The authors present Hilbert-CNN, a convolutional neural network for DNA sequence classification.  Unlike existing methods, their model does not use the raw one-dimensional (1D) DNA sequence as input, but two-dimensional (2D) images obtained by mapping sequences to images using spacing-filling Hilbert-Curves.  They further present a model (Hilbert-CNN) that is explicitly designed for Hilbert-transformed DNA sequences.  The authors show that their approach can increase classification accuracy and decrease training time when applied to predicting histone-modification marks and splice junctions.  Major comments=============1. The motivation of transforming sequences into images is unclear  and claimed benefits are not sufficiently supported by experiments.  The essence of deep neural networks is to learn a hierarchy of features from the raw data instead of engineering features manually.  Using space filling methods such as Hilbert-curves to transform (DNA) sequences into images can be considered as unnecessary feature-engineering.  The authors claim that ‘CNNs have proven to be most powerful when operating on multi-dimensional input, such as in image classification’, which is wrong.  Sequence-based convolutional and recurrent models have been successfully applied for modeling natural languages (translation, sentiment classification, …), acoustic signals (speech recognition, audio generation), or biological sequences (e.g. predicting various epigenetic marks from DNA as reviewed in Angermueller et al).     They further claim that their method can ‘better take the spatial features of DNA sequences into account’ and  can better model ‘long-term interactions’ between distant regions.  This is not obvious  since Hilbert-curves map adjacent sequence characters to pixels that are close to each other as described by the authors, but distant characters to distant pixels.  Hence, 2D CNN must be deep enough for modeling interactions between distant image features, in the same way as a 1D CNN. Transforming sequences to images has several drawbacks.  1) Since the resulting images have a small width and height but many channels,  existing 2D CNNs such as ResNet or Inception can not be applied,  which also required the authors to design a specific model (Hilbert-CNN).  2) Hilbert-CNN requires more memory due to empty image regions.  3) Due to the high number of channels, convolutional filters have more parameters.  4) The sequence-to-image transformation makes model-interpretability hard, which is in particular important in biology.  For example, motifs of the first convolutional layers can not be interpreted as sequence motifs (as described in Angermueller et al)  and it is unclear how to analyze the influence of sequence characters using attention or gradient-based methods. The authors should more clearly motivate their model in the introduction, tone-down the benefit of sequence-to-image transformations, and discuss drawbacks of their model.  This requires major changes of introduction and discussion. 2. The authors should more clearly describe which and how they optimized hyper-parameters.  The authors should optimize the most important hyper-parameters of their model (learning rate, batch size, weight decay, max vs. average pooling, ELU vs. ReLU, …) and baseline models on a holdout validation set.  The authors should also report the validation accuracy for different sequence lengths, k-mer sizes, and space filling functions.  Can their model be applied to longer sequences (>= 1kbp) which had been shown to improve performance (e.g. 10.1101/gr.200535.115)?  Does Figure 4 show the performance on the training, validation, or test set? 3. It is unclear if the performance gain is due the proposed sequence-to-image transformation, or due to the proposed network architecture (Hilbert-CNN).  It is also unclear if Hilbert-CNNs are applicable to DNA sequence classification tasks beyond predicting chromatin states and splice junctions.  To address these points, the authors should compare Hilbert-CNN to models of the same capacity (number of parameters) and optimize hyper-parameters (k-mer size, convolutional filter size, learning rate, …) in the same way as they did for Hilbert-CNN.  The authors should report the number of parameters of all models (Hilbert-CNN, Seq-CNN, 1D-sequence-CNN (Table 5), and LSTM (Table 6), …) in an additional table.  The authors should also compare Hilbert-CNN to the DanQ architecture on predicting epigenetic markers using the same dataset as reported in the DanQ publication (DOI: 10.1093/nar/gkw226).  The authors should also compare Hilbert-CNNs to gapped-kmer SVM, a shallow model that had been successfully applied for genomic prediction tasks. 4. The authors should report the AUC and area under precision-recall curve (APR) in additional to accuracy (ACC) in Table 3. 5. It is unclear how training time was measured for baseline models (Seq-CNN, LSTM, …).  The authors should use the same early stopping criterion as they used for training Hilber-CNNs.  The authors should also report the training time of SVM and gkm-SVM (see comment 3) in Table 3. Minor comments=============1. The authors should avoid uninformative adjectives and clutter throughout the manuscript, for example ‘DNA is often perceived’, ‘Chromatin can assume’,  ‘enlightening’, ‘very’, ‘we first have to realize’, ‘do not mean much individually’, ‘very much like the tensor’, ‘full swing’, ‘in tight communication’, ‘two methods available in the literature’. The authors should point out in section two that k-mers can be overlapping. 2. Section 2.1: One-hot vectors is not the only way for embedding words.  The authors should also mention Glove and word2vec.  Similar approaches had been applied to protein sequences  (DOI: 10.1371/journal.pone.0141287) 3. The authors should more clearly describe how Hilbert-curves map sequences to images and how images are cropped.  What does ‘that is constructed in a recursive manner’ mean?  Simply cropping the upper half of Figure 1c would lead to two disjoint sequences.  What is the order of Figure 1e? 4. The authors should consistently use ‘channels’ instead of ‘full vector of length’ to denote the dimensionality of image pixels. 5. The authors should use ‘Batch norm’ instead of ‘BN’ in Figure 2 for clarification. 6. Hilber-CNN is similar to ResNet  (DOI: 10.1371/journal.pone.0141287),  which consists of multiple ‘residual blocks’, where each block is a sequence of ‘residual units’.  A ‘computational block’ in Hilbert-CNN contains two parallel ‘residual blocks’ (Figure 3) instead of a sequence of ‘residual units’.  The authors should use ‘residual block’ instead of ‘computational block’, and ‘residual units’ as in the original ResNet publication.  The authors should also motivate why two residual units/blocks are applied parallely instead of sequentially. 7. Caption table 1: the authors should clarify if ‘Output size’ is ‘height, width, channels’, and explain the notation in ‘Description’ (or refer to the text.)