{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.10.13","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"gpu","dataSources":[],"dockerImageVersionId":30699,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":true}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"import numpy as np\n\nnp.random.seed(0)  # 设置随机种子以获得可重复的结果\n\nX = np.random.randn(4, 8)  # 假设我们的向量维度是8，即从768变成8，还是\"LLM with me\"的4个Token\nW = np.random.randn(8, 1)  # 权重矩阵W，形状为[8, 1]\nb = np.random.randn(1)  # 偏置向量b，形状为[1]\n# 线性变换Y = XW + b\n# 这里使用np.dot进行矩阵乘法，然后加上偏置\nY = np.dot(X, W) + b\n# 输出结果Y，形状为[4, 1]， 为了得到形状[4,]的输出，我们可以将结果压缩到一维\nY = np.squeeze(Y)\n\nprint(\"Input X shape:\", X.shape)\nprint(\"Weight W shape:\", W.shape)\nprint(\"Bias b shape:\", b.shape)\nprint(\"Output Y shape:\", Y.shape)\nprint(\"Output Y:\", Y)","metadata":{"_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","execution":{"iopub.status.busy":"2024-05-03T10:10:29.150978Z","iopub.execute_input":"2024-05-03T10:10:29.151830Z","iopub.status.idle":"2024-05-03T10:10:29.159883Z","shell.execute_reply.started":"2024-05-03T10:10:29.151794Z","shell.execute_reply":"2024-05-03T10:10:29.158888Z"},"trusted":true},"execution_count":15,"outputs":[{"name":"stdout","text":"Input X shape: (4, 8)\nWeight W shape: (8, 1)\nBias b shape: (1,)\nOutput Y shape: (4,)\nOutput Y: [-2.59709604 -0.78316274 -4.6765379   3.25016417]\n","output_type":"stream"}]},{"cell_type":"code","source":"import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\n\n# 假设的词汇表和词嵌入\nvocab = {'LLM': 0, 'with': 1, 'me': 2, '<PAD>': 3}  # 一个简化的词汇表\nvocab_size = len(vocab)  # 词汇表大小\nembedding_dim = 768  # 嵌入维度，与GPT-2的小型版本相同\n\ntext = \"LLM with me\"\ninput_ids = torch.tensor([[vocab[word] for word in text.split()]], dtype=torch.long)\n\n# 模拟Transformer流程\nembedding_layer = nn.Embedding(vocab_size, embedding_dim)\nembedded = embedding_layer(input_ids)\ntransformer_output = torch.rand(embedded.size())  # 假设的Transformer输出\n# 创建一个线性层，将Transformer输出映射到词汇表空间\nlinear_layer = nn.Linear(embedding_dim, vocab_size)\nvocab_space_scores = linear_layer(transformer_output)\n# 输出概率分布\nprobabilities = F.softmax(vocab_space_scores, dim=-1)\nprint(probabilities)","metadata":{"execution":{"iopub.status.busy":"2024-05-03T09:49:56.395154Z","iopub.execute_input":"2024-05-03T09:49:56.395831Z","iopub.status.idle":"2024-05-03T09:49:56.407684Z","shell.execute_reply.started":"2024-05-03T09:49:56.395797Z","shell.execute_reply":"2024-05-03T09:49:56.406645Z"},"trusted":true},"execution_count":7,"outputs":[{"name":"stdout","text":"tensor([[[0.2306, 0.2478, 0.2688, 0.2528],\n         [0.1928, 0.3077, 0.2768, 0.2227],\n         [0.2562, 0.2568, 0.2837, 0.2033]]], grad_fn=<SoftmaxBackward0>)\n","output_type":"stream"}]},{"cell_type":"code","source":"vocab_space_scores","metadata":{"execution":{"iopub.status.busy":"2024-05-03T09:50:05.253992Z","iopub.execute_input":"2024-05-03T09:50:05.254936Z","iopub.status.idle":"2024-05-03T09:50:05.261793Z","shell.execute_reply.started":"2024-05-03T09:50:05.254901Z","shell.execute_reply":"2024-05-03T09:50:05.260661Z"},"trusted":true},"execution_count":8,"outputs":[{"execution_count":8,"output_type":"execute_result","data":{"text/plain":"tensor([[[-0.1818, -0.1099, -0.0287, -0.0901],\n         [-0.6043, -0.1369, -0.2430, -0.4603],\n         [-0.1816, -0.1795, -0.0799, -0.4130]]], grad_fn=<ViewBackward0>)"},"metadata":{}}]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]}]}