answers.md

We thank the reviewers for the detailed reviews and the insightful comments and suggestions that could greatly help improve the presentation of our work. The replies to the specific questions raised by the reviewers are given as follows.

Reviewer 1:

1. The schedule strategy in Sec4.4 enumerates the main schedule primitives we applied including a series of loop transformations, operator inlining, and thread binding. While other optimizations such as data layout transformation have not been used. We would like to formalize Sec4.4 in the later version to clarify more schedule details.
2. The optimizations enabled by the usage of views are in computation performance impovement and memory reuse. The computation performance impovement lies in operator fusion, which could be quantified with the reduction of device kernels in Table 4 and reduced running time of functions and neural networks in Figure 7-9. Memory reuse mainly embodies as the reduction of memory allocations and data movement. We add an experiment to test the data movement operations for test cases in sec5.1, e.g the global data movement operations are reduced from * to * for the case delta2bbox. Besides, by anlyzing the operations of delta2bbox, we find 21 memory allocations could be reduced. We would like to add a new chart for the quantized description of memory optimizations in the later version.
3. The categorization is primarily based on whether the view varies the metadata compared with the tensor definition. Next, whether the view context modifies the underlying tensor data is the other consideration of the categorization, since that read operations retrieve the correct values should be ensured. According to the analysis of RAR, RAW, WAW and WAR, the seven view types are enough to keep the consistent read and write order with the source satements, and keep the correct metadata in the meanwhile.
4. The JAX, XLA(TensorFlow), and TorchScript(Pytorch) version we use are 0.2.27, 2.7.0 and 1.10.2, respectively. The version of the TVM codebase we use is 0.6. The Pytorch-like deep learning framework has not been open source, but could be functionally equal to Pytorch 1.10.2. Besides, the tuning mechanism is simple since we aim at element-wise operations. The thread number is set to 64, and the thread block number is set to dim/64, where dim is the product of the dimensions of the corresponding output tensor.
5. Since computer vision (CV) is an important area in AI community, we choose the typical or innovative networks in the popular open source library MMDetection, which contains amounts of view-related operations and affects the performance. It is worth noting that our proposal is not limited to the CV networks. Besides, we would like to explore other networks to find the bottleneck operationto enrich the operator fusion.

Reviewer 2:

1. The source example of Figure 4 illustrate a fabled function, which include six possible examples corresponding to the categorized tensor views. The Tensor C column of the right subgraph in Figure 4 labels the six kinds of examples corresponding to each tensor C corresponding to each stage. Besides, the test cases in our experiment section also include different kinds of example belong to each category. We would like to clarify more by expanding Table 4 to clarify more example of categorized examples.

Reviewer 3:

1. The experiment setup could be referred to the 4th item of the list in our responds to Reviewer1. The operator fusion in our implementation mainly supports element-wise operations. Some complex code structures like branch statements and unsupported operations such as new_tensor would still result in the division of graphs and generate more device kernels. Table 4 reveals the reduced kernels due to the support of views. As for delta2bbox, 8 device kernels are generated without scheduling views which are divided by a new_tensor operation, four adjacent view operations, two adjacent view operations， four adjacent view operations, four adjacent view operations, four adjacent view operations, and two adjacent view operations. And the device kernels are reduced two due to the support of all the view operations in the case.
2. Tensor Expression (TE) are used to describe tensor computations in TVM, which is a SSA format IR. Hence, non-SSA view syntax in the high-level language could not be directly expressed in TE, especially inplace udpate with respect to basic indexing operations including sophistacated index computations.
3. The categorization is primarily based on whether the view varies the metadata compared with the tensor definition. Next, whether the view context modifies the underlying tensor data is the other consideration of the categorization, since that read operations retrieve the correct values should be ensured. According to the analysis of RAR, RAW, WAW and WAR, the seven view types are enough to keep the consistent read and write order with the source satements, and keep the correct metadata in the meanwhile.
4. We quite agree TorchScript are mainly used to create serializable models from Pytorch code. However, TorchScript lowers operations and provide lots of optimization passes including operation fusion. Hence, we provide the experemental result as a reference.

Reviewer 4:

1. Reference semantic allows multiple tensor views in the high-level language refer to the same memory, and modifications in a view would result in modifications on the other views of the same tensor. The dependence tracking approach mainly analyzes the RAR, RAW, WAW and WAR data dependence relationships based the seven categorized tensor views, which essentially lies in the reference semantic of various contexts.
2. In this article our fusion scope includes variou element-wise operations satisfying SSA Tensor Expression IR format including various arithmetic and logical operations, tensor construction operations like stack and permutation, activation operations, etc. Besides, non-SSA element-wise operations in terms of views are also supported.