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State-space models are used to describe and analyse dynamical systems. They are ubiquitously used in many scientific fields such as signal processing, finance and ecology to name a few. Particle filters are popular inferential methods used for state-space methods. Integrated Nested Laplace Approximation (INLA), an approximate Bayesian inference method, can also be used for this kind of models in case the transition distribution is Gaussian. We present a way to use this framework in order to approximate the particle filter's proposal distribution that incorporates information about the observations, parameters and the previous latent variables. Further, we demonstrate the performance of this proposal on data simulated from a Poisson state-space model used for count data. We also show how INLA can be used to estimate the parameters of certain state-space models (a task that is often challenging) that would be used for Sequential Monte Carlo algorithms.

Grounding navigational commands to linear temporal logic (LTL) leverages its unambiguous semantics for reasoning about long-horizon tasks and verifying the satisfaction of temporal constraints. Existing approaches require training data from the specific environment and landmarks that will be used in natural language to understand commands in those environments. We propose Lang2LTL, a modular system and a software package that leverages large language models (LLMs) to ground temporal navigational commands to LTL specifications in environments without prior language data. We comprehensively evaluate Lang2LTL for five well-defined generalization behaviors. Lang2LTL demonstrates the state-of-the-art ability of a single model to ground navigational commands to diverse temporal specifications in 21 city-scaled environments. Finally, we demonstrate a physical robot using Lang2LTL can follow 52 semantically diverse navigational commands in two indoor environments.

Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR is critical but challenging. In this paper, we propose a new method called functional slicing-free inverse regression (FSFIR) to estimate the central subspace in FSDR. FSFIR is based on the martingale difference divergence operator, which is a novel metric introduced to characterize the conditional mean independence of a functional predictor on a multivariate response. We also provide a specific convergence rate for the FSFIR estimator. Compared with existing functional sliced inverse regression methods, FSFIR does not require the selection of a slice number. Simulations demonstrate the efficiency and convenience of FSFIR.

Generative Adversarial Networks (GAN) is a model for data synthesis, which creates plausible data through the competition of generator and discriminator. Although GAN application to image synthesis is extensively studied, it has inherent limitations to natural language generation. Because natural language is composed of discrete tokens, a generator has difficulty updating its gradient through backpropagation; therefore, most text-GAN studies generate sentences starting with a random token based on a reward system. Thus, the generators of previous studies are pre-trained in an autoregressive way before adversarial training, causing data memorization that synthesized sentences reproduce the training data. In this paper, we synthesize sentences using a framework similar to the original GAN. More specifically, we propose Text Embedding Space Generative Adversarial Networks (TESGAN) which generate continuous text embedding spaces instead of discrete tokens to solve the gradient backpropagation problem. Furthermore, TESGAN conducts unsupervised learning which does not directly refer to the text of the training data to overcome the data memorization issue. By adopting this novel method, TESGAN can synthesize new sentences, showing the potential of unsupervised learning for text synthesis. We expect to see extended research combining Large Language Models with a new perspective of viewing text as an continuous space.

Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK kernel and given data (a concept referred to as alignment in this paper) can govern the rate of convergence of gradient descent, as well as generalization to unseen data. Building upon this concept, we investigate NTKs and alignment in the context of graph neural networks (GNNs), where our analysis reveals that optimizing alignment translates to optimizing the graph representation or the graph shift operator in a GNN. Our results further establish the theoretical guarantees on the optimality of the alignment for a two-layer GNN and these guarantees are characterized by the graph shift operator being a function of the cross-covariance between the input and the output data. The theoretical insights drawn from the analysis of NTKs are validated by our experiments focused on a multi-variate time series prediction task for a publicly available dataset. Specifically, they demonstrate that GNNs with cross-covariance as the graph shift operator indeed outperform those that operate on the covariance matrix from only the input data.

We develop a Bayesian inference method for discretely-observed stochastic differential equations (SDEs). Inference is challenging for most SDEs, due to the analytical intractability of the likelihood function. Nevertheless, forward simulation via numerical methods is straightforward, motivating the use of approximate Bayesian computation (ABC). We propose a conditional simulation scheme for SDEs that is based on lookahead strategies for sequential Monte Carlo (SMC) and particle smoothing using backward simulation. This leads to the simulation of trajectories that are consistent with the observed trajectory, thereby increasing the ABC acceptance rate. We additionally employ an invariant neural network, previously developed for Markov processes, to learn the summary statistics function required in ABC. The neural network is incrementally retrained by exploiting an ABC-SMC sampler, which provides new training data at each round. Since the SDE simulation scheme differs from standard forward simulation, we propose a suitable importance sampling correction, which has the added advantage of guiding the parameters towards regions of high posterior density, especially in the first ABC-SMC round. Our approach achieves accurate inference and is about three times faster than standard (forward-only) ABC-SMC. We illustrate our method in four simulation studies, including three examples from the Chan-Karaolyi-Longstaff-Sanders SDE family.

In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlapping, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these type of relaxations are widely used.

In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random linear code consists in recovering a basis of a random noise vector that was used to perturb a set of random linear equations sharing a secret solution. Assuming the intractability of this problem, we introduce a new construction of injective one-way trapdoor functions. Our solution departs from the frequent way of building public key primitives from error-correcting codes where, to establish the security, ad hoc assumptions about a hidden structure are made. Our method produces a hard-to-distinguish linear code together with low weight vectors which constitute the secret that helps recover the inputs.The key idea is to focus on trapdoor functions that take sufficiently enough input vectors sharing the same support. Applying then the error correcting algorithm designed for Low Rank Parity Check (LRPC) codes, we obtain an inverting algorithm that recovers the inputs with overwhelming probability.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.