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The Kalman filter (KF) is a state estimation algorithm that optimally combines system knowledge and measurements to minimize the mean squared error of the estimated states. While KF was initially designed for linear systems, numerous extensions of it, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc., have been proposed for nonlinear systems. Although different types of nonlinear KFs have different pros and cons, they all use the same framework of linear KF, which, according to what we found in this paper, tends to give overconfident and less accurate state estimations when the measurement functions are nonlinear. Therefore, in this study, we designed a new framework for nonlinear KFs and showed theoretically and empirically that the new framework estimates the states and covariance matrix more accurately than the old one. The new framework was tested on four different nonlinear KFs and five different tasks, showcasing its ability to reduce the estimation errors by several orders of magnitude in low-measurement-noise conditions, with only about a 10 to 90% increase in computational time. All types of nonlinear KFs can benefit from the new framework, and the benefit will increase as the sensors become more and more accurate in the future. As an example, EKF, the simplest nonlinear KF that was previously believed to work poorly for strongly nonlinear systems, can now provide fast and fairly accurate state estimations with the help of the new framework. The codes are available at //github.com/Shida-Jiang/A-new-framework-for-nonlinear-Kalman-filters.

A new variational inference method, SPH-ParVI, based on smoothed particle hydrodynamics (SPH), is proposed for sampling partially known densities (e.g. up to a constant) or sampling using gradients. SPH-ParVI simulates the flow of a fluid under external effects driven by the target density; transient or steady state of the fluid approximates the target density. The continuum fluid is modelled as an interacting particle system (IPS) via SPH, where each particle carries smoothed properties, interacts and evolves as per the Navier-Stokes equations. This mesh-free, Lagrangian simulation method offers fast, flexible, scalable and deterministic sampling and inference for a class of probabilistic models such as those encountered in Bayesian inference and generative modelling.

ROME and MEMIT are largely believed to be two different model editing algorithms, with the major difference between them being the ability to perform batched edits. In this paper, we unify these two algorithms under a single conceptual umbrella, optimizing for the same goal, which we call the preservation-memorization objective. ROME uses an equality constraint to optimize this objective to perform one edit at a time, whereas MEMIT employs a more flexible least-square constraint that allows for batched edits. We generalize ROME and enable batched editing with equality constraint in the form of EMMET - an Equality-constrained Mass Model Editing algorithm for Transformers, a new batched memory-editing algorithm. EMMET can perform batched-edits up to a batch-size of 10,000, with very similar performance to MEMIT across multiple dimensions. With the introduction of EMMET, we truly unify ROME and MEMIT and show that both algorithms are equivalent in terms of their optimization objective, their abilities (singular and batched editing), their model editing performance and their limitations.

Generalized Locally Toeplitz (GLT) matrix sequences arise from large linear systems that approximate Partial Differential Equations (PDEs), Fractional Differential Equations (FDEs), and Integro-Differential Equations (IDEs). GLT sequences of matrices have been developed to study the spectral/singular value behaviour of the numerical approximations to various PDEs, Fades and IDEs. These approximations can be achieved using any discretization method on appropriate grids through local techniques such as Finite Differences, Finite Elements, Finite Volumes, Isogeometric Analysis, and Discontinuous Galerkin methods. Spectral and singular value symbols are essential for analyzing the eigenvalue and singular value distributions of matrix sequences in the Weyl sense. In this article, we provide a comprehensive overview of the operator-theoretic aspect of GLT sequences. The theory of GLT sequences, along with findings on the asymptotic spectral distribution of perturbed matrix sequences, is a highly effective and successful method for calculating the spectral symbol f. Therefore, developing an automatic procedure to compute the spectral symbols of these matrix sequences would be advantageous, a task that Ahmed Ratnani, N S Sarathkumar, S. Serra-Capizzano have partially undertaken. As an application of the theory developed here, we propose an automatic procedure for computing the symbol of the underlying sequences of matrices, assuming they form a GLT sequence that meets mild conditions.

We apply functional acceleration to the Policy Mirror Descent (PMD) general family of algorithms, which cover a wide range of novel and fundamental methods in Reinforcement Learning (RL). Leveraging duality, we propose a momentum-based PMD update. By taking the functional route, our approach is independent of the policy parametrization and applicable to large-scale optimization, covering previous applications of momentum at the level of policy parameters as a special case. We theoretically analyze several properties of this approach and complement with a numerical ablation study, which serves to illustrate the policy optimization dynamics on the value polytope, relative to different algorithmic design choices in this space. We further characterize numerically several features of the problem setting relevant for functional acceleration, and lastly, we investigate the impact of approximation on their learning mechanics.

A Normalizing Flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g. normal) distribution. Such a flow can be used to address different tasks, e.g. anomaly detection, once such a mapping has been learned. In this work we introduce Normalizing Flows for Quantum architectures, describe how to model and optimize such a flow and evaluate our method on example datasets. Our proposed models show competitive performance for anomaly detection compared to classical methods, esp. those ones where there are already quantum inspired algorithms available. In the experiments we compare our performance to isolation forests (IF), the local outlier factor (LOF) or single-class SVMs.

Retrieval augmented generation (RAG) enhances the accuracy and reliability of generative AI models by sourcing factual information from external databases, which is extensively employed in document-grounded question-answering (QA) tasks. Off-the-shelf RAG flows are well pretrained on general-purpose documents, yet they encounter significant challenges when being applied to knowledge-intensive vertical domains, such as electronic design automation (EDA). This paper addresses such issue by proposing a customized RAG framework along with three domain-specific techniques for EDA tool documentation QA, including a contrastive learning scheme for text embedding model fine-tuning, a reranker distilled from proprietary LLM, and a generative LLM fine-tuned with high-quality domain corpus. Furthermore, we have developed and released a documentation QA evaluation benchmark, ORD-QA, for OpenROAD, an advanced RTL-to-GDSII design platform. Experimental results demonstrate that our proposed RAG flow and techniques have achieved superior performance on ORD-QA as well as on a commercial tool, compared with state-of-the-arts. The ORD-QA benchmark and the training dataset for our customized RAG flow are open-source at //github.com/lesliepy99/RAG-EDA.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.