numerical method is based on a perturbation analysis with an asymptotic expansion. It exploits the formulation of the slow dynamics with reduced dimension. It relies on the invariant operators of the local and nominal dissipative dynamics attached to each subsystem. Second-order expansion can be computed only with local numerical calculations. It avoids computations on the tensor-product Hilbert space attached to the full system. This numerical method is particularly well suited for autonomous quantum error correction schemes. Simulations of such reduced models agree with complete full model simulations for typical gates acting on one and two cat-qubits (Z, ZZ and CNOT) when the mean photon number of each cat-qubit is less than 8. For larger mean photon numbers and gates with three cat-qubits (ZZZ and CCNOT), full model simulations are almost impossible whereas reduced model simulations remain accessible. In particular, they capture both the dominant phase-flip error-rate and the very small bit-flip error-rate with its exponential suppression versus the mean photon number.

Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms utilize elements indicating prior information, such as (linear) structural causal models, interventional data, or weak supervision. Unfortunately, in exploratory causal representation learning, such elements and prior information may not be available or warranted. Alternatively, scientific datasets often have multiple modalities or physics-based constraints, and the use of such scientific, multimodal data has been shown to improve disentanglement in fully unsupervised settings. Consequently, we introduce a causal representation learning algorithm (causalPIMA) that can use multimodal data and known physics to discover important features with causal relationships. Our innovative algorithm utilizes a new differentiable parametrization to learn a directed acyclic graph (DAG) together with a latent space of a variational autoencoder in an end-to-end differentiable framework via a single, tractable evidence lower bound loss function. We place a Gaussian mixture prior on the latent space and identify each of the mixtures with an outcome of the DAG nodes; this novel identification enables feature discovery with causal relationships. Tested against a synthetic and a scientific dataset, our results demonstrate the capability of learning an interpretable causal structure while simultaneously discovering key features in a fully unsupervised setting.

Pretrained transformers exhibit the remarkable ability of in-context learning (ICL): they can learn tasks from just a few examples provided in the prompt without updating any weights. This raises a foundational question: can ICL solve fundamentally $\textit{new}$ tasks that are very different from those seen during pretraining? To probe this question, we examine ICL's performance on linear regression while varying the diversity of tasks in the pretraining dataset. We empirically demonstrate a $\textit{task diversity threshold}$ for the emergence of ICL. Below this threshold, the pretrained transformer cannot solve unseen regression tasks, instead behaving like a Bayesian estimator with the $\textit{non-diverse pretraining task distribution}$ as the prior. Beyond this threshold, the transformer significantly outperforms this estimator; its behavior aligns with that of ridge regression, corresponding to a Gaussian prior over $\textit{all tasks}$, including those not seen during pretraining. Thus, when pretrained on data with task diversity greater than the threshold, transformers $\textit{can}$ optimally solve fundamentally new tasks in-context. Importantly, this capability hinges on it deviating from the Bayes optimal estimator with the pretraining distribution as the prior. This study also explores the effect of regularization, model capacity and task structure and underscores, in a concrete example, the critical role of task diversity, alongside data and model scale, in the emergence of ICL. Code is available at //github.com/mansheej/icl-task-diversity.

This study investigates the potential of automated deep learning to enhance the accuracy and efficiency of multi-class classification of bird vocalizations, compared against traditional manually-designed deep learning models. Using the Western Mediterranean Wetland Birds dataset, we investigated the use of AutoKeras, an automated machine learning framework, to automate neural architecture search and hyperparameter tuning. Comparative analysis validates our hypothesis that the AutoKeras-derived model consistently outperforms traditional models like MobileNet, ResNet50 and VGG16. Our approach and findings underscore the transformative potential of automated deep learning for advancing bioacoustics research and models. In fact, the automated techniques eliminate the need for manual feature engineering and model design while improving performance. This study illuminates best practices in sampling, evaluation and reporting to enhance reproducibility in this nascent field. All the code used is available at https: //github.com/giuliotosato/AutoKeras-bioacustic Keywords: AutoKeras; automated deep learning; audio classification; Wetlands Bird dataset; comparative analysis; bioacoustics; validation dataset; multi-class classification; spectrograms.