def mps_decomposition(tensor):
    """
    Decomposes a high-dimensional tensor into a chain of lower-dimensional tensors.
    """
    # Use singular value decomposition (SVD)
    # ...
    return mps_tensors

def low_rank_approximation(tensor, rank):
    """
    Approximates a tensor using a lower rank representation.
    """
    u, s, v = torch.svd(tensor)
    approx_tensor = torch.matmul(u[:, :rank], torch.matmul(torch.diag(s[:rank]), v[:, :rank].t()))
    return approx_tensor