We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.
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Quadrotors are widely used for surveillance, mapping, and deliveries. In several scenarios the quadrotor operates in pure inertial navigation mode resulting in a navigation solution drift. To handle such situations and bind the navigation drift, the quadrotor dead reckoning (QDR) approach requires flying the quadrotor in a periodic trajectory. Then, using model or learning based approaches the quadrotor position vector can be estimated. We propose to use multiple inertial measurement units (MIMU) to improve the positioning accuracy of the QDR approach. Several methods to utilize MIMU data in a deep learning framework are derived and evaluated. Field experiments were conducted to validate the proposed approach and show its benefits.
We propose a differentiable vertex fitting algorithm that can be used for secondary vertex fitting, and that can be seamlessly integrated into neural networks for jet flavour tagging. Vertex fitting is formulated as an optimization problem where gradients of the optimized solution vertex are defined through implicit differentiation and can be passed to upstream or downstream neural network components for network training. More broadly, this is an application of differentiable programming to integrate physics knowledge into neural network models in high energy physics. We demonstrate how differentiable secondary vertex fitting can be integrated into larger transformer-based models for flavour tagging and improve heavy flavour jet classification.
We devise a version of Linear Temporal Logic (LTL) on a denotational domain of streams. We investigate this logic in terms of domain theory, (point-free) topology and geometric logic. This yields the first steps toward an extension of the "Domain Theory in Logical Form" paradigm to temporal liveness properties. We show that the negation-free formulae of LTL induce sober subspaces of streams, but that this is in general not the case in presence of negation. We propose a direct, inductive, translation of negation-free LTL to geometric logic. This translation reflects the approximations used to compute the usual fixpoint representations of LTL modalities. As a motivating example, we handle a natural input-output specification for the usual filter function on streams.
Recently, asynchronous coarse-space correction has been achieved within both the overlapping Schwarz and the primal Schur frameworks. Both additive and multiplicative corrections have been discussed. In this paper, we address some implementation drawbacks of the proposed additive correction scheme. In the existing approach, each coarse solution is applied only once, leaving most of the iterations of the solver without coarse-space information while building the right-hand side of the coarse problem. Moreover, one-sided routines of the Message Passing Interface (MPI) standard were considered, which introduced the need for a sleep statement in the iterations loop of the coarse solver. This implies a tuning of the sleep period, which is a non-discrete quantity. In this paper, we improve the accuracy of the coarse right-hand side, which allowed for more frequent corrections. In addition, we highlight a two-sided implementation which better suits the asynchronous coarse-space correction scheme. Numerical experiments show a significant performance gain with such increased incorporation of the coarse space.
Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.
We consider a fully-decentralized scenario in which no central trusted entity exists and all clients are honest-but-curious. The state-of-the-art approaches to this problem often rely on cryptographic protocols, such as multiparty computation (MPC), that require mapping real-valued data to a discrete alphabet, specifically a finite field. These approaches, however, can result in substantial accuracy losses due to computation overflows. To address this issue, we propose A-MPC, a private analog MPC protocol that performs all computations in the analog domain. We characterize the privacy of individual datasets in terms of $(\epsilon, \delta)$-local differential privacy, where the privacy of a single record in each client's dataset is guaranteed against other participants. In particular, we characterize the required noise variance in the Gaussian mechanism in terms of the required $(\epsilon,\delta)$-local differential privacy parameters by solving an optimization problem. Furthermore, compared with existing decentralized protocols, A-MPC keeps the privacy of individual datasets against the collusion of all other participants, thereby, in a notably significant improvement, increasing the maximum number of colluding clients tolerated in the protocol by a factor of three compared with the state-of-the-art collaborative learning protocols. Our experiments illustrate that the accuracy of the proposed $(\epsilon,\delta)$-locally differential private logistic regression and linear regression models trained in a fully-decentralized fashion using A-MPC closely follows that of a centralized one performed by a single trusted entity.
Recent artificial intelligence (AI) systems have reached milestones in "grand challenges" ranging from Go to protein-folding. The capability to retrieve medical knowledge, reason over it, and answer medical questions comparably to physicians has long been viewed as one such grand challenge. Large language models (LLMs) have catalyzed significant progress in medical question answering; Med-PaLM was the first model to exceed a "passing" score in US Medical Licensing Examination (USMLE) style questions with a score of 67.2% on the MedQA dataset. However, this and other prior work suggested significant room for improvement, especially when models' answers were compared to clinicians' answers. Here we present Med-PaLM 2, which bridges these gaps by leveraging a combination of base LLM improvements (PaLM 2), medical domain finetuning, and prompting strategies including a novel ensemble refinement approach. Med-PaLM 2 scored up to 86.5% on the MedQA dataset, improving upon Med-PaLM by over 19% and setting a new state-of-the-art. We also observed performance approaching or exceeding state-of-the-art across MedMCQA, PubMedQA, and MMLU clinical topics datasets. We performed detailed human evaluations on long-form questions along multiple axes relevant to clinical applications. In pairwise comparative ranking of 1066 consumer medical questions, physicians preferred Med-PaLM 2 answers to those produced by physicians on eight of nine axes pertaining to clinical utility (p < 0.001). We also observed significant improvements compared to Med-PaLM on every evaluation axis (p < 0.001) on newly introduced datasets of 240 long-form "adversarial" questions to probe LLM limitations. While further studies are necessary to validate the efficacy of these models in real-world settings, these results highlight rapid progress towards physician-level performance in medical question answering.
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.
Aspect level sentiment classification aims to identify the sentiment expressed towards an aspect given a context sentence. Previous neural network based methods largely ignore the syntax structure in one sentence. In this paper, we propose a novel target-dependent graph attention network (TD-GAT) for aspect level sentiment classification, which explicitly utilizes the dependency relationship among words. Using the dependency graph, it propagates sentiment features directly from the syntactic context of an aspect target. In our experiments, we show our method outperforms multiple baselines with GloVe embeddings. We also demonstrate that using BERT representations further substantially boosts the performance.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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