Semi-supervised multiscale dual-encoding method for faulty traffic data detection

Inspired by the recent success of deep learning in multiscale information encoding, we introduce a variational autoencoder (VAE) based semi-supervised method for detection of faulty traffic data, which is cast as a classification problem. Continuous wavelet transform (CWT) is applied to the time series of traffic volume data to obtain rich features embodied in time-frequency representation, followed by a twin of VAE models to separately encode normal data and faulty data. The resulting multiscale dual encodings are concatenated and fed to an attention-based classifier, consisting of a self-attention module and a multilayer perceptron. For comparison, the proposed architecture is evaluated against five different encoding schemes, including (1) VAE with only normal data encoding, (2) VAE with only faulty data encoding, (3) VAE with both normal and faulty data encodings, but without attention module in the classifier, (4) siamese encoding, and (5) cross-vision transformer (CViT) encoding. The first four encoding schemes adopted the same convolutional neural network (CNN) architecture while the fifth encoding scheme follows the transformer architecture of CViT. Our experiments show that the proposed architecture with the dual encoding scheme, coupled with attention module, outperforms other encoding schemes and results in classification accuracy of 96.4%, precision of 95.5%, and recall of 97.7%.Comment: 16 pages, 8 figure

SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic unified understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training, which employs joint contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the pre-trained embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in few-shot learning scenarios where available data is limited

Your Transformer May Not be as Powerful as You Expect

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative -- RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is. One key reason lies in that most RPEs are placed in the softmax attention that always generates a right stochastic matrix. This restricts the network from capturing positional information in the RPEs and limits its capacity. To overcome the problem and make the model more powerful, we first present sufficient conditions for RPE-based Transformers to achieve universal function approximation. With the theoretical guidance, we develop a novel attention module, called Universal RPE-based (URPE) Attention, which satisfies the conditions. Therefore, the corresponding URPE-based Transformers become universal function approximators. Extensive experiments covering typical architectures and tasks demonstrate that our model is parameter-efficient and can achieve superior performance to strong baselines in a wide range of applications. The code will be made publicly available at https://github.com/lsj2408/URPE.Comment: 22 pages; NeurIPS 2022, Camera Ready Versio

Dynamic Position Encoding for Transformers

Recurrent models have been dominating the field of neural machine translation (NMT) for the past few years. Transformers \citep{vaswani2017attention}, have radically changed it by proposing a novel architecture that relies on a feed-forward backbone and self-attention mechanism. Although Transformers are powerful, they could fail to properly encode sequential/positional information due to their non-recurrent nature. To solve this problem, position embeddings are defined exclusively for each time step to enrich word information. However, such embeddings are fixed after training regardless of the task and the word ordering system of the source or target language. In this paper, we propose a novel architecture with new position embeddings depending on the input text to address this shortcoming by taking the order of target words into consideration. Instead of using predefined position embeddings, our solution \textit{generates} new embeddings to refine each word's position information. Since we do not dictate the position of source tokens and learn them in an end-to-end fashion, we refer to our method as \textit{dynamic} position encoding (DPE). We evaluated the impact of our model on multiple datasets to translate from English into German, French, and Italian and observed meaningful improvements in comparison to the original Transformer