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Register a new userLearnable Fourier Features for Multi-Dimensional Spatial Positional Encoding
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Added by
Yang Li
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where $L_2$ distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.
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It is well noted that coordinate based MLPs benefit greatly -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.
Without positional information, attention-based transformer neural networks are permutation-invariant. Absolute or relative positional embeddings are the most popular ways to feed transformer models positional information. Absolute positional embeddings are simple to implement, but suffer from generalization issues when evaluating on sequences of different length than those seen at training time. Relative positions are more robust to length change, but are more complex to implement and yield inferior model throughput. In this paper, we propose an augmentation-based approach (CAPE) for absolute positional embeddings, which keeps the advantages of both absolute (simplicity and speed) and relative position embeddings (better generalization). In addition, our empirical evaluation on state-of-the-art models in machine translation, image and speech recognition demonstrates that CAPE leads to better generalization performance as well as increased stability with respect to training hyper-parameters.
Natural language processing has made significant inroads into learning the semantics of words through distributional approaches, however representations learnt via these methods fail to capture certain kinds of information implicit in the real world. In particular, spatial relations are encoded in a way that is inconsistent with human spatial reasoning and lacking invariance to viewpoint changes. We present a system capable of capturing the semantics of spatial relations such as behind, left of, etc from natural language. Our key contributions are a novel multi-modal objective based on generating images of scenes from their textual descriptions, and a new dataset on which to train it. We demonstrate that internal representations are robust to meaning preserving transformations of descriptions (paraphrase invariance), while viewpoint invariance is an emergent property of the system.
Learning node representations that incorporate information from graph structure benefits wide range of tasks on graph. The majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given node. The idea of positioning nodes with selected anchors has been exploited, yet mainly relying on explicit labeling of distance information. Here we propose Graph Inference Representation (GIR), an anchor based GNN model encoding path information related to pre-selected anchors for each node. Abilities to get position-aware embeddings are theoretically and experimentally investigated on GIR and its core variants. Further, the complementarity between GIRs and typical GNNs is demonstrated. We show that GIRs get outperformed results in position-aware scenarios, and performances on typical GNNs could be improved by fusing GIR embeddings.
SinGAN shows impressive capability in learning internal patch distribution despite its limited effective receptive field. We are interested in knowing how such a translation-invariant convolutional generator could capture the global structure with just a spatially i.i.d. input. In this work, taking SinGAN and StyleGAN2 as examples, we show that such capability, to a large extent, is brought by the implicit positional encoding when using zero padding in the generators. Such positional encoding is indispensable for generating images with high fidelity. The same phenomenon is observed in other generative architectures such as DCGAN and PGGAN. We further show that zero padding leads to an unbalanced spatial bias with a vague relation between locations. To offer a better spatial inductive bias, we investigate alternative positional encodings and analyze their effects. Based on a more flexible positional encoding explicitly, we propose a new multi-scale training strategy and demonstrate its effectiveness in the state-of-the-art unconditional generator StyleGAN2. Besides, the explicit spatial inductive bias substantially improve SinGAN for more versatile image manipulation.
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