Signal Temporal Logic (STL) is a powerful framework for describing the complex temporal and logical behaviour of the dynamical system. Numerous studies have attempted to employ reinforcement learning to learn a controller that enforces STL specifications; however, they have been unable to effectively tackle the challenges of ensuring robust satisfaction in continuous state space and maintaining tractability. In this paper, leveraging the concept of funnel functions, we propose a tractable reinforcement learning algorithm to learn a time-dependent policy for robust satisfaction of STL specification in continuous state space. We demonstrate the utility of our approach on several STL tasks using different environments.
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The Bounded Knapsack problem is one of the most fundamental NP-complete problems at the intersection of computer science, optimization, and operations research. A recent line of research worked towards understanding the complexity of pseudopolynomial-time algorithms for Bounded Knapsack parameterized by the maximum item weight $w_{\mathrm{max}}$ and the number of items $n$. A conditional lower bound rules out that Bounded Knapsack can be solved in time $O((n+w_{\mathrm{max}})^{2-\delta})$ for any $\delta > 0$ [Cygan, Mucha, Wegrzycki, Wlodarczyk'17, K\"unnemann, Paturi, Schneider'17]. This raised the question whether Bounded Knapsack can be solved in time $\tilde O((n+w_{\mathrm{max}})^2)$. The quest of resolving this question lead to algorithms that run in time $\tilde O(n^3 w_{\mathrm{max}}^2)$ [Tamir'09], $\tilde O(n^2 w_{\mathrm{max}}^2)$ and $\tilde O(n w_{\mathrm{max}}^3)$ [Bateni, Hajiaghayi, Seddighin, Stein'18], $O(n^2 w_{\mathrm{max}}^2)$ and $\tilde O(n w_{\mathrm{max}}^2)$ [Eisenbrand and Weismantel'18], $O(n + w_{\mathrm{max}}^3)$ [Polak, Rohwedder, Wegrzycki'21], and very recently $\tilde O(n + w_{\mathrm{max}}^{12/5})$ [Chen, Lian, Mao, Zhang'23]. In this paper we resolve this question by designing an algorithm for Bounded Knapsack with running time $\tilde O(n + w_{\mathrm{max}}^2)$, which is conditionally near-optimal.
We propose employing a debiased-regularized, high-dimensional generalized method of moments (GMM) framework to perform inference on large-scale spatial panel networks. In particular, network structure with a flexible sparse deviation, which can be regarded either as latent or as misspecified from a predetermined adjacency matrix, is estimated using debiased machine learning approach. The theoretical analysis establishes the consistency and asymptotic normality of our proposed estimator, taking into account general temporal and spatial dependency inherent in the data-generating processes. The dimensionality allowance in presence of dependency is discussed. A primary contribution of our study is the development of uniform inference theory that enables hypothesis testing on the parameters of interest, including zero or non-zero elements in the network structure. Additionally, the asymptotic properties for the estimator are derived for both linear and nonlinear moments. Simulations demonstrate superior performance of our proposed approach. Lastly, we apply our methodology to investigate the spatial network effect of stock returns.
Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly because it needs many forward and reverse steps. We propose a faster and cheaper approach that adds noise not until the data become pure random noise, but until they reach a hidden noisy data distribution that we can confidently learn. Then, we use fewer reverse steps to generate data by starting from this hidden distribution that is made similar to the noisy data. We reveal that the proposed model can be cast as an adversarial auto-encoder empowered by both the diffusion process and a learnable implicit prior. Experimental results show even with a significantly smaller number of reverse diffusion steps, the proposed truncated diffusion probabilistic models can provide consistent improvements over the non-truncated ones in terms of performance in both unconditional and text-guided image generations.
The design process of centrifugal compressors requires applying an optimization process which is computationally expensive due to complex analytical equations underlying the compressor's dynamical equations. Although the regression surrogate models could drastically reduce the computational cost of such a process, the major challenge is the scarcity of data for training the surrogate model. Aiming to strategically exploit the labeled samples, we propose the Active-CompDesign framework in which we combine a thermodynamics-based compressor model (i.e., our internal software for compressor design) and Gaussian Process-based surrogate model within a deployable Active Learning (AL) setting. We first conduct experiments in an offline setting and further, extend it to an online AL framework where a real-time interaction with the thermodynamics-based compressor's model allows the deployment in production. ActiveCompDesign shows a significant performance improvement in surrogate modeling by leveraging on uncertainty-based query function of samples within the AL framework with respect to the random selection of data points. Moreover, our framework in production has reduced the total computational time of compressor's design optimization to around 46% faster than relying on the internal thermodynamics-based simulator, achieving the same performance.
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language equivalence (under the standard language valuation) for Kleene algebra terms, this coincidence is broken if we extend the terms with complements. In this paper, we prove the decidability of some fragments of the equational theory: the universality problem is coNP-complete, and the inequational theory t <= s is coNP-complete when t does not contain Kleene-star. To this end, we introduce words-to-letters valuations; they are sufficient valuations for the equational theory and ease us in investigating the equational theory w.r.t. languages. Additionally, we prove that for words with variable complements, the equational theory coincides with the word equivalence.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
TransMIL: Transformer based Correlated Multiple Instance Learning for Whole Slide Image Classication
Multiple instance learning (MIL) is a powerful tool to solve the weakly supervised classification in whole slide image (WSI) based pathology diagnosis. However, the current MIL methods are usually based on independent and identical distribution hypothesis, thus neglect the correlation among different instances. To address this problem, we proposed a new framework, called correlated MIL, and provided a proof for convergence. Based on this framework, we devised a Transformer based MIL (TransMIL), which explored both morphological and spatial information. The proposed TransMIL can effectively deal with unbalanced/balanced and binary/multiple classification with great visualization and interpretability. We conducted various experiments for three different computational pathology problems and achieved better performance and faster convergence compared with state-of-the-art methods. The test AUC for the binary tumor classification can be up to 93.09% over CAMELYON16 dataset. And the AUC over the cancer subtypes classification can be up to 96.03% and 98.82% over TCGA-NSCLC dataset and TCGA-RCC dataset, respectively.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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