Optimizing a CUDA-based Loss Function for Neural Network Training

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I have been working on the following loss function to train neural networks based on a statistical invariant. I have tried to port the function to GPU/CUDA, and I have the following code. It works correctly; however, since I am new to CUDA, I would like to ask if anyone knows or can think of any optimization that could speed up the code. Thank you very much.

The loss function is,

function sliced_invariant_statistical_loss_optimized_gpu_2(nn_model, loader, hparams)
    @assert loader.batchsize == hparams.samples
    @assert length(loader) == hparams.epochs
    losses = Vector{Float32}()
    optim = Flux.setup(Flux.Adam(hparams.η), nn_model)

    @showprogress for data in loader
        data = gpu(data) # Move data to GPU once per epoch
        Ω = gpu([sample_random_direction(size(data)[1]) for _ in 1:(hparams.m)])
        total = 0.0f0 # Use a scalar for accumulation

        # Generate all random noise in one batch and move to GPU
        x_batch = gpu(rand(hparams.noise_model, hparams.samples * hparams.K))

        # Pre-compute column indices for slicing
        start_cols = hparams.K * (1:(hparams.samples - 1))
        end_cols = hparams.K * (2:(hparams.samples)) .- 1

        loss, grads = Flux.withgradient(nn_model) do nn
            # Process batch through nn_model
            yₖ_batch = nn(x_batch)

            for ω in Ω
                s = transpose(ω) * yₖ_batch

                aₖ = mapreduce(+, 1:length(start_cols)) do i
                    slice = s[:, start_cols[i]:end_cols[i]]
                    dot_product = dot(ω, data[:, i + 1])
                    generate_aₖ(slice, dot_product)
                total += scalar_diff(aₖ ./ sum(aₖ))
            total / hparams.m
        Flux.update!(optim, nn_model, grads[1])
        push!(losses, loss)
    return losses

and I called it like this,

dim = 100

device = gpu

model = device(Generator(latent_dim)) #this what ever is neural network

# Mean vector (zero vector of length dim)
mean_vector = zeros(dims)

# Covariance matrix (identity matrix of size dim x dim)
cov_matrix = Diagonal(ones(dims))

# Create the multivariate normal distribution
noise_model = device(MvNormal(mean_vector, cov_matrix))

hparams = device(
        K=2, samples=1000, epochs=60, η=1e-3, noise_model=noise_model, m=2

sliced_invariant_statistical_loss_optimized_gpu_2(model, train_loader, hparams)

The rest of the functions are,

function _sigmoid(
    ŷ::Transpose{T,CUDA.CuArray{T,1,CUDA.Mem.DeviceBuffer}}, y::T
) where {T<:AbstractFloat}
    return sigmoid_fast.((y .- ŷ) .* 10.0f0)

function ϕ(
    yₖ::Transpose{T,CUDA.CuArray{T,1,CUDA.Mem.DeviceBuffer}}, yₙ::T
) where {T<:AbstractFloat}
    return CUDA.sum(_sigmoid(yₖ, yₙ))

function γ(
    yₖ::Transpose{T,CUDA.CuArray{T,1,CUDA.Mem.DeviceBuffer}}, yₙ::T, m::Int64
) where {T<:AbstractFloat}
    function eₘ_cuda(m, length)
        return CuArray([j == m ? T(1.0) : T(0.0) for j in 0:length])

    return eₘ_cuda(m, size(yₖ, 2)) * ψₘ(ϕ(yₖ, yₙ), m)

function generate_aₖ(
    ŷ::Transpose{T,CUDA.CuArray{T,1,CUDA.Mem.DeviceBuffer}}, y::T
) where {T<:AbstractFloat}
    # Calculate the squared differences
    return CUDA.sum([γ(ŷ, y, k) for k in 0:length(ŷ)])

@inline scalar_diff(q::CuArray{T}) where {T<:AbstractFloat} =
    sum((q .- (T(1.0f0) ./ T(length(q)))) .^ 2)