Typo fixes to index.md

Comparison.md

@@ -22,7 +22,7 @@ The following figure shows a comparison between Tiramisu, cuDNN, TVM, Halide and
 
 #### Tiramisu can Express Programs with Cyclic DataFlow Graphs
 
-While Halide can implement a simple version of LSTMs (Long Short Term Memory), it is limited to LSTMs where the number of recurrence steps (i.e., cells) is known at compile time. Supporting a dynamic number of recurrence steps is important in case the number of steps is unkonw at compile time (which is usually the case in graph and tree LSTMs for example). The inability to express RNNs is mainly because Halide has a restricted language that prevents the user from writing a program that has a cycle in its data flow graph since it cannot guarantee the correctness of loop optimizations in that case. Unlike Halide, Tiramisu performs polyhedral dependence analysis and uses transformation legality checks to guarantee the correctness of code transformations. This gives the compiler more flexibility and removes an important restriction on the Tiramisu language.
+While Halide can implement a simple version of LSTMs (Long Short Term Memory), it is limited to LSTMs where the number of recurrence steps (i.e., cells) is known at compile time. Supporting a dynamic number of recurrence steps is important in case the number of steps is unknown at compile time (which is usually the case in graph and tree LSTMs for example). The inability to express RNNs is mainly stems from the fact that Halide has a restricted language that prevents the user from writing a program that has a cycle in its data flow graph since it cannot guarantee the correctness of loop optimizations in that case. Unlike Halide, Tiramisu performs polyhedral dependence analysis and uses transformation legality checks to guarantee the correctness of code transformations. This gives the compiler more flexibility and removes an important restriction on the Tiramisu language.
 
 #### Tiramisu can Represent Non-rectangular Loops Naturally
 

index.md

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-(*) Standard DNN data sizes are used. The density level (non-zero elemenets) is 20% for all the benchmarks except VGG where we use 2% (the density levels are obtained from state-of-the-art weifht compression techniques.
+(*) Standard DNN data sizes are used. The density level (non-zero elements) is 20% for all the benchmarks except VGG where we use 2% (the density levels are obtained from state-of-the-art weight compression techniques.
 
 (**) Tensor Comprehensions and Halide cannot express LSTM because LSTM is a recurrent algorithm that creates a cycle in the data-flow graph.