
Implement Layer Normalization over the last 3 dimensions (F, D1, D2) of a 4D tensor.

The formula for Layer Normalization is:
$$
\text{y} = \frac{x - \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta
$$
where the mean $\mathrm{E}[x]$ and variance $\mathrm{Var}[x]$ are computed over the normalization dimensions (F, D1, D2) for each element in the first dimension (B). $\gamma$ and $\beta$ are learnable affine parameters (elementwise scale and shift), and $\epsilon$ is a small value added to the variance for numerical stability.

## Input:
- Tensor $\text{X}$ of shape $(\text{B}, \text{F}, \text{D1}, \text{D2})$ (input data)
- Vector $\text{gamma}$ of shape $(\text{F}, \text{D1}, \text{D2})$ (scale parameters)
- Vector $\text{beta}$ of shape $(\text{F}, \text{D1}, \text{D2})$ (shift parameters)
- Epsilon $\epsilon$ (a small float, typically 1e-5)

## Output:
- Tensor $\text{Y}$ of shape $(\text{B}, \text{F}, \text{D1}, \text{D2})$ (normalized data)

## Notes:
- Compute the mean and variance across the last three dimensions $(\text{F}, \text{D1}, \text{D2})$ independently for each sample in the batch $\text{B}$.
- Apply the normalization using the computed mean/variance and the provided $\gamma$ and $\beta$.
- Use $\epsilon = 10^{-5}$
- This problem is adapted from [KernelBench](https://github.com/ScalingIntelligence/KernelBench/blob/main/KernelBench/level1/40_LayerNorm.py)

Rank	User	Runtime	GPU	Date
1	sampan26	124.82 μs	B200	2 months ago
2	Parth-Badgujar	131.87 μs	H100	6 months ago
3	abaoai	135.72 μs	B200	22 days ago
4	yassa9	166.23 μs	B200	9 months ago
5	MrNobody65	172.72 μs	B200	6 months ago
6	sagarreddypatil	180.92 μs	B200	10 months ago
7	mananchawla2005	182.70 μs	B200	10 months ago
8	mananchawla2005	188.80 μs	H100	12 months ago
9	sagarreddypatil	189.27 μs	H100	11 months ago
10	ell-hol	192.37 μs	H100	11 months ago
11	MrNobody65	192.63 μs	H100	7 months ago
12	yassa9	236.35 μs	H100	9 months ago
13	yassa9	249.82 μs	L40S	9 months ago
14	sagarreddypatil	250.40 μs	A100-80GB	11 months ago
15	sampan26	250.62 μs	H100	11 months ago
16	mananchawla2005	254.92 μs	H200	10 months ago
17	RohanGudur	262.53 μs	B200	9 months ago
18	sagarreddypatil	270.84 μs	L40S	11 months ago
19	Firojpaudel	274.54 μs	H100	12 months ago
20	RohanGudur	280.59 μs	H100	10 months ago
21	yassa9	300.03 μs	H200	9 months ago
22	sssuhasss	414.13 μs	H100	11 months ago
23	sagarreddypatil	414.16 μs	A10G	11 months ago
24	sampan26	421.50 μs	T4	2 months ago
25	ell-hol	451.66 μs	T4	11 months ago
26	sagarreddypatil	469.05 μs	L4	11 months ago
27	yassa9	495.34 μs	T4	9 months ago
28	michaelgranado	511.08 μs	T4	11 days ago
29	rotem154154	533.26 μs	B200	2 months ago
30	Parth-Badgujar	542.93 μs	T4	9 months ago
31	Firojpaudel	551.08 μs	T4	12 months ago
32	RohanGudur	621.73 μs	T4	10 months ago
33	648trindade	788.09 μs	L40S	8 months ago
34	moppywhip	799.70 μs	H200	4 months ago
35	648trindade	885.61 μs	H100	8 months ago
36	648trindade	923.89 μs	B200	8 months ago
37	Krishna-D-Mohan	1.05 ms	H100	about 1 year ago
38	ShlokVFX	1.23 ms	B200	21 days ago
39	moppywhip	1.32 ms	T4	4 months ago
40	harmya	1.46 ms	H100	about 1 year ago
41	kingsleykimm	1.58 ms	T4	7 months ago
42	MrNobody65	1.80 ms	T4	6 months ago
43	knightron0	2.49 ms	T4	about 1 year ago
44	mananchawla2005	3.65 ms	T4	12 months ago
45	JINO-ROHIT	3.69 ms	B200	9 months ago
46	doudi25	3.99 ms	H100	about 1 year ago
47	JINO-ROHIT	4.28 ms	H100	9 months ago
48	JINO-ROHIT	4.44 ms	H200	9 months ago
49	vectorquantized	4.91 ms	T4	12 months ago
50	tamoghnokandar	10.02 ms	L40S	6 months ago
51	tamoghnokandar	10.54 ms	H100	6 months ago
52	tamoghnokandar	18.66 ms	T4	6 months ago
53	Infatoshi	27.75 ms	H100	about 1 year ago
54	Infatoshi	32.18 ms	T4	about 1 year ago