We introduce a novel diffusion transformer, LazyDiffusion, that generates partial image updates efficiently. Our approach targets interactive image editing applications in which, starting from a blank canvas or an image, a user specifies a sequence of localized image modifications using binary masks and text prompts. Our generator operates in two phases. First, a context encoder processes the current canvas and user mask to produce a compact global context tailored to the region to generate. Second, conditioned on this context, a diffusion-based transformer decoder synthesizes the masked pixels in a "lazy" fashion, i.e., it only generates the masked region. This contrasts with previous works that either regenerate the full canvas, wasting time and computation, or confine processing to a tight rectangular crop around the mask, ignoring the global image context altogether. Our decoder's runtime scales with the mask size, which is typically small, while our encoder introduces negligible overhead. We demonstrate that our approach is competitive with state-of-the-art inpainting methods in terms of quality and fidelity while providing a 10x speedup for typical user interactions, where the editing mask represents 10% of the image.
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Capturing complex temporal patterns and relationships within multivariate data streams is a difficult task. We propose the Temporal Kolmogorov-Arnold Transformer (TKAT), a novel attention-based architecture designed to address this task using Temporal Kolmogorov-Arnold Networks (TKANs). Inspired by the Temporal Fusion Transformer (TFT), TKAT emerges as a powerful encoder-decoder model tailored to handle tasks in which the observed part of the features is more important than the a priori known part. This new architecture combined the theoretical foundation of the Kolmogorov-Arnold representation with the power of transformers. TKAT aims to simplify the complex dependencies inherent in time series, making them more "interpretable". The use of transformer architecture in this framework allows us to capture long-range dependencies through self-attention mechanisms.
We develop here a novel transfer learning methodology called Profiled Transfer Learning (PTL). The method is based on the \textit{approximate-linear} assumption between the source and target parameters. Compared with the commonly assumed \textit{vanishing-difference} assumption and \textit{low-rank} assumption in the literature, the \textit{approximate-linear} assumption is more flexible and less stringent. Specifically, the PTL estimator is constructed by two major steps. Firstly, we regress the response on the transferred feature, leading to the profiled responses. Subsequently, we learn the regression relationship between profiled responses and the covariates on the target data. The final estimator is then assembled based on the \textit{approximate-linear} relationship. To theoretically support the PTL estimator, we derive the non-asymptotic upper bound and minimax lower bound. We find that the PTL estimator is minimax optimal under appropriate regularity conditions. Extensive simulation studies are presented to demonstrate the finite sample performance of the new method. A real data example about sentence prediction is also presented with very encouraging results.
Deep priors have emerged as potent methods in hyperspectral image (HSI) reconstruction. While most methods emphasize space-domain learning using image space priors like non-local similarity, frequency-domain learning using image frequency priors remains neglected, limiting the reconstruction capability of networks. In this paper, we first propose a Hyperspectral Frequency Correlation (HFC) prior rooted in in-depth statistical frequency analyses of existent HSI datasets. Leveraging the HFC prior, we subsequently establish the frequency domain learning composed of a Spectral-wise self-Attention of Frequency (SAF) and a Spectral-spatial Interaction of Frequency (SIF) targeting low-frequency and high-frequency components, respectively. The outputs of SAF and SIF are adaptively merged by a learnable gating filter, thus achieving a thorough exploitation of image frequency priors. Integrating the frequency domain learning and the existing space domain learning, we finally develop the Correlation-driven Mixing Domains Transformer (CMDT) for HSI reconstruction. Extensive experiments highlight that our method surpasses various state-of-the-art (SOTA) methods in reconstruction quality and computational efficiency.
Audio fingerprinting, exemplified by pioneers like Shazam, has transformed digital audio recognition. However, existing systems struggle with accuracy in challenging conditions, limiting broad applicability. This research proposes an AI and ML integrated audio fingerprinting algorithm to enhance accuracy. Built on the Dejavu Project's foundations, the study emphasizes real-world scenario simulations with diverse background noises and distortions. Signal processing, central to Dejavu's model, includes the Fast Fourier Transform, spectrograms, and peak extraction. The "constellation" concept and fingerprint hashing enable unique song identification. Performance evaluation attests to 100% accuracy within a 5-second audio input, with a system showcasing predictable matching speed for efficiency. Storage analysis highlights the critical space-speed trade-off for practical implementation. This research advances audio fingerprinting's adaptability, addressing challenges in varied environments and applications.
We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These components are identified through the autocovariance structure of the underlying functional time series. The model parameters are consistently estimated using the eigencomponents of a cumulative autocovariance operator and an information criterion is proposed to determine the appropriate number of factors. The methodology is applied to yield curve modeling and forecasting. Our results indicate that more than three factors are required to characterize the dynamics of the term structure of bond yields.
This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid systems. Refinements are useful e.g. for simplifying proofs by relating a concrete hybrid system to an abstract one from which the property can be proved more easily. Uniform substitution is the key to parsimonious prover microkernels. It enables the verbatim use of single axiom formulas instead of axiom schemata with soundness-critical side conditions scattered across the proof calculus. The uniform substitution rule can then be used to instantiate all axioms soundly. Access to differential variables in dRL enables more control over the notion of refinement, which is shown to be decidable on a fragment of hybrid programs.
Technology ecosystems often undergo significant transformations as they mature. For example, telephony, the Internet, and PCs all started with a single provider, but in the United States each is now served by a competitive market that uses comprehensive and universal technology standards to provide compatibility. This white paper presents our view on how the cloud ecosystem, barely over fifteen years old, could evolve as it matures.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.
Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.
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