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# [Nash Learning from Human Feedback](http://arxiv.org/abs/2312.00886)


import os
import math
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader, Dataset

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# Reference: [Half-Quadratic Quantization of Large Machine Learning Models](https://mobiusml.github.io/hqq_blog/)


import numpy as np

# Define the shrinkage function for soft-thresholding
def shrink(x, beta, p):
    return np.sign(x) * np.maximum(np.abs(x) - (np.abs(x)**(p-1))/beta, 0)

# Define the quantization and dequantization operators

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# [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://arxiv.org/abs/2312.00752)

import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader, Dataset
from torch.nn import functional as F
from einops import rearrange, repeat
from tqdm import tqdm

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import torch
from torch import nn
import torch.nn.functional as F
import torchvision
import torchvision.transforms as transforms
from tqdm import tqdm

# Custom fast linear layer
class FastLinear(nn.Module):
    def __init__(self, in_features, out_features):

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sequence_id,sequence,experiment_type,dataset_name,reads,signal_to_noise,SN_filter,reactivity_0001,reactivity_0002,reactivity_0003,reactivity_0004,reactivity_0005,reactivity_0006,reactivity_0007,reactivity_0008,reactivity_0009,reactivity_0010,reactivity_0011,reactivity_0012,reactivity_0013,reactivity_0014,reactivity_0015,reactivity_0016,reactivity_0017,reactivity_0018,reactivity_0019,reactivity_0020,reactivity_0021,reactivity_0022,reactivity_0023,reactivity_0024,reactivity_0025,reactivity_0026,reactivity_0027,reactivity_0028,reactivity_0029,reactivity_0030,reactivity_0031,reactivity_0032,reactivity_0033,reactivity_0034,reactivity_0035,reactivity_0036,reactivity_0037,reactivity_0038,reactivity_0039,reactivity_0040,reactivity_0041,reactivity_0042,reactivity_0043,reactivity_0044,reactivity_0045,reactivity_0046,reactivity_0047,reactivity_0048,reactivity_0049,reactivity_0050,reactivity_0051,reactivity_0052,reactivity_0053,reactivity_0054,reactivity_0055,reactivity_0056,reactivity_0057,reactivity_0058,reactivity_005

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\documentclass{article}
\usepackage{amsmath}

\NewDocumentCommand{\Qubit}{ O{1} }{%
	\ensuremath{%
		\mathbf{%
			#1%
		}%
	}%
}