
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 (ms)	GPU	Date
1	sampan26	0.12	B200	18 days ago
2	Parth-Badgujar	0.13	H100	4 months ago
3	yassa9	0.17	B200	7 months ago
4	MrNobody65	0.17	B200	5 months ago
5	sagarreddypatil	0.18	B200	9 months ago
6	mananchawla2005	0.18	B200	9 months ago
7	mananchawla2005	0.19	H100	10 months ago
8	sagarreddypatil	0.19	H100	10 months ago
9	ell-hol	0.19	H100	9 months ago
10	MrNobody65	0.19	H100	5 months ago
11	yassa9	0.24	H100	7 months ago
12	yassa9	0.25	L40S	7 months ago
13	sagarreddypatil	0.25	A100-80GB	10 months ago
14	sampan26	0.25	H100	9 months ago
15	mananchawla2005	0.25	H200	9 months ago
16	RohanGudur	0.26	B200	8 months ago
17	sagarreddypatil	0.27	L40S	10 months ago
18	Firojpaudel	0.27	H100	10 months ago
19	RohanGudur	0.28	H100	8 months ago
20	yassa9	0.30	H200	7 months ago
21	sssuhasss	0.41	H100	10 months ago
22	sagarreddypatil	0.41	A10G	10 months ago
23	sampan26	0.42	T4	18 days ago
24	ell-hol	0.45	T4	9 months ago
25	sagarreddypatil	0.47	L4	10 months ago
26	yassa9	0.50	T4	7 months ago
27	rotem154154	0.53	B200	16 days ago
28	Parth-Badgujar	0.54	T4	7 months ago
29	Firojpaudel	0.55	T4	10 months ago
30	RohanGudur	0.62	T4	8 months ago
31	648trindade	0.79	L40S	7 months ago
32	moppywhip	0.80	H200	2 months ago
33	648trindade	0.89	H100	7 months ago
34	648trindade	0.92	B200	7 months ago
35	Krishna-D-Mohan	1.05	H100	11 months ago
36	moppywhip	1.32	T4	2 months ago
37	harmya	1.46	H100	11 months ago
38	kingsleykimm	1.58	T4	5 months ago
39	MrNobody65	1.80	T4	5 months ago
40	knightron0	2.49	T4	11 months ago
41	mananchawla2005	3.65	T4	10 months ago
42	JINO-ROHIT	3.69	B200	8 months ago
43	doudi25	3.99	H100	11 months ago
44	JINO-ROHIT	4.28	H100	8 months ago
45	JINO-ROHIT	4.44	H200	8 months ago
46	vectorquantized	4.91	T4	10 months ago
47	tamoghnokandar	10.02	L40S	4 months ago
48	tamoghnokandar	10.54	H100	4 months ago
49	tamoghnokandar	18.66	T4	4 months ago
50	Infatoshi	27.75	H100	11 months ago
51	Infatoshi	32.18	T4	11 months ago