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Dear authors,

I have some questions about the proof of Theorem 3.1 and 3.2.

Specifically, in Proof of Theorem 3.1, I don't understand why this inequality holds

Also, from reference [42] (High-Dimensional Data Analysis with Low-Dimensional Models: Principles, Computation, and Applications), the mutual coherence of a matrix is the largest normalized inner product between two distinct columns, instead of rows (embedding is a row vector of a matrix). In Lemma 8.1, A is an n x m matrix, while in Theorem 3.5 of [42], A is an m x n matrix.

So I am really confused about the conclusion of Theorem 3.1 in your paper. Do I have some misunderstandings?

In Proof of Theorem 3.2, the conclusion is

But taking a two-layer LightGCN as an example,

I am afraid the multiply of two underlined terms can not be represented by \beta_k R (R^T R)^k for any k.

I am looking forward to your reply!

Does this project support other versions of torch?
When I execute the file of requirment.txt , I always get an error

ERROR: Could not find a version that satisfies the requirement torch==1.4.0 (from versions: 1.11.0, 1.12.0, 1.12.1, 1.13.0, 1.13.1, 2.0.0, 2.0.1, 2.1.0, 2.1.1, 2.1.2, 2.2.0, 2.2.1)
ERROR: No matching distribution found for torch==1.4.0

Then I tried to download different cuda torche，but it still reported an error.

Looking in links: https://download.pytorch.org/whl/torch_stable.html
ERROR: Could not find a version that satisfies the requirement torch==1.4.0+cu92 (from versions: 1.11.0, 1.11.0+cpu, 1.11.0+cu102, 1.11.0+cu113, 1.11.0+cu115, 1.11.0+rocm4.3.1, 1.11.0+rocm4.5.2, 1.12.0, 1.12.0+cpu, 1.12.0+cu102, 1.12.0+cu113, 1.12.0+cu116, 1.12.0+rocm5.0, 1.12.0+rocm5.1.1, 1.12.1, 1.12.1+cpu, 1.12.1+cu102, 1.12.1+cu113, 1.12.1+cu116, 1.12.1+rocm5.0, 1.12.1+rocm5.1.1, 1.13.0, 1.13.0+cpu, 1.13.0+cu116, 1.13.0+cu117, 1.13.0+cu117.with.pypi.cudnn, 1.13.0+rocm5.1.1, 1.13.0+rocm5.2, 1.13.1, 1.13.1+cpu, 1.13.1+cu116, 1.13.1+cu117, 1.13.1+cu117.with.pypi.cudnn, 1.13.1+rocm5.1.1, 1.13.1+rocm5.2, 2.0.0, 2.0.0+cpu, 2.0.0+cpu.cxx11.abi, 2.0.0+cu117, 2.0.0+cu117.with.pypi.cudnn, 2.0.0+cu118, 2.0.0+rocm5.3, 2.0.0+rocm5.4.2, 2.0.1, 2.0.1+cpu, 2.0.1+cpu.cxx11.abi, 2.0.1+cu117, 2.0.1+cu117.with.pypi.cudnn, 2.0.1+cu118, 2.0.1+rocm5.3, 2.0.1+rocm5.4.2, 2.1.0, 2.1.0+cpu, 2.1.0+cpu.cxx11.abi, 2.1.0+cu118, 2.1.0+cu121, 2.1.0+cu121.with.pypi.cudnn, 2.1.0+rocm5.5, 2.1.0+rocm5.6, 2.1.1, 2.1.1+cpu, 2.1.1+cpu.cxx11.abi, 2.1.1+cu118, 2.1.1+cu121, 2.1.1+cu121.with.pypi.cudnn, 2.1.1+rocm5.5, 2.1.1+rocm5.6, 2.1.2, 2.1.2+cpu, 2.1.2+cpu.cxx11.abi, 2.1.2+cu118, 2.1.2+cu121, 2.1.2+cu121.with.pypi.cudnn, 2.1.2+rocm5.5, 2.1.2+rocm5.6, 2.2.0, 2.2.0+cpu, 2.2.0+cpu.cxx11.abi, 2.2.0+cu118, 2.2.0+cu121, 2.2.0+rocm5.6, 2.2.0+rocm5.7, 2.2.1, 2.2.1+cpu, 2.2.1+cpu.cxx11.abi, 2.2.1+cu118, 2.2.1+cu121, 2.2.1+rocm5.6, 2.2.1+rocm5.7)
ERROR: No matching distribution found for torch==1.4.0+cu92

I don't know how to solve it……

Dear Authors,
I have some questions about the proof of theorem 3.2 in Section 8.2. Concretely, I am very confusing about the derivation of the limitation of $S$ when $d$ tends to infinity. I am also confusing about the statement

For a pair of matrices X, Y, if the rows of X \in R^{* \times d}, Y \in R^{* \times d} follow independently identical distribution, due to the linearity of dot product, we have lim_{d -> \inf} X Y^T = \mathbb{E}[x_1 y_1^T].

Why do the above equations hold? Can you explain more about that? Thanks very much!

Hi, authors, I tried to run the untrained LightGCN with dimension of 4096 (The pytorch version of LightGCN), but didn't get the similar result as you provided, so I wonder why is it and are there any settings that different from the original LightGCN code? Thanks.

nohup: ignoring input
�[0;30;43mCpp extension not loaded�[0m
>>SEED: 2020
�[0;30;43mloading [../data/gowalla]�[0m
810128 interactions for training
217242 interactions for testing
gowalla Sparsity : 0.0008396216228570436
gowalla is ready to go
===========config================
{'A_n_fold': 100,
 'A_split': False,
 'bigdata': False,
 'bpr_batch_size': 2048,
 'decay': 0.0001,
 'dropout': 0,
 'keep_prob': 0.6,
 'latent_dim_rec': 4096,
 'lightGCN_n_layers': 3,
 'lr': 0.001,
 'multicore': 0,
 'pretrain': 0,
 'test_u_batch_size': 100}
cores for test: 48
comment: lgn
tensorboard: 1
LOAD: 0
Weight path: ./checkpoints
Test Topks: [20]
using bpr loss
===========end===================
�[0;30;43muse NORMAL distribution initilizer�[0m
loading adjacency matrix
successfully loaded...
don't split the matrix
lgn is already to go(dropout:0)
load and save to ./code/checkpoints/lgn-gowalla-3-4096.pth.tar
�[0;30;43m[TEST]�[0m
{'precision': array([0.00277982]), 'recall': array([0.00980375]), 'ndcg': array([0.00742985])}

-- My questions are clealy solved. Thank you :)