## 1 Introduction
In recent advancements, deep learning techniques have demonstrated remarkable efficacy in translation initiation site (TIS) prediction. A notable contribution by [13] introduced TISRover, a convolutional neural network (CNN) approach capable of autonomously extracting critical biological features directly from genomic sequences (e.g., Kozak consensus sequences [5], reading frame characteristics, and donor splice site motifs). Unlike modular systems such as MANTS and StackTIS that explicitly engineer and combine discrete feature sets, TISRover operates through implicit feature learning. Later, we proposed a method, called NeuroTIS [24], for TIS prediction in mRNA sequences based on a hybrid dependency network and deep learning framework that explicitly models label dependencies among coding sequences (CDSs) between CDSs and TISs. NeuroTIS explicitly exploits coding features like StackTIS and implicitly learns consensus motifs like TISRover, and it achieves considerable improvements over other methods in terms of its predictive results. Despite its effectiveness, NeuroTIS has two key limitations in mRNA primary structural information utilization. First, it incompletely models codon label consistency in a neighboring region. Meanwhile, its skip-connected bidirectional RNN (skipBRNN) aggregates the two most informative neighboring positions into their current positions; however, as shown in Figure 1, the CDS is a continuous region where codon labels are consistent with a multiple of three; hence, all the neighboring positions can provide more or less information regarding the current position. Technically speaking, it is difficult for skipBRNN to aggregate more informative neighboring positions to the current position because the network is sequentially connected. Furthermore, the network is also low-scaled and hence has too limited expressive power to model complex non-linear relationships between inputs and outputs. Second, positive TISs initiate triplet decoding in the first reading frame, while negative TISs may reside in any frame without triggering sustained translation, resulting in heterogeneous coding features around negative TISs, as shown in Figure 1. For positive TISs, the coding features around \(t_{1}\) are homogeneous, but, for negative TISs, such as \(t_{2}\) and \(t_{3}\), they are located in different reading frames, and hence the coding features around them are heterogeneous. During the process of TIS prediction, it is difficult for a CNN to map these heterogeneous features to the same label. This is because the weights of a CNN are global and shared by all the data, so they must reconcile to fit all the heterogeneous features when they are updated by the backpropagation algorithm [25]. In this study, we address the aforementioned limitations through the development of NeuroTIS+, an enhanced method for TIS prediction leveraging primary structural information in mRNA sequences. NeuroTIS+ models codon label consistency by using a Temporal Convolutional Network (TCN) [26], which allows for more expressive power to model coding probability outputs and more flexible codon label information aggregation than NeuroTIS. Moreover, NeuroTIS+ considers the heterogeneity of negative samples and trains three frame-specific CNNs for translation initiation site prediction. Comparative evaluations on human and mouse transcriptome-wide mRNA sequences reveal that our method substantially outperforms the existing state-of-the-art methods in terms of prediction performance. There are three key innovations that contribute to the enhanced performance of our proposed framework:  
* The proposed method, NeuroTIS+, is an improved version of NeuroTIS, which preserves the basic framework of NeuroTIS and hence inherits the merits of explicitly modeling statistic dependencies among variables and automatic feature learning. Meanwhile, it assumes a stronger dependency relationship among codon labels and integrates novel frame information for TIS inference.