You write custom CUDA kernels to replace the pytorch operators in the given architecture to get speedups. 

    You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.


        Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is: 

        ``` 

        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()

    def forward(self, a, b):
        return a + b


def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]


def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

        ``` 

        The example new arch with custom CUDA kernels looks like this:
        ```
        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline

# Define the custom CUDA kernel for element-wise addition
elementwise_add_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>

__global__ void elementwise_add_kernel(const float* a, const float* b, float* out, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        out[idx] = a[idx] + b[idx];
    }
}

torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b) {
    auto size = a.numel();
    auto out = torch::zeros_like(a);

    const int block_size = 256;
    const int num_blocks = (size + block_size - 1) / block_size;

    elementwise_add_kernel<<<num_blocks, block_size>>>(a.data_ptr<float>(), b.data_ptr<float>(), out.data_ptr<float>(), size);

    return out;
}
"""

elementwise_add_cpp_source = (
    "torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b);"
)

# Compile the inline CUDA code for element-wise addition
elementwise_add = load_inline(
    name="elementwise_add",
    cpp_sources=elementwise_add_cpp_source,
    cuda_sources=elementwise_add_source,
    functions=["elementwise_add_cuda"],
    verbose=True,
    extra_cflags=[""],
    extra_ldflags=[""],
)


class ModelNew(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.elementwise_add = elementwise_add

    def forward(self, a, b):
        return self.elementwise_add.elementwise_add_cuda(a, b)

        ``` 

        
    You are given the following architecture: 

    ```
    # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn

class Model(nn.Module):
    """
    A model that computes Hinge Loss for binary classification tasks.

    Parameters:
        None
    """
    def __init__(self):
        super(Model, self).__init__()

    def forward(self, predictions, targets):
        """
        Computes mean hinge loss.

        Args:
            predictions (torch.Tensor): Predictions tensor of shape (batch_size, num_classes), float32.
            targets (torch.Tensor): Targets tensor of shape (batch_size,), float32.

        Returns:
            torch.Tensor: Scalar mean hinge loss.
        """
        return torch.mean(torch.clamp(1 - predictions * targets, min=0))
    ```
    
Optimize the architecture named Model with custom CUDA operators! Name your optimized output architecture ModelNew. Output the new code in codeblocks. Please generate real code, NOT pseudocode, make sure the code compiles and is fully functional. Just output the new model code, no other text, and NO testing code! 



This is turn 3 of 6 for this task. Your previous solution (turn 2) was:
```python
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

# Fused CUDA implementation of:
#     mean(clamp(1 - predictions * targets, min=0))
#
# Turn-2 improvements over turn 1:
#  * The generic N-D broadcast kernel (64-bit div/mod per element per dim) was
#    the bottleneck (~10.5 ms). It is replaced by specialized 2-D broadcast
#    kernels that need NO per-element div/mod: a 2-D grid walks rows/columns
#    directly with pointer arithmetic.
#  * The 2-D kernels are templated on whether each operand's column stride is
#    0 (broadcast along the row) or 1 (row-contiguous), and use float4 loads
#    when alignment permits. This covers all common patterns:
#      contiguous x contiguous, matrix x row-vector, matrix x col-vector,
#      col-vector x row-vector (outer), anything x scalar, 1-D broadcasts.
#  * A fully general strided 2-D kernel and the old N-D kernel remain as
#    fallbacks for arbitrary inputs.
_hinge_loss_cuda_src = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <ATen/ExpandUtils.h>
#include <c10/cuda/CUDAGuard.h>
#include <cuda_runtime.h>
#include <algorithm>
#include <cstdint>
#include <limits>

namespace {

constexpr int kBlockSize = 256;
constexpr int kMaxDims = 8;

struct BroadcastInfo {
    long long sizes[kMaxDims];
    long long stride_p[kMaxDims];
    long long stride_t[kMaxDims];
    int ndim;
};

// Block-wide sum reduction. Result is valid in thread 0 only.
__device__ __forceinline__ float block_reduce_sum(float sum) {
    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1) {
        sum += __shfl_down_sync(0xffffffffu, sum, offset);
    }
    __shared__ float sdata[32];
    const int lane = threadIdx.x & 31;
    const int wid  = threadIdx.x >> 5;
    if (lane == 0) {
        sdata[wid] = sum;
    }
    __syncthreads();
    if (wid == 0) {
        const int nwarps = (blockDim.x + 31) >> 5;
        sum = (lane < nwarps) ? sdata[lane] : 0.0f;
        #pragma unroll
        for (int offset = 16; offset > 0; offset >>= 1) {
            sum += __shfl_down_sync(0xffffffffu, sum, offset);
        }
    }
    return sum;
}

// Fast path: both operands contiguous with identical layout.
__global__ void __launch_bounds__(kBlockSize)
hinge_contiguous_kernel(const float* __restrict__ pred,
                        const float* __restrict__ targ,
                        float* __restrict__ out,
                        const long long n,
                        const float inv_n,
                        const int use_vec4) {
    const long long tid =
        static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
    const long long stride = static_cast<long long>(gridDim.x) * blockDim.x;

    float sum = 0.0f;
    if (use_vec4) {
        const long long n4 = n >> 2;
        const float4* pred4 = reinterpret_cast<const float4*>(pred);
        const float4* targ4 = reinterpret_cast<const float4*>(targ);
        for (long long k = tid; k < n4; k += stride) {
            const float4 p = pred4[k];
            const float4 t = targ4[k];
            sum += fmaxf(1.0f - p.x * t.x, 0.0f);
            sum += fmaxf(1.0f - p.y * t.y, 0.0f);
            sum += fmaxf(1.0f - p.z * t.z, 0.0f);
            sum += fmaxf(1.0f - p.w * t.w, 0.0f);
        }
        for (long long k = (n4 << 2) + tid; k < n; k += stride) {
            sum += fmaxf(1.0f - pred[k] * targ[k], 0.0f);
        }
    } else {
        for (long long k = tid; k < n; k += stride) {
            sum += fmaxf(1.0f - pred[k] * targ[k], 0.0f);
        }
    }

    sum = block_reduce_sum(sum);
    if (threadIdx.x == 0) {
        atomicAdd(out, sum * inv_n);
    }
}

// 2-D broadcast kernel, no div/mod anywhere.
// SP1/ST1: column stride of pred/targ, restricted to 0 or 1 (compile time).
// VEC4: use float4 loads for the row-contiguous operands (compile time).
// Element (r, c): pred[r * sp0 + c * SP1] * targ[r * st0 + c * ST1].
template<int SP1, int ST1, bool VEC4>
__global__ void __launch_bounds__(kBlockSize)
hinge_2d_kernel(const float* __restrict__ pred,
                const float* __restrict__ targ,
                float* __restrict__ out,
                const long long R, const long long C,
                const float inv_n,
                const long long sp0, const long long st0) {
    const long long cid =
        static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
    const long long cstride =
        static_cast<long long>(gridDim.x) * blockDim.x;

    float sum = 0.0f;
    for (long long r = blockIdx.y; r < R; r += gridDim.y) {
        const float* pr = pred + r * sp0;
        const float* tr = targ + r * st0;
        float ps = 0.0f, ts = 0.0f;
        if (SP1 == 0) { ps = pr[0]; }
        if (ST1 == 0) { ts = tr[0]; }
        if (VEC4) {
            const long long n4 = C >> 2;
            const float4* pr4 = reinterpret_cast<const float4*>(pr);
            const float4* tr4 = reinterpret_cast<const float4*>(tr);
            for (long long c4 = cid; c4 < n4; c4 += cstride) {
                float4 pv, tv;
                if (SP1 == 1) { pv = pr4[c4]; }
                else          { pv = make_float4(ps, ps, ps, ps); }
                if (ST1 == 1) { tv = tr4[c4]; }
                else          { tv = make_float4(ts, ts, ts, ts); }
                sum += fmaxf(1.0f - pv.x * tv.x, 0.0f);
                sum += fmaxf(1.0f - pv.y * tv.y, 0.0f);
                sum += fmaxf(1.0f - pv.z * tv.z, 0.0f);
                sum += fmaxf(1.0f - pv.w * tv.w, 0.0f);
            }
            for (long long c = (n4 << 2) + cid; c < C; c += cstride) {
                const float pv = (SP1 == 1) ? pr[c] : ps;
                const float tv = (ST1 == 1) ? tr[c] : ts;
                sum += fmaxf(1.0f - pv * tv, 0.0f);
            }
        } else {
            for (long long c = cid; c < C; c += cstride) {
                const float pv = (SP1 == 1) ? pr[c] : ps;
                const float tv = (ST1 == 1) ? tr[c] : ts;
                sum += fmaxf(1.0f - pv * tv, 0.0f);
            }
        }
    }

    sum = block_reduce_sum(sum);
    if (threadIdx.x == 0) {
        atomicAdd(out, sum * inv_n);
    }
}

// General 2-D kernel for arbitrary (e.g. sliced) strides, still no div/mod.
__global__ void __launch_bounds__(kBlockSize)
hinge_2d_general_kernel(const float* __restrict__ pred,
                        const float* __restrict__ targ,
                        float* __restrict__ out,
                        const long long R, const long long C,
                        const float inv_n,
                        const long long sp0, const long long sp1,
                        const long long st0, const long long st1) {
    const long long cid =
        static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
    const long long cstride =
        static_cast<long long>(gridDim.x) * blockDim.x;

    float sum = 0.0f;
    for (long long r = blockIdx.y; r < R; r += gridDim.y) {
        const float* pr = pred + r * sp0;
        const float* tr = targ + r * st0;
        for (long long c = cid; c < C; c += cstride) {
            sum += fmaxf(1.0f - pr[c * sp1] * tr[c * st1], 0.0f);
        }
    }

    sum = block_reduce_sum(sum);
    if (threadIdx.x == 0) {
        atomicAdd(out, sum * inv_n);
    }
}

// General N-D fallback: handles arbitrary broadcasting without materializing.
__global__ void __launch_bounds__(kBlockSize)
hinge_broadcast_kernel(const float* __restrict__ pred,
                       const float* __restrict__ targ,
                       float* __restrict__ out,
                       const long long n,
                       const float inv_n,
                       const BroadcastInfo bc) {
    const long long tid =
        static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
    const long long stride = static_cast<long long>(gridDim.x) * blockDim.x;

    float sum = 0.0f;
    for (long long k = tid; k < n; k += stride) {
        long long rem = k;
        long long off_p = 0;
        long long off_t = 0;
        for (int d = bc.ndim - 1; d >= 0; --d) {
            const long long s = bc.sizes[d];
            const long long c = rem % s;
            rem /= s;
            off_p += c * bc.stride_p[d];
            off_t += c * bc.stride_t[d];
        }
        sum += fmaxf(1.0f - pred[off_p] * targ[off_t], 0.0f);
    }

    sum = block_reduce_sum(sum);
    if (threadIdx.x == 0) {
        atomicAdd(out, sum * inv_n);
    }
}

int sm_count() {
    return at::cuda::getCurrentDeviceProperties()->multiProcessorCount;
}

void launch_contiguous(const float* p, const float* t, float* o,
                       long long n, float inv_n, cudaStream_t stream) {
    const bool aligned =
        ((reinterpret_cast<std::uintptr_t>(p) & 0xF) == 0) &&
        ((reinterpret_cast<std::uintptr_t>(t) & 0xF) == 0);
    const int use_vec4 = aligned ? 1 : 0;
    const long long work = use_vec4 ? ((n + 3) >> 2) : n;
    long long grid = (work + kBlockSize - 1) / kBlockSize;
    const long long cap = static_cast<long long>(sm_count()) * 16;
    if (grid > cap) grid = cap;
    if (grid < 1) grid = 1;
    hinge_contiguous_kernel<<<static_cast<int>(grid), kBlockSize, 0, stream>>>(
        p, t, o, n, inv_n, use_vec4);
}

dim3 pick_grid_2d(long long chunks_per_row, long long R) {
    const long long target = static_cast<long long>(sm_count()) * 16;
    long long gx = (chunks_per_row + kBlockSize - 1) / kBlockSize;
    if (gx > target) gx = target;
    if (gx < 1) gx = 1;
    long long gy = target / gx;
    if (gy > R) gy = R;
    if (gy < 1) gy = 1;
    if (gy > 65535) gy = 65535;
    return dim3(static_cast<unsigned>(gx), static_cast<unsigned>(gy));
}

template<int SP1, int ST1>
void launch_2d_simple(const float* p, const float* t, float* o,
                      long long R, long long C, float inv_n,
                      long long sp0, long long st0, bool vec4,
                      cudaStream_t stream) {
    const long long chunks = vec4 ? ((C + 3) >> 2) : C;
    const dim3 grid = pick_grid_2d(chunks, R);
    if (vec4) {
        hinge_2d_kernel<SP1, ST1, true><<<grid, kBlockSize, 0, stream>>>(
            p, t, o, R, C, inv_n, sp0, st0);
    } else {
        hinge_2d_kernel<SP1, ST1, false><<<grid, kBlockSize, 0, stream>>>(
            p, t, o, R, C, inv_n, sp0, st0);
    }
}

}  // namespace

torch::Tensor hinge_loss_cuda(torch::Tensor pred, torch::Tensor targ) {
    TORCH_CHECK(pred.is_cuda() && targ.is_cuda(),
                "inputs must be CUDA tensors");
    TORCH_CHECK(pred.scalar_type() == at::kFloat &&
                targ.scalar_type() == at::kFloat,
                "inputs must be float32");

    const c10::cuda::CUDAGuard device_guard(pred.device());
    auto stream = at::cuda::getCurrentCUDAStream();

    auto out = torch::zeros({}, pred.options());

    // Match PyTorch broadcasting semantics of `predictions * targets`.
    const auto shape = at::infer_size(pred.sizes(), targ.sizes());
    auto pred_b = pred.expand(shape);
    auto targ_b = targ.expand(shape);

    const long long n = static_cast<long long>(pred_b.numel());
    if (n == 0) {
        // torch.mean of an empty tensor returns NaN.
        out.fill_(std::numeric_limits<float>::quiet_NaN());
        return out;
    }
    const float inv_n = 1.0f / static_cast<float>(n);
    const int ndim = static_cast<int>(shape.size());

    const float* p_ptr = pred_b.data_ptr<float>();
    const float* t_ptr = targ_b.data_ptr<float>();
    float* o_ptr = out.data_ptr<float>();

    // Fast path: identical contiguous layouts.
    if (pred_b.is_contiguous() && targ_b.is_contiguous()) {
        launch_contiguous(p_ptr, t_ptr, o_ptr, n, inv_n, stream);
        return out;
    }

    // Specialized 2-D broadcast paths (covers the common cases and any
    // 1-D broadcast by treating it as 1 x C).
    if (ndim <= 2) {
        long long R, C, sp0, sp1, st0, st1;
        if (ndim == 2) {
            R = shape[0]; C = shape[1];
            sp0 = pred_b.stride(0); sp1 = pred_b.stride(1);
            st0 = targ_b.stride(0); st1 = targ_b.stride(1);
        } else {
            R = 1; C = shape[0];
            sp0 = 0; sp1 = pred_b.stride(0);
            st0 = 0; st1 = targ_b.stride(0);
        }
        const bool simple =
            (sp1 == 0 || sp1 == 1) && (st1 == 0 || st1 == 1);
        if (simple) {
            // float4 needs 16B-aligned row starts for row-contiguous operands.
            const bool p_ok = (sp1 == 0) ||
                (((reinterpret_cast<std::uintptr_t>(p_ptr) & 0xF) == 0) &&
                 ((sp0 & 3) == 0));
            const bool t_ok = (st1 == 0) ||
                (((reinterpret_cast<std::uintptr_t>(t_ptr) & 0xF) == 0) &&
                 ((st0 & 3) == 0));
            const bool vec4 = p_ok && t_ok;
            const int key = static_cast<int>(sp1) * 2 + static_cast<int>(st1);
            switch (key) {
                case 0:
                    launch_2d_simple<0, 0>(p_ptr, t_ptr, o_ptr, R, C, inv_n,
                                           sp0, st0, vec4, stream);
                    break;
                case 1:
                    launch_2d_simple<0, 1>(p_ptr, t_ptr, o_ptr, R, C, inv_n,
                                           sp0, st0, vec4, stream);
                    break;
                case 2:
                    launch_2d_simple<1, 0>(p_ptr, t_ptr, o_ptr, R, C, inv_n,
                                           sp0, st0, vec4, stream);
                    break;
                default:
                    launch_2d_simple<1, 1>(p_ptr, t_ptr, o_ptr, R, C, inv_n,
                                           sp0, st0, vec4, stream);
                    break;
            }
        } else {
            const dim3 grid = pick_grid_2d(C, R);
            hinge_2d_general_kernel<<<grid, kBlockSize, 0, stream>>>(
                p_ptr, t_ptr, o_ptr, R, C, inv_n, sp0, sp1, st0, st1);
        }
        return out;
    }

    // Very high-rank broadcasts: materialize contiguously and use fast path.
    if (ndim > kMaxDims) {
        auto pc = pred_b.contiguous();
        auto tc = targ_b.contiguous();
        launch_contiguous(pc.data_ptr<float>(), tc.data_ptr<float>(),
                          o_ptr, n, inv_n, stream);
        return out;
    }

    // Generic N-D fallback.
    BroadcastInfo bc;
    bc.ndim = ndim;
    for (int d = 0; d < ndim; ++d) {
        bc.sizes[d]    = shape[d];
        bc.stride_p[d] = pred_b.stride(d);
        bc.stride_t[d] = targ_b.stride(d);
    }
    long long grid = (n + kBlockSize - 1) / kBlockSize;
    const long long cap = static_cast<long long>(sm_count()) * 16;
    if (grid > cap) grid = cap;
    if (grid < 1) grid = 1;
    hinge_broadcast_kernel<<<static_cast<int>(grid), kBlockSize, 0, stream>>>(
        p_ptr, t_ptr, o_ptr, n, inv_n, bc);
    return out;
}
"""

_hinge_loss_cpp_src = (
    "torch::Tensor hinge_loss_cuda(torch::Tensor pred, torch::Tensor targ);"
)

_hinge_loss_ext = load_inline(
    name="hinge_loss_fused_ext_v2",
    cpp_sources=_hinge_loss_cpp_src,
    cuda_sources=_hinge_loss_cuda_src,
    functions=["hinge_loss_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Fused CUDA implementation of mean hinge loss for binary classification:
        mean(clamp(1 - predictions * targets, min=0))
    """

    def __init__(self):
        super(ModelNew, self).__init__()
        self._hinge_loss = _hinge_loss_ext.hinge_loss_cuda

    def forward(self, predictions, targets):
        if (predictions.is_cuda and targets.is_cuda
                and predictions.dtype == torch.float32
                and targets.dtype == torch.float32):
            return self._hinge_loss(predictions, targets)
        # Reference fallback for any unexpected input configuration.
        return torch.mean(torch.clamp(1 - predictions * targets, min=0))
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 3.23 ms; the PyTorch reference (with TF32 enabled) takes 21.7 ms; speedup 6.718x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void (anonymous namespace)::hinge_2d_kernel<1, 1, true>(float const*, float const*, float* | 3205.8 | 1 |
| void at::native::vectorized_elementwise_kernel<4, at::native::FillFunctor<float>, std::arr | 2.2 | 1 |

Write an improved complete ModelNew: fix any error, and if the solution is already correct, make it faster. Output the new code in one ```python codeblock. Just the model code, no other text, and NO testing code.


Precision rule: the timed forward must compute in FP32 (TF32 tensor-core math is allowed, as in the PyTorch reference). Do not cast inputs, weights or intermediate results to float16 or bfloat16 and do not call half-precision kernels in forward().
