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

How to Fine-Tune BERT for Text Classification?

Language model pre-training has proven to be useful in learning universal language representations. As a state-of-the-art language model pre-training model, BERT (Bidirectional Encoder Representations from Transformers) has achieved amazing results in many language understanding tasks. In this paper, we conduct exhaustive experiments to investigate different fine-tuning methods of BERT on text classification task and provide a general solution for BERT fine-tuning. Finally, the proposed solution obtains new state-of-the-art results on eight widely-studied text classification datasets

Small Transformers Compute Universal Metric Embeddings

We study representations of data from an arbitrary metric space $\mathcal{X}$ in the space of univariate Gaussian mixtures with a transport metric (Delon and Desolneux 2020). We derive embedding guarantees for feature maps implemented by small neural networks called \emph{probabilistic transformers}. Our guarantees are of memorization type: we prove that a probabilistic transformer of depth about $n\log(n)$ and width about $n^2$ can bi-H\"{o}lder embed any $n$-point dataset from $\mathcal{X}$ with low metric distortion, thus avoiding the curse of dimensionality. We further derive probabilistic bi-Lipschitz guarantees, which trade off the amount of distortion and the probability that a randomly chosen pair of points embeds with that distortion. If $\mathcal{X}$'s geometry is sufficiently regular, we obtain stronger, bi-Lipschitz guarantees for all points in the dataset. As applications, we derive neural embedding guarantees for datasets from Riemannian manifolds, metric trees, and certain types of combinatorial graphs. When instead embedding into multivariate Gaussian mixtures, we show that probabilistic transformers can compute bi-H\"{o}lder embeddings with arbitrarily small distortion.Comment: 42 pages, 10 Figures, 3 Table

A Universal Latent Fingerprint Enhancer Using Transformers

Forensic science heavily relies on analyzing latent fingerprints, which are crucial for criminal investigations. However, various challenges, such as background noise, overlapping prints, and contamination, make the identification process difficult. Moreover, limited access to real crime scene and laboratory-generated databases hinders the development of efficient recognition algorithms. This study aims to develop a fast method, which we call ULPrint, to enhance various latent fingerprint types, including those obtained from real crime scenes and laboratory-created samples, to boost fingerprint recognition system performance. In closed-set identification accuracy experiments, the enhanced image was able to improve the performance of the MSU-AFIS from 61.56\% to 75.19\% in the NIST SD27 database, from 67.63\% to 77.02\% in the MSP Latent database, and from 46.90\% to 52.12\% in the NIST SD302 database. Our contributions include (1) the development of a two-step latent fingerprint enhancement method that combines Ridge Segmentation with UNet and Mix Visual Transformer (MiT) SegFormer-B5 encoder architecture, (2) the implementation of multiple dilated convolutions in the UNet architecture to capture intricate, non-local patterns better and enhance ridge segmentation, and (3) the guided blending of the predicted ridge mask with the latent fingerprint. This novel approach, ULPrint, streamlines the enhancement process, addressing challenges across diverse latent fingerprint types to improve forensic investigations and criminal justice outcomes

On a New Notion of Partial Refinement

Formal specification techniques allow expressing idealized specifications, which abstract from restrictions that may arise in implementations. However, partial implementations are universal in software development due to practical limitations. Our goal is to contribute to a method of program refinement that allows for partial implementations. For programs with a normal and an exceptional exit, we propose a new notion of partial refinement which allows an implementation to terminate exceptionally if the desired results cannot be achieved, provided the initial state is maintained. Partial refinement leads to a systematic method of developing programs with exception handling.Comment: In Proceedings Refine 2013, arXiv:1305.563