Open set recognition (OSR) requires the model to classify samples that belong to closed sets while rejecting unknown samples during test. Currently, generative models often perform better than discriminative models in OSR, but recent studies show that generative models may be computationally infeasible or unstable on complex tasks. In this paper, we provide insights into OSR and find that learning supplementary representations can theoretically reduce the open space risk. Based on the analysis, we propose a new model, namely Multi-Expert Diverse Attention Fusion (MEDAF), that learns diverse representations in a discriminative way. MEDAF consists of multiple experts that are learned with an attention diversity regularization term to ensure the attention maps are mutually different. The logits learned by each expert are adaptively fused and used to identify the unknowns through the score function. We show that the differences in attention maps can lead to diverse representations so that the fused representations can well handle the open space. Extensive experiments are conducted on standard and OSR large-scale benchmarks. Results show that the proposed discriminative method can outperform existing generative models by up to 9.5% on AUROC and achieve new state-of-the-art performance with little computational cost. Our method can also seamlessly integrate existing classification models. Code is available at //github.com/Vanixxz/MEDAF.
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The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to improve the approximation accuracy and further reduce the discrete systems' stiffness. Firstly and most naturally, we generalize SoftFEM by adding a least-square term to the mass bilinear form. Superconvergent results of rates $h^6$ and $h^8$ for eigenvalues are established for linear uniform elements; $h^8$ is the highest order of convergence known in the literature. Secondly, we generalize SoftFEM by applying the blended Gaussian-type quadratures. We demonstrate further reductions in stiffness compared to traditional FEM and SoftFEM. The coercivity and analysis of the optimal error convergences follow the work of SoftFEM. Thus, this paper focuses on the numerical study of these generalizations. For linear and uniform elements, analytical eigenpairs, exact eigenvalue errors, and superconvergent error analysis are established. Various numerical examples demonstrate the potential of generalized SoftFEMs for spectral approximation, particularly in high-frequency regimes.
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one spanned by a finite basis of inducing points and the other capturing the remaining variation. We show that this formulation recovers existing approximations and at the same time allows to obtain tighter lower bounds on the marginal likelihood and new stochastic variational inference algorithms. We demonstrate the efficiency of these algorithms in several Gaussian process models ranging from standard regression to multi-class classification using (deep) convolutional Gaussian processes and report state-of-the-art results on CIFAR-10 among purely GP-based models.
Stein variational gradient descent (SVGD) is a prominent particle-based variational inference method used for sampling a target distribution. SVGD has attracted interest for application in machine-learning techniques such as Bayesian inference. In this paper, we propose novel trainable algorithms that incorporate a deep-learning technique called deep unfolding,into SVGD. This approach facilitates the learning of the internal parameters of SVGD, thereby accelerating its convergence speed. To evaluate the proposed trainable SVGD algorithms, we conducted numerical simulations of three tasks: sampling a one-dimensional Gaussian mixture, performing Bayesian logistic regression, and learning Bayesian neural networks. The results show that our proposed algorithms exhibit faster convergence than the conventional variants of SVGD.
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true regression function lies in an $L_2$-fractional Sobolev space with order $s\in (0,1)$. This function class is a Hilbert space lying between the space of square-integrable functions and the first-order Sobolev space consisting of differentiable functions. It contains fractional power functions, piecewise constant or polynomial functions and bump function as canonical examples. For the proposed approach, we prove upper bounds on the in-sample mean-squared estimation error of order $n^{-\frac{2s}{2s+d}}$, where $d$ is the dimension, $s$ is the aforementioned order parameter and $n$ is the number of observations. We also provide preliminary empirical results validating the practical performance of the developed estimators.
We propose a noble, comprehensive and robust agile requirements change management (ARCM) model that addresses the limitations of existing models and is tailored for agile software development in the global software development paradigm. To achieve this goal, we conducted an exhaustive literature review and an empirical study with RCM industry experts. Our study evaluated the effectiveness of the proposed RCM model in a real-world setting and identifies any limitations or areas for improvement. The results of our study provide valuable insights into how the proposed RCM model can be applied in agile global software development environments to improve software development practices and optimize project success rates.
We explore the sampling problem within the framework where parallel evaluations of the gradient of the log-density are feasible. Our investigation focuses on target distributions characterized by smooth and strongly log-concave densities. We revisit the parallelized randomized midpoint method and employ proof techniques recently developed for analyzing its purely sequential version. Leveraging these techniques, we derive upper bounds on the Wasserstein distance between the sampling and target densities. These bounds quantify the runtime improvement achieved by utilizing parallel processing units, which can be considerable.
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and do not map well onto sparse data representations. We build a vectorized and parallel matrix-multiplication system A X B = C that eliminates unnecessary computations and avoids branches based on a runtime evaluation of sparsity. We use a combination of dynamic code lookup to adapt to the specific sparsity encoded in the B matrix and preprocessing of sparsity maps of the A and B matrices to compute conditional branches once for the whole computation. For a wide range of sparsity, from 60% to 95% zeros, our implementation performs fewer instructions and increases performance when compared with Intel MKL's dense or sparse matrix multiply routines. Benefits can be as large as 2 times speedup and 4 times fewer instructions.
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.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.
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