# CoreTemp: Coreset Sampled Templates for Multimodal Mobile Biometrics
## 1 Introduction
The PIEformer intends to resemble the effect of having multiple models by having multiple learnable embedding inputs, where various experiments show its soundness. However, the global attention mechanism introduces some dependency between these embeddings, thus introducing a marginal limitation on the original objective. In this work, we primarily address the observations above. First, realizing the necessity of a method of reducing the template to a user-representative, robust subset, we propose CoreTemp: coreset-reduced templates. Motivated from the memory-reduction technique [24], where the combination of iterative greedy approximation [25; 26] and Johnson-Lindenstrauss (JL) [27] results in an effective reduction of templates. Moreover, based on the integrity of the reduction of dimensionality attributed to the JL theorem, we further put forth a quick-authentication mechanism, where the claimants' features are also reduced to be compared to the template reduced both in size (CoreTemp) and dimension, that is, a dimensional-reduced CoreTemp. Achieving a user-representative template of much smaller size and dimensionality leads us to explore its new capabilities further. Noticing that some mobile devices are shared, such as educational tablets, we utilize the smaller capacity of CoreTemp to enable identification, i.e., one-to-many matching by simply tagging multiple (identity) CoreTemps with their corresponding identity. We note that a mere application of the original templates within this framework of OSA leads to a substantial computational overhead, deviating from the objective of behavioral biometric authentication. Second, we improve the PIEformer by introducing a masking layer between the learnable embedding inputs. The main idea of PIEformer comes from resembling an ex plicit ensemble [28] of multiple Transformers by adopting multiple aggregated learnable embedding inputs. However, unlike the explicit ensemble where the performance enhancement is dependent on the diversity of individual sets of model parameters, attributed to predominantly by independent randomized initialization of model parameters and independent training of each model, the independence between embedding inputs in PIEformer is jeopardized due to the attention mechanism itself. Thus, by including an extra masking layer in the attention between the learnable embeddings, we achieve a clearer partitioning of information across the embedding inputs, achieving a closer approximation to the behavior of an explicit ensemble. This modified architecture, now referred to as PIEformer+ and illustrated in Figure 2, reaches state-of-the-art performance while maintaining the identical computation and model complexity as PIEformer. Our main contributions are as follows:  
* We propose utilizing greedy coreset sampling upon the touchstroke template. Extracting a user-representative yet reduced template efficiently uses limited memory on mobile devices. Moreover, we also propose a fast match algorithm conceived from the JL theorem adopted in greedy coreset sampling, leading to much more efficient authentication. * We introduce a novel variant of PIEformer suitable for initially generating user-discriminative templates, PIEformer+. While [16] has deeply investigated simulating an ensembled effect of Transformers with multiple learnable embedding inputs at a low computational cost, PIEformer+ simulates this phenomenon more closely by introducing a masking block in between the learnable parameters. * We demonstrate the feasibility of authentication and identification with the reduced templates. This highlights the importance of extracting a robust, user-representative touchstroke template. The proposed methods are evaluated on two datasets, HMOG and BBMAS, where they reach state-of-the-art performance in authentication and identification tasks. Building on these foundation, our study aims to enhance the efficiency and effectiveness of mobile biometric authentication systems through several key innovations, i.e., CoreTemp and PIEformer+.