mamba/index.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "id": "adc19a97-5001-4a15-907b-93d844694a65",
   "metadata": {},
   "source": [
    "---\n",
    "categories:\n",
    "  - nlp\n",
    "  - llm\n",
    "date: '2024-02-23T08:34:00+10:00'\n",
    "image: ./mamba_architecture.png\n",
    "title: Mamba Lanugage Model Inference\n",
    "aliases:\n",
    "  - mamba.html\n",
    "format:\n",
    "  html:\n",
    "    toc: true\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "204d277d-d4bb-4e09-9ed0-2e24399bdc7a",
   "metadata": {},
   "source": [
    "[Mamba](https://arxiv.org/abs/2312.00752) is an alternative kind of neural network model to Transformers inspired by State Space Models.\n",
    "It can train as efficiently as a transformer (thanks to some hardware tricks), scales as well with compute as transformers in language modelling, but can handle very long context because computation is *linear* in the length of the input, not quadratic like in transformers.\n",
    "These models are related to Recurrent Neural Networks, and at inference time just need to store a relatively small state at each step which makes them much faster to generate text than transformers which need to reprocess the whole input.\n",
    "\n",
    "The ideas behind Mamba are quite novel and I found working through the code illuminating.\n",
    "The [source code](https://github.com/state-spaces/mamba) covers both efficient training and inference, but is a little opaque to be high performance.\n",
    "The [Mamba minimal](https://github.com/johnma2006/mamba-minimal/tree/master) repository makes it easier to understand efficient parallel training, but doesn't have the linear time inference code.\n",
    "\n",
    "This notebook breaks the Mamba model down and builds it up again using elementary PyTorch.\n",
    "The first half of this notebook starts with the official implementation and works through each of the pieces in detail, slowly expanding out the code into PyTorch.\n",
    "The second half then puts the pieces back together to reproduce predictions for inference.\n",
    "The final model is much less efficient and less numerically stable than the original model, but is useful for understanding conceptually how Mamba works.\n",
    "\n",
    "\n",
    "::: {.callout-note}\n",
    "This is a Jupyter notebook you can [download the notebook](https://github.com/EdwardJRoss/skeptric/blob/master/mamba/index.ipynb).\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1287a0f8-4de4-4a3a-92b7-77dc92406416",
   "metadata": {},
   "source": [
    "# Running Mamba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8471ad61-db49-4847-8ecf-ac5b103378aa",
   "metadata": {},
   "source": [
    "We start by importing the MambaLMHeadModel from the [source repository](https://github.com/state-spaces/mamba)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "185001db-dabd-4fb6-b223-5e50890621b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from transformers import AutoTokenizer\n",
    "from mamba_ssm.models.mixer_seq_simple import MambaLMHeadModel\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import torch.nn.functional as F\n",
    "\n",
    "from einops import rearrange, repeat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1024fe9-7f89-4907-92ef-60b721a8fe07",
   "metadata": {},
   "source": [
    "For testing we will load the smallest model released (130 million parameter) in CUDA for an NVIDIA GPU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6f4c91e9-f6dc-42ed-a473-87e851c6fa66",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_name = \"state-spaces/mamba-130m\"\n",
    "device = 'cuda'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa0c641-d5a9-4ac3-bbca-8df6ce681296",
   "metadata": {},
   "source": [
    "We can load the model, which uses the GPT tokenizer, from Huggingface:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dbbf8ca3-2d60-4a81-b67e-62003e3b1453",
   "metadata": {},
   "outputs": [],
   "source": [
    "tokenizer = AutoTokenizer.from_pretrained(\"EleutherAI/gpt-neox-20b\")\n",
    "model = MambaLMHeadModel.from_pretrained(model_name,\n",
    "                                         device=device,\n",
    "                                         dtype=torch.float16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d146b456-adcc-461d-916c-574d278b376c",
   "metadata": {},
   "source": [
    "Given a prompt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "583adc0e-df27-409d-b988-560768e42233",
   "metadata": {},
   "outputs": [],
   "source": [
    "prompt = \"So I was made to\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e738aec-0de9-43a0-ba0f-93aacf20e166",
   "metadata": {},
   "source": [
    "We can convert it into tokens:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "183bf174-d216-423d-ab8e-9bbc57ece6d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2598,  309,  369, 1160,  281]], device='cuda:0')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_tokens = tokenizer(prompt, return_tensors=\"pt\").to(device)\n",
    "input_ids = input_tokens['input_ids']\n",
    "input_ids"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e011d1f2-77c9-4220-b408-c531bb47e34c",
   "metadata": {},
   "source": [
    "Which we then use to generate text:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d31b8cf1-8bb9-4b10-93e7-c0ff66b93b23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "So I was made to feel like I was a part of the team. I\n"
     ]
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    preds = model.generate(input_ids, len(input_tokens[0]) + 11)\n",
    "    \n",
    "for result in tokenizer.batch_decode(preds):\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c66e7ca7-a7ee-46c1-ab08-45dc04b272e4",
   "metadata": {},
   "source": [
    "This works by passing the input into the model to get the logits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ff679b57-e629-40d0-ad64-02a8c6613076",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 5, 50280])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    logits = model(input_ids).logits.cpu().float()\n",
    "logits.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a8dc865-d387-4451-9845-be228243c226",
   "metadata": {},
   "source": [
    "For each token the softmax of the logit gives the probability of the next token.\n",
    "We can find the probabilities of the next token to occur in the sequence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5ea74db1-6f71-4ff5-9082-d91fbcda40a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prob.\t  Token      \t Id\n",
      "17.99%\t  feel      \t 1928\n",
      "5.24%\t  think     \t 1158\n",
      "5.16%\t  believe   \t 2868\n",
      "3.33%\t  do        \t 513\n",
      "2.80%\t  go        \t 564\n",
      "2.51%\t  sit       \t 1790\n",
      "2.36%\t  understand \t 2096\n",
      "2.08%\t  see       \t 923\n",
      "2.05%\t  work      \t 789\n",
      "1.90%\t  take      \t 1379\n"
     ]
    }
   ],
   "source": [
    "probs = logits[:,-1].softmax(dim=-1)\n",
    "\n",
    "print(f'Prob.\\t ',\n",
    "      \"{:10s}\".format(\"Token\"),\n",
    "      '\\t', \"Id\")\n",
    "for idx in torch.argsort(probs[0], descending=True)[:10]:\n",
    "    print(f'{probs[0, idx].item():0.2%}\\t',\n",
    "          \"{:10s}\".format(tokenizer.decode([idx])),\n",
    "          '\\t', idx.item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7eae82b8-bdb8-4617-9612-bb5fde8b889f",
   "metadata": {},
   "source": [
    "To expand the sequence this is done in a loop; for Mamba by keeping track of the state we can do this efficiently with minimal recomputation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31ee7501-f124-4666-80a6-fbbf152e19bc",
   "metadata": {},
   "source": [
    "# Deconstructing the model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46469fa4-f5f2-446d-b49b-e40969ba225f",
   "metadata": {},
   "source": [
    "The Mamba model consists of:\n",
    "\n",
    "* A backbone (MixerModel) with\n",
    "  + An embedding model mapping the vocabulary to dense embeddings (768 here)\n",
    "  + Multiple mixer (Mamba) layers, that we will dig more into later\n",
    "  + A final norm_f RMSNorm\n",
    "* A lanugage modelling head (lm_head) mapping the embeddings back to the vocabulary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0491037c-bcd6-40dc-9a4e-cbfa2d639e56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MambaLMHeadModel(\n",
       "  (backbone): MixerModel(\n",
       "    (embedding): Embedding(50280, 768)\n",
       "    (layers): ModuleList(\n",
       "      (0-23): 24 x Block(\n",
       "        (mixer): Mamba(\n",
       "          (in_proj): Linear(in_features=768, out_features=3072, bias=False)\n",
       "          (conv1d): Conv1d(1536, 1536, kernel_size=(4,), stride=(1,), padding=(3,), groups=1536)\n",
       "          (act): SiLU()\n",
       "          (x_proj): Linear(in_features=1536, out_features=80, bias=False)\n",
       "          (dt_proj): Linear(in_features=48, out_features=1536, bias=True)\n",
       "          (out_proj): Linear(in_features=1536, out_features=768, bias=False)\n",
       "        )\n",
       "        (norm): RMSNorm()\n",
       "      )\n",
       "    )\n",
       "    (norm_f): RMSNorm()\n",
       "  )\n",
       "  (lm_head): Linear(in_features=768, out_features=50280, bias=False)\n",
       ")"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "181bf482-c4bd-40d1-a728-b75ff9906ca2",
   "metadata": {},
   "source": [
    "We can re-implement the model by:\n",
    "\n",
    "* Passing the input into the embedding\n",
    "* Iteratively passing the hidden state and residuals through the mixer layers\n",
    "* Applying layer norm to the hidden_state + residual\n",
    "* Using the lm_head to get back to the original state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1c84e444-b35d-469e-9ef8-1958660675ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "backbone = model.backbone\n",
    "\n",
    "embedding = backbone.embedding\n",
    "mixers = backbone.layers\n",
    "norm_f = backbone.norm_f\n",
    "lm_head = model.lm_head\n",
    "\n",
    "from mamba_ssm.ops.triton.layernorm import rms_norm_fn\n",
    "\n",
    "with torch.inference_mode():\n",
    "    hs = embedding(input_ids)\n",
    "    rs = None\n",
    "    for mixer in mixers:\n",
    "        hs, rs = mixer(hs, rs)\n",
    "    prelogits = rms_norm_fn(hs, norm_f.weight, norm_f.bias,\n",
    "                            eps=norm_f.eps, residual=rs,\n",
    "                            prenorm=False, residual_in_fp32=True)\n",
    "    logits2 = lm_head(prelogits)\n",
    "    \n",
    "    logits2 = logits2.cpu().float()\n",
    "    \n",
    "\n",
    "assert (logits2 == logits).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeebea9b-2a8d-4ee1-b4f4-89d24a017aa6",
   "metadata": {},
   "source": [
    "## RMS Norm"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "74f19dfe-7073-4e78-8e11-f927ed6905f7",
   "metadata": {},
   "source": [
    "The `rms_norm_fn` is a CUDA fused version of add and norm for efficiency.\n",
    "We can calculate it directly using PyTorch, which gives similar results, although there is a substantial difference of up to 10% for extreme values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f9d393ab-3d09-4a67-bac0-5e52dc58126a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    prelogits2 = norm_f(hs+rs)\n",
    "\n",
    "actual = prelogits[0,-1].cpu()\n",
    "target = prelogits2[0,-1].cpu()\n",
    "diff = actual - target\n",
    "\n",
    "plt.title(\"Difference in fused RMS Norm with PyTorch\");\n",
    "plt.xlabel(\"Input value\")\n",
    "plt.ylabel(\"Difference in output\")\n",
    "plt.scatter(actual, diff);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1136a8a-0424-4ec3-ba0a-dcca92bc8aed",
   "metadata": {},
   "source": [
    "This kind of plot, seeing how much two varaiables differ as a function of the first variable, is useful for getting a picture of the absolute and relative errors.\n",
    "\n",
    "We'll use this a lot so let's wrap it in a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b85f03a8-21ac-424f-830e-c8a90956525d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00704193115234375"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_diff(actual, pred,\n",
    "              xlabel=\"Input value\",\n",
    "              ylabel=\"Difference in output\",\n",
    "              axs=None):    \n",
    "    if axs is None:\n",
    "        axs = plt.subplot()\n",
    "\n",
    "    actual = actual.cpu().detach().float().flatten()\n",
    "    pred = pred.cpu().detach().float().flatten()\n",
    "\n",
    "    if actual.shape != pred.shape:\n",
    "        raise ValueError(\"Incompatible shapes\")\n",
    "    \n",
    "    diff = actual - pred\n",
    "\n",
    "    axs.set_xlabel(\"Input value\")\n",
    "    axs.set_ylabel(\"Difference in output\")\n",
    "    axs.scatter(actual, diff);\n",
    "    return axs\n",
    "\n",
    "def max_diff(actual, pred):\n",
    "    actual = actual.cpu().detach().float().flatten()\n",
    "    pred = pred.cpu().detach().float().flatten()\n",
    "    diff = actual - pred\n",
    "    return diff.abs().max().item()\n",
    "\n",
    "plot_diff(actual, target)\n",
    "max_diff(actual, target)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9575826-b896-42c0-9119-61d927070d80",
   "metadata": {},
   "source": [
    "Even though the logits were different there is only a very small difference in probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "03809199-e7e2-4a35-82d7-7f8ead193a48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1391937732696533e-05"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ePTVo0CDl5+dXWX/z5s0aM2aMPv30U2VkZCgqKkq33367jh8/7lAvKSlJOTk59teaNWvqojt1KqlbhJbc00fWYMdbbdbgAC25pw/zLAEAUA2LYRhe87x4fHy8rr/+er300kuSJJvNpqioKD344IN67LHHaty/vLxcrVu31ksvvaSxY8dKunhlqbCwUO+8806t21VcXKzg4GAVFRUpKCio1sepC8zgDQDARc7+fnvNDN7nzp3Ttm3bNGvWLHuZj4+PEhMTlZGR4dQxzp49q/Pnzys01HFszubNmxUeHq7WrVtrwIABevzxx9WmTRu3tr+h8PWxKKFT7ftG2AIANDVeE5ZOnjyp8vJytWvXzqG8Xbt22rdvn1PHmDlzpiIjI5WYmGgvS0pK0l133aWYmBgdOnRIf/7znzV48GBlZGTI19e3yuOUlZWprKzM/r64uLgWPWo4nA1ALJcCAGiKvCYsXa6nnnpKa9eu1ebNmxUQ8N9xO6NHj7b/uXv37urRo4c6deqkzZs3a+DAgVUea8GCBUpNTfV4m+uCswGoYrmUX96zrVguhXFPAIDGymsGeLdt21a+vr7Ky8tzKM/Ly5PVajXd95lnntFTTz2ljz/+WD169DCt27FjR7Vt21YHDx6sts6sWbNUVFRkfx09etT5jjQgzq4Xx3IpAICmzGvCkp+fn/r27av09HR7mc1mU3p6uhISEqrdb9GiRZo/f77S0tLUr1+/Gj/n2LFjOnXqlCIiqr9K4u/vr6CgIIeXt3ElALFcCgCgKfOasCRJ06ZN06uvvqrXX39de/fu1ZQpU3TmzBlNmDBBkjR27FiHAeALFy7U7NmztWzZMkVHRys3N1e5ubkqKSmRJJWUlOhPf/qTvvnmGx0+fFjp6ekaPny4OnfurEGDBtVLH+uKKwGI5VIAAE2ZV41ZGjVqlH766SfNmTNHubm56tWrl9LS0uyDvrOzs+Xj89/8t2TJEp07d07/8z//43CclJQUzZ07V76+vtq1a5def/11FRYWKjIyUrfffrvmz58vf3//Ou1bXXM22Gzck6vbYs1vc1ZguRQAQGPkVfMsNVTeNM9ShYxDpzTm1W+cqvv/ftdH8z/Yo9yi0ipv21l0cXLLL2cOYBoBAIDXcPb326tuw8F9KtaLq4lF0vwP9mj20Gvt73+5XWK5FABA40VYaiTKbYYyDp3SuzuOK+PQqRqfTLt0vTgzFWOXWrfyZ7kUAECT5FVjllDZuQs2/Xn9Ln24O1dnz5Xby52ZLDKpW4Qm3hit1746XOPn5J8u1fBeV+q2WCszeAMAmhTCkhdb8OEe/f3zrCrHETk7WWRirNWpsFQxePtyl0sBAMDbuHwbrmPHjjp16lSl8sLCQnXs2NEtjULNFny4R69UE5Qk5yeLrBi7VN21IYsuXqWKiwmtpgYAAI2by2Hp8OHDKi8vr1ReVlam48ePu6VRMHfugk2vfpFVYz1nJou8dOwSg7cBAKjM6dtw7733nv3P//rXvxQcHGx/X15ervT0dEVHR7u1cajaPzIOy5WVRWqaUympW4SW3NOn0hpxVhbJBQDA+bA0YsQISZLFYtG4ceMctjVv3lzR0dF69tln3do4VO1IwVmX6jszWWRStwgGbwMAUAWnw5LNZpMkxcTEaOvWrWrbtq3HGgVzHUJbOl3XlfFGDN4GAKAyl8csZWVlEZTq2b0J0XLmgo9FjDcCAOByuTx1wLx580y3z5kzp9aNgXP8mvlo0s0xeuXz6gd5t/L31bN392S8EQAAl8nlsPT22287vD9//ryysrLUrFkzderUibBUR2YNufgE26tfZDkM9rZI+k0PqxaP7sMVJQAA3MAtC+kWFxdr/PjxuvPOO3Xvvfe6o11epT4X0j13waZ/ZBzWkYKz6hDaUr+L76AdRwsZpA0AQA2c/f12S1iSpO+//17Dhg3T4cOH3XE4r1KfYelSabtzKj3+78yyJwAANEXO/n67bSHdoqIiFRUVuetwcFHa7hxNWbXdIShJ/132JG13Tj21DAAA7+bymKUXXnjB4b1hGMrJydE//vEPDR482G0Ng/PKbYZSN+ypcukTQxfHMaVu2KPbYq3ckgMAwEUuh6Xnn3/e4b2Pj4/CwsI0btw4zZo1y20Ng/MyswoqXVG61KXLnjCPEgAArnE5LGVl1bwmGTyn3GZUmmW7puVMKnx18CQDvwEAcJHLYelSR48elSRFRUW5pTEw9+GuE/rru7tVcOa8vSwiOECjr3fu//9Lnx502I+B3wAA1MzlAd4XLlzQ7NmzFRwcrOjoaEVHRys4OFh//etfdf78+ZoPgFpZ8OEe/eGN7xyCknTx9trznxxQSMvmcuU6EQO/AQBwjstXlh588EGtX79eixYtUkJCgiQpIyNDc+fO1alTp7RkyRK3N7Kp+3BXjuls3ZeySFUO9P4lBn4DAOAcl+dZCg4O1tq1ays9+fbhhx9qzJgxTXL6AE/Os1RuM3T9E5+o4My5Guv+MbGr1m7NNh3sXZU1k25g4DcAoMnx2DxL/v7+io6OrlQeExMjPz8/Vw+HGmRmFTgVlCSp6Odzmj30Wpc/w9kB4gAANEUuh6WpU6dq/vz5Kisrs5eVlZXpiSee0NSpU93aOLgWZN7ZcULz3t/j8meEBwa4vA8AAE2Fy2OWvvvuO6Wnp6t9+/bq2bOnJGnnzp06d+6cBg4cqLvuusted/369e5raRPlSpBx9gpUBYska/DFaQQAAEDVXA5LISEhGjlypEMZUwd4TlxMqNq08NWpn8vdetyK4dwpw2IZ3A0AgAmXw9Ly5cs90Q5Uo/e8j1Vc6t6gJF28osQ8SwAA1MzlMUsDBgxQYWFhpfLi4mINGDDAHW3C/+kx918qLr3g0j7BLZqZzrcU0rK5Vk+M15czBxCUAABwgsthafPmzTp3rvLYmNLSUn3xxRduaRSkn4rLXA5KkvS/N8ZIUqXAZPm/11N3ddeNXdpy6w0AACc5fRtu165d9j/v2bNHubm59vfl5eVKS0vTlVde6d7WNWF3/r8vXd6ndcvmmjqgi662Bip1wx6H+ZZat2qux4d342oSAAAucjos9erVSxaLRRaLpcrbbS1atNCLL77o1sY1ZadcfLJNkmz/N79oUrcI2Wz6v3XkLh6n4Mx5zf9gr3x8LAQmAABc4HRYysrKkmEY6tixozIzMxUWFmbf5ufnp/DwcPn6+nqkkU3Rz+dtLu9T9PMFzX1vt7ILftZnP/5UaXvFenBL7ulDYAIAwElOh6UOHTpIkmw213/E4ZoJy7fUet9/fJNd7TbWgwMAwHUuTx2wcuVK0+1jx46tdWMg/XyuXJ/uP+mx4xuScopKlZlVwHpwAAA4weWw9PDDDzu8P3/+vM6ePSs/Pz+1bNnS42Hp5Zdf1tNPP63c3Fz17NlTL774ouLi4qqtv27dOs2ePVuHDx9Wly5dtHDhQg0ZMsS+3TAMpaSk6NVXX1VhYaFuvPFGLVmyRF26dPFoP6oza/2OOvmc6pZRKbcZyswqUP7pUoUHXpzdmytQAICmzOWpA/7zn/84vEpKSrR//37ddNNNWrNmjSfaaPfmm29q2rRpSklJ0fbt29WzZ08NGjRI+fn5Vdb/+uuvNWbMGE2cOFHfffedRowYoREjRmj37t32OosWLdILL7ygpUuXasuWLWrVqpUGDRqk0tL6WVz2nR25NVdyg6qWUUnbnaObFm7SmFe/0cNrd2jMq9/opoWblLY757I/r9xmKOPQKb2747gyDp1Suc247GMCAFAXLIZhuOVX69tvv9U999yjffv2ueNwVYqPj9f111+vl156SdLF8VNRUVF68MEH9dhjj1WqP2rUKJ05c0bvv/++veyGG25Qr169tHTpUhmGocjISE2fPl0zZsyQJBUVFaldu3ZasWKFRo8e7VS7iouLFRwcrKKiIgUFBdW6f9GPfVDrfZ1VsR7clzMHOFwxStudoymrtuuXfxkqalzOoPC03TmVpjKIYAZxAEA9c/b32+UrS9Vp1qyZTpw44a7DVXLu3Dlt27ZNiYmJ9jIfHx8lJiYqIyOjyn0yMjIc6kvSoEGD7PWzsrKUm5vrUCc4OFjx8fHVHlOSysrKVFxc7PDyBtWtB1duM5S6YU+loCTJXpa6YU+trgZVhLBLg5L03yfz3HHVCgAAT3J5zNJ7773n8N4wDOXk5Oill17SjTfe6LaG/dLJkydVXl6udu3aOZS3a9eu2qtZubm5VdavmFCz4r9mdaqyYMECpaamutyH+lbdenCZWQWVwsylajsovKYQxpN5AABv4HJYGjFihMN7i8WisLAwDRgwQM8++6y72tWgzZo1S9OmTbO/Ly4uVlRUVD22yFzvqBDd2LmNEjq21Q1VhJ3qBnvXtl4FT4UwAADqksthqb7mWWrbtq18fX2Vl5fnUJ6Xlyer1VrlPlar1bR+xX/z8vIUERHhUKdXr17VtsXf31/+/v616Uada+nnq++OFuq7o4V66dNDVY4Vqmqwd1WcrVfBUyEMAIC6dFljlgzDkJvGh9fIz89Pffv2VXp6ur3MZrMpPT1dCQkJVe6TkJDgUF+SNm7caK8fExMjq9XqUKe4uFhbtmyp9pjews/34m2ts+fKHcqrGisUFxOqiOCASovvVrDo4oDsuJhQl9rgqRAGAEBdqlVYWrlypbp3764WLVqoRYsW6tGjh/7xj3+4u22VTJs2Ta+++qpef/117d27V1OmTNGZM2c0YcIESRcnxJw1a5a9/sMPP6y0tDQ9++yz2rdvn+bOnatvv/1WU6dOlXTxFuIjjzyixx9/XO+9956+//57jR07VpGRkZVuN9aFw08NdduxzpdXHWKrGrDt62NRyrBYSaoUmKobFO4MT4UwAADqksth6bnnntOUKVM0ZMgQvfXWW3rrrbeUlJSk+++/X88//7wn2mg3atQoPfPMM5ozZ4569eqlHTt2KC0tzT5AOzs7Wzk5/71i0r9/f73xxhv6+9//rp49e+qf//yn3nnnHXXr1s1e59FHH9WDDz6oyZMn6/rrr1dJSYnS0tIUEFA/VzvWTLrBLccxu9536VihCkndIrTknj6yBjv22xocUOtpAzwVwgAAqEsuz7MUExOj1NTUSjN1v/7665o7d66ysrLc2kBv4K55lqSLT5D1X5CuvNNlbmpd9f42upeG97qy0ue7ewZv5lkCADREzv5+uzzAOycnR/37969U3r9/f4erOqgdXx+LUodfp/tXbff4Z1U1VsjXx+L2J9OSukXotlgry6gAALySy7fhOnfurLfeeqtS+Ztvvllv66k1NkndIhQU4Oux49fHWKGKEDa815VK6NSGoAQA8BouX1lKTU3VqFGj9Pnnn9snofzqq6+Unp5eZYhC7Vwf3Vrp+05e1jEq4ohRRVlNY4VYUBcAgItqtTbctm3b9Pzzz2vv3r2SpGuvvVbTp09X79693d5Ab+DOMUsVSkovqNvcf13WMRJi2uhwwRmXxwoxxggA0BQ4+/vttoV0mzJPhCVJuuOlL7TrWO3XnWvp56sdc27XtiP/cfoKkScX1AUAoCGp84V04X7vTb1ZPdrXPnydPVeubUf+4/RYIU8uqAsAgLciLDVw7029WbvnDlKH0Ba12t+VpURcWcsNAICmgrDkBfya+ejof36u1b6HT551uu7GPblO1WMtNwBAU0JY8gL/yDis2t75Wrs126nbZuU2Q+/sOOHUMVnLDQDQlBCWvMCRAuevDv2Ss7fNMrMKVHDmXI31Qls1Zy03AECT4vI8S2fOnNFTTz2l9PR05efny2azOWz/97//7bbG4aIOoS0va39nbps5e2vtzl5XMt8SAKBJcTks3Xffffrss8907733KiIiQhYLP5yedm9CtJ74cG+tb8WdPF2md3ccN506wNlba4mx1to1AgAAL+VyWProo4/0wQcf2Gfvhuf5NfPRpJtj9Mrnri9S7GOR5n+w1/6+uskl42JCFREcoNyi0iqnDrBIstbxEikAADQELo9Zat26tUJD+cGsa7OGxOr3v4qRq3fAfnk1KreoVFNWbVfabsdFj319LEoZFivpvxNQVnB2iRQAABojl2fwXrVqld599129/vrratny8sbSNBaemsG7Kucu2PSPjMM6UnBWZ8su6J/bj7t8jIqrRF/OHFAp/LDUCQCgqfDYcie9e/fWoUOHZBiGoqOj1bx5c4ft27dvr12LvVhdhqVfqircBAb46nRpeY37rpl0gxI6talUziK6AICmwNnfb5fHLI0YMeJy2gU3S+oWodtirQ7hJre4VH98c0eN+1b3BJyvj6XKEAUAQFPkclhKSUnxRDtwGX4ZbjIOnXJqPyaXBACgZkxK2QhVPNlW3Y0ziy6OQ+LJNgAAauZUWAoNDdXJkycl/fdpuOpeqH882QYAgPs4dRvu+eefV2BgoCRp8eLFnmwPLlPF4OyyCzY9kthVazKzlVv837FJVp5sAwDAJS4/DYfK6vNpuEtV9WScNchfY+KuUnTbVm57so2n5QAAjYHHnoZDw5S2O0dTVm2vNPt2XnGZFn9yQEvu6eOWJ9yYhwkA0NQwwLsRKLcZSt2wp8plSirKUjfsUXltF5f7PxWB7NKgJFU/KzgAAI0BYakRyMwqqBRgLmVIyikqVWZWQa0/o64CGQAADQ1hqRGobnLJ2tarSl0EMgAAGqJah6WDBw/qX//6l37++WdJEuPE64+zk0teziSUdRHIAABoiFwOS6dOnVJiYqK6du2qIUOGKCfn4jiViRMnavr06W5vIGpWF5NQ1kUgAwCgIXI5LP3xj39Us2bNlJ2drZYtW9rLR40apbS0NLc2Ds6pi0komRUcANBUuRyWPv74Yy1cuFDt27d3KO/SpYuOHDnitobBNUndIrTknj6yBjte2bEGB2jJPX0u+7F+ZgUHADRVLs+zdObMGYcrShUKCgrk7+/vlkahdpK6Rei2WKvHJoysCGSVJr5kniUAQCPmcli6+eabtXLlSs2fP1+SZLFYZLPZtGjRIv361792ewPhGl8fi1smn6yOs4GMWb4BAI2Fy2Fp0aJFGjhwoL799ludO3dOjz76qH744QcVFBToq6++8kQb0cDUFMiY5RsA0Ji4PGapW7du+vHHH3XTTTdp+PDhOnPmjO666y5999136tSpkyfaKOnibb7k5GQFBQUpJCREEydOVElJiWn9Bx98UFdffbVatGihq666Sg899JCKiooc6lkslkqvtWvXeqwfjR2zfAMAGptarQ0XHBysv/zlL+5ui6nk5GTl5ORo48aNOn/+vCZMmKDJkyfrjTfeqLL+iRMndOLECT3zzDOKjY3VkSNHdP/99+vEiRP65z//6VB3+fLlSkpKsr8PCQnxZFcaLWdm+X5s/fcK9G+uGzq14bYcAMArWAwXZ5Ncvny5rrjiCt19990O5evWrdPZs2c1btw4tzZQkvbu3avY2Fht3bpV/fr1kySlpaVpyJAhOnbsmCIjI506zrp163TPPffozJkzatbsYk60WCx6++23NWLEiFq3z9lVixu7jEOnNObVb5yqy205AEB9c/b32+XbcAsWLFDbtm0rlYeHh+vJJ5909XBOycjIUEhIiD0oSVJiYqJ8fHy0ZcsWp49T8T+jIihVeOCBB9S2bVvFxcVp2bJlNc5GXlZWpuLiYocXXJu9m9tyAABv4XJYys7OVkxMTKXyDh06KDs72y2N+qXc3FyFh4c7lDVr1kyhoaHKzc116hgnT57U/PnzNXnyZIfyefPm6a233tLGjRs1cuRI/eEPf9CLL75oeqwFCxYoODjY/oqKinKtQ42UK7N3s/guAMBbuByWwsPDtWvXrkrlO3fuVJs2rj2y/thjj1U5wPrS1759+1xtYiXFxcUaOnSoYmNjNXfuXIdts2fP1o033qjevXtr5syZevTRR/X000+bHm/WrFkqKiqyv44ePXrZbWwMaprl+5dYfBcA4A1cHuA9ZswYPfTQQwoMDNSvfvUrSdJnn32mhx9+WKNHj3bpWNOnT9f48eNN63Ts2FFWq1X5+fkO5RcuXFBBQYGsVqvp/qdPn1ZSUpICAwP19ttvq3nz5qb14+PjNX/+fJWVlVU7yaa/vz8TcFahYpbvKau2yyJVOdC7Kiy+CwBoyFwOS/Pnz9fhw4c1cOBA+9gfm82msWPHujxmKSwsTGFhYTXWS0hIUGFhobZt26a+fftKkjZt2iSbzab4+Phq9ysuLtagQYPk7++v9957TwEBNd8m2rFjh1q3bk0YqqXqZvk2w+K7AICGzOWn4Sr8+OOP2rlzp1q0aKHu3burQ4cO7m6bg8GDBysvL09Lly61Tx3Qr18/+9QBx48f18CBA7Vy5UrFxcWpuLhYt99+u86ePau3335brVq1sh8rLCxMvr6+2rBhg/Ly8nTDDTcoICBAGzdu1IwZMzRjxgylpqY63Taehqus3Gbom3+f0gOrt6vw5/NV1rHo4lIpX84cwDQCAIA65+zvd63mWZKkrl27qmvXrrXd3WWrV6/W1KlTNXDgQPn4+GjkyJF64YUX7NvPnz+v/fv36+zZs5Kk7du325+U69y5s8OxsrKyFB0drebNm+vll1/WH//4RxmGoc6dO+u5557TpEmT6qxfjZWvj0U3dm6rp0Z215RV2yU53par7eK7LKMCAKhrLl9ZKi8v14oVK5Senq78/HzZbDaH7Zs2bXJrA70BV5bMuWv5E5ZRAQC4k8euLD388MNasWKFhg4dqm7dusli4V/1MOfs4rtmKpZR+WWyr5ivack9fQhMAACPcDksrV27Vm+99ZaGDBniifagkapp8V0zNS2jYtHF+Zpui7VySw4A4HYuz7Pk5+dXaQwQ4EmZWQWmT9YxXxMAwJNcDkvTp0/X3/72txqXBAHcxdl5mJivCQDgCS7fhvvyyy/16aef6qOPPtJ1111XaZLH9evXu61xgOT8PEzM1wQA8ASXw1JISIjuvPNOT7QFqFLFMiq5RaVVjluqmK8pLia0rpsGAGgCXA5Ly5cv90Q7gGqZLaNS2/maAABwlstjlqSL67J98skneuWVV3T69GlJ0okTJ1RSUuLWxgEVKpZRsQY73mqzBgcwbQAAwKNcvrJ05MgRJSUlKTs7W2VlZbrtttsUGBiohQsXqqysTEuXLvVEOwG3zNcEAICrajUpZb9+/bRz5061afPfeXPuvPNOlgmBx13OfE0AANSGy2Hpiy++0Ndffy0/Pz+H8ujoaB0/ftxtDQMAAGgIXB6zZLPZVF5eXqn82LFjCgwMdEujAAAAGgqXw9Ltt9+uxYsX299bLBaVlJQoJSWFJVAAAECjYzFcnIr76NGjSkpKkmEYOnDggPr166cDBw6obdu2+vzzzxUeHu6ptjZYzq5aDAAAnFduMzz6UI+zv98uhyXp4tQBb775pnbu3KmSkhL16dNHycnJatGixWU12lsRli6Pp78MAADvk7Y7R6kb9jisDRoRHKCUYbFumy7GI2Hp/Pnzuuaaa/T+++/r2muvdUtDGwPCUu3VxZcBAOBd0nbnaMqq7ZVWbaj4Z7S75tdz9vfbpTFLzZs3V2kpi5XCPSq+DJcGJUnKLSrVlFXblbY7p55aBgCoL+U2Q6kb9lS5vFVFWeqGPSq3uXxjrNZcHuD9wAMPaOHChbpw4YIn2oMmoiF+GQAA9S8zq6DSP6IvZUjKKSpVZlZBnbXJ5XmWtm7dqvT0dH388cfq3r27WrVq5bB9/fr1bmscGi9XvgxMQgkATUf+aefuYDlbzx1cDkshISEaOXKkJ9qCJqQhfhkAAPUvPDCg5kou1HMHl8PS8uXLPdEONDEN8csAAKh/cTGhiggOUG5RaZVDNSy6uIh6XExonbXJ5TFL0sWpAz755BO98sorOn36tCTpxIkTKikpcWvj0HhVfBmqmyDAootPxdXllwEAUP98fSxKGRYrSZV+IyrepwyLrdMpZlwOS0eOHFH37t01fPhwPfDAA/rpp58kSQsXLtSMGTPc3kA0Tg3xywAAaBiSukVoyT19ZA12vLtgDQ5w27QBrnD5NtzDDz+sfv36aefOnWrT5r8Db++8805NmjTJrY1D41bxZfjlPEtW5lkCgCYvqVuEbou1NohJi10OS1988YW+/vpr+fn5OZRHR0fr+PHjbmsYmoaG9GUAADQsvj6WBvFEtMthyWazqby8vFL5sWPHFBgY6JZGoWlpKF8GAACq4vKYpdtvv12LFy+2v7dYLCopKVFKSoqGDBnizrYBAADUO5cX0j127JgGDRokwzB04MAB9evXTwcOHFDbtm31+eefKzw83FNtbbBYGw4AAO/jkYV0K1y4cEFvvvmmdu7cqZKSEvXp00fJyclq0aLFZTXaWxGWAADwPm4NS3369FF6erpat26tefPmacaMGWrZsqVbG+zNCEsAAHgfZ3+/nRqztHfvXp05c0aSlJqayuSTAACgyXDqabhevXppwoQJuummm2QYhp555hldccUVVdadM2eOWxsIAABQn5y6Dbd//36lpKTo0KFD2r59u2JjY9WsWeWcZbFYtH37do80tCHjNhwAAN7Hrbfhrr76aq1du1Zbt26VYRhKT0/Xd999V+nlyaBUUFCg5ORkBQUFKSQkRBMnTqzxduCtt94qi8Xi8Lr//vsd6mRnZ2vo0KFq2bKlwsPD9ac//UkXLlzwWD8AAIB3ceo23KUDvFNSUqq9BedJycnJysnJ0caNG3X+/HlNmDBBkydP1htvvGG636RJkzRv3jz7+0sHppeXl2vo0KGyWq36+uuvlZOTo7Fjx6p58+Z68sknPdYXAADgPZy6DdeiRQsdOHBA7du3l6+vr3Jycup0PqW9e/cqNjZWW7duVb9+/SRJaWlpGjJkiI4dO6bIyMgq97v11lvVq1cvh0k0L/XRRx/pN7/5jU6cOKF27dpJkpYuXaqZM2fqp59+qrSkS3W4DQcAgPdx9vfbKwZ4Z2RkKCQkxB6UJCkxMVE+Pj7asmWL7rzzzmr3Xb16tVatWiWr1aphw4Zp9uzZ9qtLGRkZ6t69uz0oSdKgQYM0ZcoU/fDDD+rdu7fb+wIAALyLU2FpxYoVSklJ0fvvvy+LxaKPPvqo2gHenghLubm5la5kNWvWTKGhocrNza12v9/97nfq0KGDIiMjtWvXLs2cOVP79+/X+vXr7ce9NChJsr83O25ZWZnKysrs74uLi13uEwAA8A5OhaWKAd6S5OPjo/T0dLfchnvssce0cOFC0zp79+6t9fEnT55s/3P37t0VERGhgQMH6tChQ+rUqVOtj7tgwQKlpqbWen8AAOA9nApLl7LZbG778OnTp2v8+PGmdTp27Cir1ar8/HyH8gsXLqigoEBWq9Xpz4uPj5ckHTx4UJ06dZLValVmZqZDnby8PEkyPe6sWbM0bdo0+/vi4mJFRUU53Q4AAOA9nApL7733ngYPHqzmzZvrvffeM617xx13OP3hYWFhCgsLq7FeQkKCCgsLtW3bNvXt21eStGnTJtlsNnsAcsaOHTskSREREfbjPvHEE8rPz7dfKdu4caOCgoIUGxtb7XH8/f3l7+/v9OcCAADv5dTTcD4+PvZxQz4+1U/NZLFYVF5e7tYGVhg8eLDy8vK0dOlS+9QB/fr1s08dcPz4cQ0cOFArV65UXFycDh06pDfeeENDhgxRmzZttGvXLv3xj39U+/bt9dlnn0m6OHVAr169FBkZqUWLFik3N1f33nuv7rvvPpemDuBpOAAAvI9bn4a79NabO2/DuWL16tWaOnWqBg4cKB8fH40cOVIvvPCCffv58+e1f/9+nT17VpLk5+enTz75RIsXL9aZM2cUFRWlkSNH6q9//at9H19fX73//vuaMmWKEhIS1KpVK40bN85hXiYAANC0OXVlCea4sgQAgPdx65WlCjabTStWrND69et1+PBhWSwWxcTE6H/+53907733ymKxXHbDAQAAGhKn1oaTJMMwdMcdd+i+++7T8ePH1b17d1133XU6cuSIxo8fbzoxJAAAgLdy+srSihUr9Pnnnys9PV2//vWvHbZt2rRJI0aM0MqVKzV27Fi3NxIAAKC+OH1lac2aNfrzn/9cKShJ0oABA/TYY49p9erVbm0cAABAfXM6LO3atUtJSUnVbh88eLB27tzplkYBAAA0FE6HpYKCgkrrqF2qXbt2+s9//uOWRgEAADQUToel8vLyKhfPreDr66sLFy64pVEAAAANhdMDvA3D0Pjx46td5qOsrMxtjQIAAGgonA5L48aNq7EOT8IBAIDGxumwtHz5ck+2AwAAoEFyaQZvAHWv3GYoM6tA+adLFR4YoLiYUPn6MFs+ANQVwhLQgKXtzlHqhj3KKSq1l0UEByhlWKySukXUY8sAoOlw+mk4AHUrbXeOpqza7hCUJCm3qFRTVm1X2u6cemoZADQthCWgASq3GUrdsEdGFdsqylI37FG5raoaAAB3IiwBDVBmVkGlK0qXMiTlFJUqM6ug7hoFAE0UYQlogPJPVx+UalMPAFB7hCWgAQoPDHBrPQBA7RGWgAYoLiZUEcEBqm6CAIsuPhUXFxNal80CgCaJsAQ0QL4+FqUMi5WkSoGp4n3KsFjmWwKAOkBYAhqopG4RWnJPH1mDHW+1WYMDtOSePsyzBAB1hEkpgQYsqVuEbou1MoM3ANQjwhLQwPn6WJTQqU19NwMAmixuwwEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJjwmrBUUFCg5ORkBQUFKSQkRBMnTlRJSUm19Q8fPiyLxVLla926dfZ6VW1fu3ZtXXQJAAB4gWb13QBnJScnKycnRxs3btT58+c1YcIETZ48WW+88UaV9aOiopSTk+NQ9ve//11PP/20Bg8e7FC+fPlyJSUl2d+HhIS4vf0AAMA7eUVY2rt3r9LS0rR161b169dPkvTiiy9qyJAheuaZZxQZGVlpH19fX1mtVoeyt99+W7/97W91xRVXOJSHhIRUqgsAACB5yW24jIwMhYSE2IOSJCUmJsrHx0dbtmxx6hjbtm3Tjh07NHHixErbHnjgAbVt21ZxcXFatmyZDMMwPVZZWZmKi4sdXgAAoHHyiitLubm5Cg8Pdyhr1qyZQkNDlZub69QxXnvtNV177bXq37+/Q/m8efM0YMAAtWzZUh9//LH+8Ic/qKSkRA899FC1x1qwYIFSU1Nd7wgAAPA69Xpl6bHHHqt2EHbFa9++fZf9OT///LPeeOONKq8qzZ49WzfeeKN69+6tmTNn6tFHH9XTTz9terxZs2apqKjI/jp69OhltxEAADRM9Xplafr06Ro/frxpnY4dO8pqtSo/P9+h/MKFCyooKHBqrNE///lPnT17VmPHjq2xbnx8vObPn6+ysjL5+/tXWcff37/abQAAoHGp17AUFhamsLCwGuslJCSosLBQ27ZtU9++fSVJmzZtks1mU3x8fI37v/baa7rjjjuc+qwdO3aodevWhCEAACDJS8YsXXvttUpKStKkSZO0dOlSnT9/XlOnTtXo0aPtT8IdP35cAwcO1MqVKxUXF2ff9+DBg/r888/14YcfVjruhg0blJeXpxtuuEEBAQHauHGjnnzySc2YMaPO+gYAABo2rwhLkrR69WpNnTpVAwcOlI+Pj0aOHKkXXnjBvv38+fPav3+/zp4967DfsmXL1L59e91+++2Vjtm8eXO9/PLL+uMf/yjDMNS5c2c999xzmjRpksf7AwAAvIPFqOk5edSouLhYwcHBKioqUlBQUH03BwAAOMHZ32+vmGcJAACgvhCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATBCWAAAATHhNWHriiSfUv39/tWzZUiEhIU7tYxiG5syZo4iICLVo0UKJiYk6cOCAQ52CggIlJycrKChIISEhmjhxokpKSjzQAwAA4I28JiydO3dOd999t6ZMmeL0PosWLdILL7ygpUuXasuWLWrVqpUGDRqk0tJSe53k5GT98MMP2rhxo95//319/vnnmjx5sie6AAAAvJDFMAyjvhvhihUrVuiRRx5RYWGhaT3DMBQZGanp06drxowZkqSioiK1a9dOK1as0OjRo7V3717FxsZq69at6tevnyQpLS1NQ4YM0bFjxxQZGelUm4qLixUcHKyioiIFBQVdVv8AAEDdcPb322uuLLkqKytLubm5SkxMtJcFBwcrPj5eGRkZkqSMjAyFhITYg5IkJSYmysfHR1u2bKn22GVlZSouLnZ4AQCAxqnRhqXc3FxJUrt27RzK27VrZ9+Wm5ur8PBwh+3NmjVTaGiovU5VFixYoODgYPsrKirKza0HAAANRb2Gpccee0wWi8X0tW/fvvpsYpVmzZqloqIi++vo0aP13SQAAOAhzerzw6dPn67x48eb1unYsWOtjm21WiVJeXl5ioiIsJfn5eWpV69e9jr5+fkO+124cEEFBQX2/avi7+8vf3//WrULAAB4l3oNS2FhYQoLC/PIsWNiYmS1WpWenm4PR8XFxdqyZYv9ibqEhAQVFhZq27Zt6tu3ryRp06ZNstlsio+P90i7AACAd/GaMUvZ2dnasWOHsrOzVV5erh07dmjHjh0OcyJdc801evvttyVJFotFjzzyiB5//HG99957+v777zV27FhFRkZqxIgRkqRrr71WSUlJmjRpkjIzM/XVV19p6tSpGj16tNNPwgEAgMatXq8suWLOnDl6/fXX7e979+4tSfr000916623SpL279+voqIie51HH31UZ86c0eTJk1VYWKibbrpJaWlpCggIsNdZvXq1pk6dqoEDB8rHx0cjR47UCy+8UDedAgAADZ7XzbPUEDHPEgAA3qfJz7MEAADgDoQlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE4QlAAAAE83quwFAXSi3GcrMKlD+6VKFBwYoLiZUvj6W+m4WAMALEJbQ6KXtzlHqhj3KKSq1l0UEByhlWKySukXUY8sAAN6A23Bo1NJ252jKqu0OQUmScotKNWXVdqXtzqmnlgEAvAVhCY1Wuc1Q6oY9MqrYVlGWumGPym1V1QAA4CLCEhqtzKyCSleULmVIyikqVWZWQd01CgDgdQhLaLTyT1cflGpTDwDQNBGW0GiFBwa4tR4AoGkiLKHRiosJVURwgKqbIMCii0/FxcWE1mWzAABehrCERsvXx6KUYbGSVCkwVbxPGRbLfEsAAFOEJTRqSd0itOSePrIGO95qswYHaMk9fZhnCQBQIyalRKOX1C1Ct8VamcEbAFArhCU0Cb4+FiV0alPfzQAAeCFuwwEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJggLAEAAJhgBm83MAxDklRcXFzPLQEAAM6q+N2u+B2vDmHJDU6fPi1JioqKqueWAAAAV50+fVrBwcHVbrcYNcUp1Mhms+nEiRMKDAyUxeK+xVmLi4sVFRWlo0ePKigoyG3H9Qb0ven1van2W2q6fW+q/Zboe0Ppu2EYOn36tCIjI+XjU/3IJK4suYGPj4/at2/vseMHBQXV+1+o+kLfm17fm2q/pabb96bab4m+N4S+m11RqsAAbwAAABOEJQAAABOEpQbM399fKSkp8vf3r++m1Dn63vT63lT7LTXdvjfVfkv03dv6zgBvAAAAE1xZAgAAMEFYAgAAMEFYAgAAMEFY8qCXX35Z0dHRCggIUHx8vDIzM03rr1u3Ttdcc40CAgLUvXt3ffjhhw7bDcPQnDlzFBERoRYtWigxMVEHDhxwqFNQUKDk5GQFBQUpJCREEydOVElJidv7VhN39v38+fOaOXOmunfvrlatWikyMlJjx47ViRMnHI4RHR0ti8Xi8Hrqqac80j8z7j7v48ePr9SvpKQkhzoN4by7u9+/7HPF6+mnn7bX8cZz/sMPP2jkyJH2ti9evLhWxywtLdUDDzygNm3a6IorrtDIkSOVl5fnzm45xd19X7Bgga6//noFBgYqPDxcI0aM0P79+x3q3HrrrZXO+/333+/urplyd7/nzp1bqU/XXHONQ53Ges6r+h5bLBY98MAD9jr1fs4NeMTatWsNPz8/Y9myZcYPP/xgTJo0yQgJCTHy8vKqrP/VV18Zvr6+xqJFi4w9e/YYf/3rX43mzZsb33//vb3OU089ZQQHBxvvvPOOsXPnTuOOO+4wYmJijJ9//tleJykpyejZs6fxzTffGF988YXRuXNnY8yYMR7v76Xc3ffCwkIjMTHRePPNN419+/YZGRkZRlxcnNG3b1+H43To0MGYN2+ekZOTY3+VlJR4vL+X8sR5HzdunJGUlOTQr4KCAofj1Pd590S/L+1vTk6OsWzZMsNisRiHDh2y1/HGc56ZmWnMmDHDWLNmjWG1Wo3nn3++Vse8//77jaioKCM9Pd349ttvjRtuuMHo37+/p7pZJU/0fdCgQcby5cuN3bt3Gzt27DCGDBliXHXVVQ7n9ZZbbjEmTZrkcN6Lioo81c1KPNHvlJQU47rrrnPo008//eRQp7Ge8/z8fId+b9y40ZBkfPrpp/Y69X3OCUseEhcXZzzwwAP29+Xl5UZkZKSxYMGCKuv/9re/NYYOHepQFh8fb/z+9783DMMwbDabYbVajaefftq+vbCw0PD39zfWrFljGIZh7Nmzx5BkbN261V7no48+MiwWi3H8+HG39a0m7u57VTIzMw1JxpEjR+xlHTp0qPKLWJc80fdx48YZw4cPr/YzG8J5r4tzPnz4cGPAgAEOZd54zi9VXftrOmZhYaHRvHlzY926dfY6e/fuNSQZGRkZl9Eb13ii77+Un59vSDI+++wze9ktt9xiPPzww7Vpslt4ot8pKSlGz549q92vKZ3zhx9+2OjUqZNhs9nsZfV9zrkN5wHnzp3Ttm3blJiYaC/z8fFRYmKiMjIyqtwnIyPDob4kDRo0yF4/KytLubm5DnWCg4MVHx9vr5ORkaGQkBD169fPXicxMVE+Pj7asmWL2/pnxhN9r0pRUZEsFotCQkIcyp966im1adNGvXv31tNPP60LFy7UvjMu8mTfN2/erPDwcF199dWaMmWKTp065XCM+jzvdXHO8/Ly9MEHH2jixImVtnnbOXfHMbdt26bz58871Lnmmmt01VVX1fpzPdFOdygqKpIkhYaGOpSvXr1abdu2Vbdu3TRr1iydPXvWbZ9pxpP9PnDggCIjI9WxY0clJycrOzvbvq2pnPNz585p1apV+t///d9Ka63W1zmXWBvOI06ePKny8nK1a9fOobxdu3bat29flfvk5uZWWT83N9e+vaLMrE54eLjD9mbNmik0NNRex9M80fdfKi0t1cyZMzVmzBiHdYUeeugh9enTR6Ghofr66681a9Ys5eTk6LnnnrvMXjnHU31PSkrSXXfdpZiYGB06dEh//vOfNXjwYGVkZMjX17fez3tdnPPXX39dgYGBuuuuuxzKvfGcu+OYubm58vPzq/SPBbP/h+7mib7/ks1m0yOPPKIbb7xR3bp1s5f/7ne/U4cOHRQZGaldu3Zp5syZ2r9/v9avX++WzzXjqX7Hx8drxYoVuvrqq5WTk6PU1FTdfPPN2r17twIDA5vMOX/nnXdUWFio8ePHO5TX5zmXCEvwMufPn9dvf/tbGYahJUuWOGybNm2a/c89evSQn5+ffv/732vBggVeNVPsL40ePdr+5+7du6tHjx7q1KmTNm/erIEDB9Zjy+rOsmXLlJycrICAAIfyxnrOcdEDDzyg3bt368svv3Qonzx5sv3P3bt3V0REhAYOHKhDhw6pU6dOdd1Mtxg8eLD9zz169FB8fLw6dOigt956q8orqo3Va6+9psGDBysyMtKhvL7PObfhPKBt27by9fWt9JRCXl6erFZrlftYrVbT+hX/ralOfn6+w/YLFy6ooKCg2s91N0/0vUJFUDpy5Ig2btxY42rV8fHxunDhgg4fPux6R2rBk32/VMeOHdW2bVsdPHjQfoz6PO+e7vcXX3yh/fv367777quxLd5wzt1xTKvVqnPnzqmwsNBtn+uJdl6OqVOn6v3339enn36q9u3bm9aNj4+XJPt3wpM83e8KISEh6tq1q8P3vLGf8yNHjuiTTz5x+rsu1c05lwhLHuHn56e+ffsqPT3dXmaz2ZSenq6EhIQq90lISHCoL0kbN26014+JiZHVanWoU1xcrC1bttjrJCQkqLCwUNu2bbPX2bRpk2w2m/0vlqd5ou/Sf4PSgQMH9Mknn6hNmzY1tmXHjh3y8fGpdIvKUzzV9186duyYTp06pYiICPsx6vO8e7rfr732mvr27auePXvW2BZvOOfuOGbfvn3VvHlzhzr79+9XdnZ2rT/XE+2sDcMwNHXqVL399tvatGmTYmJiatxnx44dkmT/TniSp/r9SyUlJTp06JC9T435nFdYvny5wsPDNXTo0Brr1uU5l8TUAZ6ydu1aw9/f31ixYoWxZ88eY/LkyUZISIiRm5trGIZh3HvvvcZjjz1mr//VV18ZzZo1M5555hlj7969RkpKSpVTB4SEhBjvvvuusWvXLmP48OFVTh3Qu3dvY8uWLcaXX35pdOnSpV6mDnBn38+dO2fccccdRvv27Y0dO3Y4PDpaVlZmGIZhfP3118bzzz9v7Nixwzh06JCxatUqIywszBg7dqxX9/306dPGjBkzjIyMDCMrK8v45JNPjD59+hhdunQxSktL7cep7/Puib/vhmEYRUVFRsuWLY0lS5ZU+kxvPedlZWXGd999Z3z33XdGRESEMWPGDOO7774zDhw44PQxDePiY+RXXXWVsWnTJuPbb781EhISjISEhLrruBPtrE3fp0yZYgQHBxubN292+K6fPXvWMAzDOHjwoDFv3jzj22+/NbKysox3333X6Nixo/GrX/3Kq/s9ffp0Y/PmzUZWVpbx1VdfGYmJiUbbtm2N/Px8e53Ges4N4+JTdVdddZUxc+bMSp/ZEM45YcmDXnzxReOqq64y/Pz8jLi4OOObb76xb7vllluMcePGOdR/6623jK5duxp+fn7GddddZ3zwwQcO2202mzF79myjXbt2hr+/vzFw4EBj//79DnVOnTpljBkzxrjiiiuMoKAgY8KECcbp06c91sfquLPvWVlZhqQqXxXzcGzbts2Ij483goODjYCAAOPaa681nnzySYdAUVfc2fezZ88at99+uxEWFmY0b97c6NChgzFp0iSHH03DaBjn3d1/3w3DMF555RWjRYsWRmFhYaVt3nrOq/v7fMsttzh9TMMwjJ9//tn4wx/+YLRu3dpo2bKlceeddxo5OTme7GaV3N336r7ry5cvNwzDMLKzs41f/epXRmhoqOHv72907tzZ+NOf/lSnc+4Yhvv7PWrUKCMiIsLw8/MzrrzySmPUqFHGwYMHHT6zsZ5zwzCMf/3rX4akSr9phtEwzrnFMAzD45evAAAAvBRjlgAAAEwQlgAAAEwQlgAAAEwQlgAAAEwQlgAAAEwQlgAAAEwQlgAAAEwQlgAAAEwQlgCgDo0fP14jRoyo72YAcAFhCUCDUV9BYsWKFQoJCanzzwXgHQhLAAAAJghLABqsW2+9VQ899JAeffRRhYaGymq1au7cuQ51LBaLlixZosGDB6tFixbq2LGj/vnPf9q3b968WRaLRYWFhfayHTt2yGKx6PDhw9q8ebMmTJigoqIiWSwWWSyWSp8hST/++KMsFov27dvnUP7888+rU6dOkqTy8nJNnDhRMTExatGiha6++mr97W9/M+1jdHS0Fi9e7FDWq1cvhzYUFhbqvvvuU1hYmIKCgjRgwADt3LnT9LgA3IewBKBBe/3119WqVStt2bJFixYt0rx587Rx40aHOrNnz9bIkSO1c+dOJScna/To0dq7d69Tx+/fv78WL16soKAg5eTkKCcnRzNmzKhUr2vXrurXr59Wr17tUL569Wr97ne/kyTZbDa1b99e69at0549ezRnzhz9+c9/1ltvvVXL3l909913Kz8/Xx999JG2bdumPn36aODAgSooKLis4wJwDmEJQIPWo0cPpaSkqEuXLho7dqz69eun9PR0hzp333237rvvPnXt2lXz589Xv3799OKLLzp1fD8/PwUHB8tischqtcpqteqKK66osm5ycrLWrFljf//jjz9q27ZtSk5OliQ1b95cqamp6tevn2JiYpScnKwJEyZcVlj68ssvlZmZqXXr1qlfv37q0qWLnnnmGYWEhDhcQQPgOYQlAA1ajx49HN5HREQoPz/foSwhIaHSe2evLLli9OjROnz4sL755htJF68q9enTR9dcc429zssvv6y+ffsqLCxMV1xxhf7+978rOzu71p+5c+dOlZSUqE2bNrriiivsr6ysLB06dOiy+wSgZs3quwEAYKZ58+YO7y0Wi2w2m9P7+/hc/DehYRj2svPnz9eqLVarVQMGDNAbb7yhG264QW+88YamTJli37527VrNmDFDzz77rBISEhQYGKinn35aW7ZsMW3fpW37ZftKSkoUERGhzZs3V9qXJ/iAukFYAuD1vvnmG40dO9bhfe/evSVJYWFhkqScnBy1bt1a0sUB3pfy8/NTeXm5U5+VnJysRx99VGPGjNG///1vjR492r7tq6++Uv/+/fWHP/zBXlbT1Z+wsDDl5OTY3xcXFysrK8v+vk+fPsrNzVWzZs0UHR3tVBsBuBe34QB4vXXr1mnZsmX68ccflZKSoszMTE2dOlWS1LlzZ0VFRWnu3Lk6cOCAPvjgAz377LMO+0dHR6ukpETp6ek6efKkzp49W+1n3XXXXTp9+rSmTJmiX//614qMjLRv69Kli7799lv961//0o8//qjZs2dr69atpm0fMGCA/vGPf+iLL77Q999/r3HjxsnX19e+PTExUQkJCRoxYoQ+/vhjHT58WF9//bX+8pe/6Ntvv63N/y4ALiIsAfB6qampWrt2rXr06KGVK1dqzZo1io2NlXTxNt6aNWu0b98+9ejRQwsXLtTjjz/usH///v11//33a9SoUQoLC9OiRYuq/azAwEANGzbM/uTdpX7/+9/rrrvu0qhRoxQfH69Tp045XGWqyqxZs3TLLbfoN7/5jYYOHaoRI0bYpyKQLt52/PDDD/WrX/1KEyZMUNeuXTV69GgdOXJE7dq1c/V/FYBasBi/vFkOAF7EYrHo7bffZgkRAB7DlSUAAAAThCUAAAATPA0HwKsxkgCAp3FlCQAAwARhCQAAwARhCQAAwARhCQAAwARhCQAAwARhCQAAwARhCQAAwARhCQAAwARhCQAAwMT/B4ZlrHpyZrxdAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    probs2 = lm_head(prelogits2.half())[:,-1].softmax(dim=-1).cpu()\n",
    "\n",
    "plot_diff(probs, probs2)\n",
    "max_diff(probs, probs2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e8f3c92-1893-4595-8b78-2fbf8a8d18e6",
   "metadata": {},
   "source": [
    "[RMSNorm](https://arxiv.org/abs/1910.07467) is essentially just [LayerNorm](https://arxiv.org/abs/1607.06450) with no shift:\n",
    "\n",
    "$$ \\operatorname{RMSNorm}(x_i) = \\frac{x_i}{\\sqrt{\\frac{1}{N}\\sum_{j=1}^{N} x_j^2 + \\epsilon}} g_i $$\n",
    "\n",
    "This is straightforward to implement directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "67d20d4e-9c38-451b-b64f-2b6b2a0f39c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rms_norm(x, weight, eps=1e-5):\n",
    "    inv_rms = (x.pow(2).mean(axis=-1, keepdim=True) + eps) ** -0.5\n",
    "    return x * inv_rms * weight\n",
    "\n",
    "with torch.inference_mode():\n",
    "    prelogits3 = rms_norm(hs + rs, weight=norm_f.weight)\n",
    "    \n",
    "assert torch.allclose(prelogits3, prelogits2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d707e2-d3c6-4c54-bf0c-79a7cac2fa1e",
   "metadata": {},
   "source": [
    "## Mixer Blocks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eea1a6c9-91f0-4dba-a3ed-1c2c85b85934",
   "metadata": {},
   "source": [
    "The Mixer Layer, along with its component S6 block, is the fundamental contribution of the Mamba paper.\n",
    "\n",
    "<img src=\"./mamba_architecture.png\" alt=\"Illustration of Mamba Mixer Block\">\n",
    "\n",
    "From Section 3.4:\n",
    "\n",
    "> This architecture involves expanding the model dimension $D$ by a controllable expansion factor $E$.\n",
    "> For each block, most of the parameters ($3ED^2$) are in the linear projections ($2ED^2$ for input projections, $ED^2$ for output projection) while the inner SSM contributes less.\n",
    "> The number of SSM parameters (projections for $\\Delta, \\mathbf{B}, \\mathbf{C}$, and the matrix $\\mathbf{A}$) are much smaller in comparison.\n",
    "> We repeat this block, interleaved with standard normalization and residual connections, to form the Mamba architecture.\n",
    "\n",
    "In our model we have model dimension $D=768$, expansion factor $E=2$ and SSM state dimension $N=16$.\n",
    "Each mixer block then consists of :\n",
    "\n",
    "* in_proj (the bottom trapezoids): The projections from $D$ to $2ED$ for the combined hidden and residual state\n",
    "* conv1d: One dimensional convolutions (with bias) for each of the $2ED$ layers, here with a kernel size of 4\n",
    "* act: The activation for both the hidden state and the residual\n",
    "* x_proj: Mappings for x onto $B$ (dimension $N$), $C$ (dimension $N$) and $\\Delta$ (here dimension 48)\n",
    "* out_proj (the top trapezoid): Projection from $ED$ back to $D$\n",
    "* norm: Pre-Norm applied at the start of the layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e7663683-f9dd-4308-9b91-a17f8317d01e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Block(\n",
       "  (mixer): Mamba(\n",
       "    (in_proj): Linear(in_features=768, out_features=3072, bias=False)\n",
       "    (conv1d): Conv1d(1536, 1536, kernel_size=(4,), stride=(1,), padding=(3,), groups=1536)\n",
       "    (act): SiLU()\n",
       "    (x_proj): Linear(in_features=1536, out_features=80, bias=False)\n",
       "    (dt_proj): Linear(in_features=48, out_features=1536, bias=True)\n",
       "    (out_proj): Linear(in_features=1536, out_features=768, bias=False)\n",
       "  )\n",
       "  (norm): RMSNorm()\n",
       ")"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mixers[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc4f4ea-8f96-43c5-8fe5-2c4284f3490f",
   "metadata": {},
   "source": [
    "We can step through a couple of layers to deconstruct what is going on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "aea58309-26c9-452c-a21f-d35e61eb04b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    hs0, rs0 = embedding(input_ids), None\n",
    "    hs1, rs1 = mixers[0](hs0, rs0)\n",
    "    hs2, rs2 = mixers[1](hs1, rs1)\n",
    "    #..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dbcc782-ea86-4daa-9b66-6094b2536466",
   "metadata": {},
   "source": [
    "## Pre-norm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a850e52-ffbd-4157-afba-97889a120612",
   "metadata": {},
   "source": [
    "Before going into the mixer block the input, made up of the hidden states and residual, are normalised with RMSNorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2f4a5998-09c4-482c-a23b-4cdc7966777b",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    hidden_states, residual = rms_norm_fn(\n",
    "        hs1,\n",
    "        mixers[1].norm.weight,\n",
    "        bias=None,\n",
    "        residual=rs1,\n",
    "        prenorm=True,\n",
    "        residual_in_fp32=True,\n",
    "        eps=1e-5\n",
    "    )\n",
    "\n",
    "assert (hs2 == mixers[1].mixer(hidden_states)).all()\n",
    "assert (rs2 == residual).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eab41fba-6c9b-43c1-8598-30dccf8b0aee",
   "metadata": {},
   "source": [
    "As before this is a fused operation and can get a similar result with the function `rms_norm` implemented previously:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ecfa6329-46af-4ffc-8f9e-0b7931a36e05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00048744678497314453"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    residual2 = (hs1 + rs1).float()\n",
    "    hidden_states2 = rms_norm(residual2, mixers[1].norm.weight)\n",
    "\n",
    "assert (residual2 == residual).all()\n",
    "plot_diff(hidden_states, hidden_states2)\n",
    "max_diff(hidden_states, hidden_states2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "946520d9-e068-487a-9a2e-3232a1116975",
   "metadata": {},
   "source": [
    "When passed through the mixer this gives a very similar result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "22d21a7e-2934-4069-b935-6f32e6a6e264",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    hs2_ =  mixers[1].mixer(hidden_states2.half())\n",
    "\n",
    "assert torch.allclose(hs2, hs2_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f817eb59-ff56-4ca8-821c-ab98aca790d9",
   "metadata": {},
   "source": [
    "Next we can step into the actual mixer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "87df2cbf-0590-4d1d-b9a9-dbd592ddfd7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Mamba(\n",
       "  (in_proj): Linear(in_features=768, out_features=3072, bias=False)\n",
       "  (conv1d): Conv1d(1536, 1536, kernel_size=(4,), stride=(1,), padding=(3,), groups=1536)\n",
       "  (act): SiLU()\n",
       "  (x_proj): Linear(in_features=1536, out_features=80, bias=False)\n",
       "  (dt_proj): Linear(in_features=48, out_features=1536, bias=True)\n",
       "  (out_proj): Linear(in_features=1536, out_features=768, bias=False)\n",
       ")"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mixer = mixers[1].mixer\n",
    "mixer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18da8c95-3103-48da-8378-ed6663cb5d12",
   "metadata": {},
   "source": [
    "## Input projection and block\n",
    "\n",
    "The normed hidden states are then projected into two expanded inputs.\n",
    "The `in_proj` takes hidden states of size $(B, L, D)$ and to produce outputs of size $(B, L, 2ED)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a850d58b-e6d3-40ef-81e6-9995ff4cf06a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 5, 768]), torch.Size([1, 5, 3072]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    xz = mixer.in_proj(hidden_states)\n",
    "\n",
    "hidden_states.shape, xz.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b975b23a-e304-48e7-a4c1-a26d4cfa532e",
   "metadata": {},
   "source": [
    "This is then passed through a fast CUDA implementation of the Mamba layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "73624266-609d-4f1a-91bd-6c0d2c114918",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mamba_ssm.ops.selective_scan_interface import mamba_inner_fn\n",
    "\n",
    "with torch.no_grad():\n",
    "    hs2_ = mamba_inner_fn(rearrange(xz, \"b l d -> b d l\"),\n",
    "               mixer.conv1d.weight,\n",
    "               mixer.conv1d.bias,\n",
    "               mixer.x_proj.weight,\n",
    "               mixer.dt_proj.weight,\n",
    "                mixer.out_proj.weight,\n",
    "                mixer.out_proj.bias,\n",
    "                -torch.exp(mixer.A_log.float()) ,\n",
    "                None,  # input-dependent B\n",
    "                None,  # input-dependent C\n",
    "                mixer.D.float(),\n",
    "                delta_bias=mixer.dt_proj.bias.float(),\n",
    "                delta_softplus=True,\n",
    "            )\n",
    "\n",
    "assert (hs2_ == hs2).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8beefc6-e50e-48b9-b8ac-590aaeead56a",
   "metadata": {},
   "source": [
    "But this isn't very illuminating; let's break this `mamba_inner_fn` down further."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9b8d101-b17e-4cd4-89a8-e274d7fc505a",
   "metadata": {},
   "source": [
    "## Mamba inner function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a1814f3-0495-4554-84c7-c90cf0907914",
   "metadata": {},
   "source": [
    "First we can separate the `pre_x` and `z` vectors (each of the two trapezoids at the bottom of the Mamba block diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "29171222-1e8d-411a-a868-85a48d22d12c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 5, 1536]), torch.Size([1, 5, 1536]))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    pre_x, z = xz.chunk(2, dim=-1)\n",
    "pre_x.shape, z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eabe643-9e5c-44d8-86fe-27c71c16676c",
   "metadata": {},
   "source": [
    "Next we want to perform the convolution on the left input (discarding the extra elements due to padding at the end), and apply the activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e7dbe316-a21a-499b-8f51-ab5059e820cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 5, 1536])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    x = rearrange(\n",
    "        mixer.act(\n",
    "        mixer.conv1d(\n",
    "            rearrange(pre_x, 'b l d -> b d l')\n",
    "        )[...,:pre_x.size(1)]),\n",
    "        'b d l -> b l d')\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a07ad532-191b-49cf-a055-a545dd5acb84",
   "metadata": {},
   "source": [
    "### SiLU Activation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ec6b3d-1637-4ddf-91e8-04700f902a4d",
   "metadata": {},
   "source": [
    "Note that the activation function is SiLU which is like a smoothed ReLU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "21b611ee-b87b-418f-8362-bc3b27e2c4bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SiLU()"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mixer.act"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7729e75e-dad1-4283-8896-bbb4dd95ae8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = torch.arange(-10,10,0.01)\n",
    "plt.plot(grid, mixer.act(grid));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33d4532-ad69-489c-bd6b-7a850d396697",
   "metadata": {},
   "source": [
    "This is defined as\n",
    "\n",
    "$$ \\operatorname{SiLU}(x) = \\frac{x}{1+\\exp(-x)} $$\n",
    "\n",
    "And we can get similar results with a direct implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "270a8425-fe5a-471e-97fb-af669f73e578",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Input value', ylabel='Difference in output'>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mysilu(x):\n",
    "    return x/(1+torch.exp(-x))\n",
    "\n",
    "plot_diff(mixer.act(grid), mysilu(grid))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a952d1f5-4fba-45b2-842a-3003c1c7ba05",
   "metadata": {},
   "source": [
    "### Applying SSM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cc6de0e-e67d-4f4d-bd64-989ddd586186",
   "metadata": {},
   "source": [
    "Next the SSM is applied to x.\n",
    "First the data-dependent transition matrices are calculated:\n",
    "\n",
    "$$\\begin{align}\n",
    "B &= s_B(x) \\\\\n",
    "C &= s_C(x) \\\\\n",
    "\\Delta &= \\tau_\\Delta({\\rm Parameter} + s_\\Delta(x)) \\\\\n",
    "\\end{align}$$\n",
    "\n",
    "Where here all the $s$ are linear and combined in the `x_proj` layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dac84aab-2734-43a0-99e7-5908678f6e85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 5, 48]), torch.Size([1, 5, 16]), torch.Size([1, 5, 16]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    dt, B, C = torch.split(mixer.x_proj(x), [mixer.dt_rank, mixer.d_state, mixer.d_state], dim=-1)\n",
    "\n",
    "dt.shape, B.shape, C.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd99df5-b58c-40e6-b2c0-372020211828",
   "metadata": {},
   "source": [
    "These inputs can be put into an efficient CUDA selective scan function to run the SSM (after reshaping everything to (batch, channel, length):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e8d30aea-add6-4e4f-8597-c8c5b9ed4c8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 1536, 5]), torch.Size([1, 1536, 16]))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mamba_ssm.ops.selective_scan_interface import selective_scan_fn\n",
    "\n",
    "with torch.inference_mode():\n",
    "    y, ssm_state = selective_scan_fn(\n",
    "                rearrange(x, \"b l d -> b d l\").contiguous(),\n",
    "                rearrange(dt @ mixer.dt_proj.weight.t(), \n",
    "                          \"b l d -> b d l\").contiguous(),\n",
    "                -torch.exp(mixer.A_log.float()),\n",
    "                rearrange(B, \"b l d -> b d l\").contiguous(),\n",
    "                rearrange(C, \"b l d -> b d l\").contiguous(),\n",
    "                mixer.D.float(),\n",
    "                z=rearrange(z, \"b l d -> b d l\").contiguous(),\n",
    "                delta_bias=mixer.dt_proj.bias.float(),\n",
    "                delta_softplus=True,\n",
    "                return_last_state=True,\n",
    "            )\n",
    "\n",
    "y.shape, ssm_state.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71e4f0c6-1c7b-4b18-a572-18d7f0e31087",
   "metadata": {},
   "source": [
    "This gives a very similar result to passing it through the model directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c1d5c864-431d-4e97-b3c0-27b3b4e2a9c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0009765625"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    out = mixer.out_proj(rearrange(y, \"b d l -> b l d\"))\n",
    "\n",
    "plot_diff(hs2, out)\n",
    "max_diff(hs2, out)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7edd5509-c405-45b0-9b5a-86936f0c7e78",
   "metadata": {},
   "source": [
    "## Running the State Space Model\n",
    "\n",
    "The selective scan function runs the SSM, let's step through how that works.\n",
    "\n",
    "### Softplus\n",
    "\n",
    "Firstly we need to calcuate $\\Delta = \\operatorname{softplus}(s_\\Delta(dt) + b)$\n",
    "\n",
    "[Softplus](https://pytorch.org/docs/stable/generated/torch.nn.Softplus.html) it's a smooth approximation to the ReLU:\n",
    "\n",
    "$$\\operatorname{softplus}(x) = \\log\\left(1+\\exp(x)\\right) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d5c6d709-d184-4104-b295-c4e7ae93f224",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = torch.arange(-10, 10, step=0.01)\n",
    "sp = F.softplus(grid)\n",
    "sp2 = F.relu(grid)\n",
    "plt.plot(grid, sp)\n",
    "plt.plot(grid, sp2)\n",
    "\n",
    "assert torch.allclose(sp, (1 + grid.exp()).log(), atol=1e-7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "888be9a7-d390-4cf5-b85b-952bb6da5aa2",
   "metadata": {},
   "source": [
    "We apply this to dt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c3a929f0-cb80-41cf-b03b-04555958cdf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 5, 1536])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    delta = F.softplus(mixer.dt_proj(dt))\n",
    "\n",
    "delta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fb880fe-0c06-441c-afc3-e8e7656c8137",
   "metadata": {},
   "source": [
    "### Discretization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c27a0de-855f-4ec0-bc08-c8a780f8a551",
   "metadata": {},
   "source": [
    "The next step is to discretize the SSM by equation 4\n",
    "\n",
    "$$\\begin{align}\n",
    "\\overline{A} &= \\exp(\\Delta A) \\\\\n",
    "\\overline{B} &= (\\Delta A)^{-1} \\left(\\exp(\\Delta A) - I\\right) \\Delta B\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The paper assumes\n",
    "\n",
    "> *Structure and Dimensions.*\n",
    "> Finally, we note that structured SSMs are so named because computing them efficiently also requires imposing structure on the A matrix.\n",
    "> The most popular form of structure is diagonal, which we also use.\n",
    "> In this case, the $A \\in \\mathbb{R}^{N\\times N}$ $B \\in \\mathbb{R}^{N \\times 1}$, $B \\in \\mathbb{R}^{1 \\times N}$ matrices can all be represented by 𝑁 numbers.\n",
    "> To operate over an input sequence $x$ of batch size $B$ and length $L$ with $D$ channels, the SSM is applied independently to each channel.\n",
    "> Note that in this case, the total hidden state has dimension $DN$ per input, and computing it over the sequence length requires $O(BLDN)$ time and memory; this is the root of the fundamental efficiency bottleneck addressed in Section 3.3.\n",
    "\n",
    "Then the matrix exponential of the diagonal matrix $A$ reduces to the elementwise exponential, and\n",
    "\n",
    "$$\\begin{align}\n",
    "\\overline{B}_i &= \\frac{1}{\\Delta A_i} \\left(\\exp(\\Delta A_i) - 1\\right) \\Delta B_i \\\\\n",
    "               &\\approx \\frac{1}{\\Delta A_i} \\left(1 + \\Delta A_i + O(\\Delta A_i)^2 - 1\\right) \\Delta B_i \\\\\n",
    "               &\\approx \\Delta B_i + O(A_i^2)\n",
    "\\end{align}$$\n",
    "\n",
    "Note that the model stores the *negative log* of A; this means the values are all less than 0 and the exponential won't overflow (but many values will underflow to zero), and we expect the error $\\Delta A_i^2$ to be small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b81706e6-db13-4047-ba8f-e698c4d1055c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1536, 16]), torch.Size([1, 5, 16]))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    A = -torch.exp(mixer.A_log.float())\n",
    "\n",
    "A.shape, B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "250aa0d6-cfc8-4a56-a462-f27126c754b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    A_bar = torch.exp(torch.einsum(\"b l d, d n -> b l d n\", delta, A))\n",
    "    B_bar = torch.einsum(\"b l d, b l n -> b l d n\", delta, B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43ed649d-24c5-4a4e-a0a2-908eeea6fa42",
   "metadata": {},
   "source": [
    "With the discrete (data dependent) transition matrices, the State Model discrete transition can be applied:\n",
    "\n",
    "$$\\begin{align}\n",
    "h_{t} &= \\overline{A} h_{t-1} + \\overline{B} x_t \\\\\n",
    "y_{t} &= C h_t + D x_t \\\\\n",
    "\\end{align}$$\n",
    "\n",
    "We need to be a bit careful about implicit shapes: this is applied independently across each element of the batch (here size 1) and each channel (here 1536)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0ef90b1f-b361-496d-9bb5-7b317b0e06e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A_bar.shape=torch.Size([1, 5, 1536, 16])\n",
      "B_bar.shape=torch.Size([1, 5, 1536, 16])\n",
      "x.shape=torch.Size([1, 5, 1536])\n",
      "C.shape=torch.Size([1, 5, 16])\n",
      "mixer.D.shape=torch.Size([1536])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(f'''\n",
    "{A_bar.shape=}\n",
    "{B_bar.shape=}\n",
    "{x.shape=}\n",
    "{C.shape=}\n",
    "{mixer.D.shape=}\n",
    "''')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb74a391-81da-4d96-b485-5ebd94b3b38a",
   "metadata": {},
   "source": [
    "We can calculate $h_t$ iteratively for each time step $t$ and use this to calculate $y_t$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d3a05b35-0fcb-4228-be97-2d31351558b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "b, l, d, n = A_bar.shape\n",
    "\n",
    "\n",
    "h = torch.zeros(b, d, n, device=A_bar.device)\n",
    "states = []\n",
    "\n",
    "with torch.inference_mode():\n",
    "    for i in range(l):\n",
    "            # At t=i          At t =i      At t=i, expand along n (hidden dimension)\n",
    "        h = A_bar[:, i] * h + B_bar[:, i] * x[:, i].unsqueeze(-1)\n",
    "        states.append(h)\n",
    "\n",
    "    # Combine all states into a single vector\n",
    "    h_t = torch.stack(states, dim=1)\n",
    "    \n",
    "    y_t = torch.einsum(\"b l n, b l d n -> b l d\", C.float(), h_t) + \\\n",
    "          torch.einsum('d, b l d -> b l d', mixer.D, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e1d9a6e-8101-410b-9976-bab649911846",
   "metadata": {},
   "source": [
    "Then we can combine the output of the SSM by multiplying with the gated MLP as in Figure 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9a59f977-8e22-4c60-8bfc-d60b526d726b",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    mixer_out = rearrange(y_t * mixer.act(z), 'b l d -> b d l')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e85e6ba-7e0e-4f21-83f5-69211575659a",
   "metadata": {},
   "source": [
    "The state we get is similar to what we got from `selective_scan_fn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9ee14e46-8a7e-4bb4-b611-467441028dab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.191036224365234e-05"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diff(ssm_state, h)\n",
    "max_diff(ssm_state, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471645d7-969a-435e-821e-706cb5cbcd40",
   "metadata": {},
   "source": [
    "Similarly our output is similar, with deviations at very small values of the output (that are relatively small)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "891409fe-f77d-4148-b413-1ac4194977ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0007761716842651367"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diff(y, mixer_out)\n",
    "max_diff(y, mixer_out)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15bf5bdf-599c-4955-b99c-44f5dfa42b87",
   "metadata": {},
   "source": [
    "# Interlude: State selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bd937ab-510c-44e3-aa0d-c9b0596a31e3",
   "metadata": {},
   "source": [
    "The Mamba paper argues that Mamba performs much better than S4 because it can selectively ignore or focus on inputs depending on the data.\n",
    "We can look at the transition matrices to understand how this works.\n",
    "\n",
    "The $\\Delta$ function at each timestep impacts how much the state gets updated in each dimension.\n",
    "\n",
    "For $\\Delta \\approx 0$ then $\\overline{A} = \\exp{\\Delta A} \\approx I$ and $\\overline{B} = \\Delta B \\approx 0$ and so $h_t \\approx h_{t-1}$ so we ignore the input in that dimension.\n",
    "\n",
    "On the other hand since for large $\\Delta$, since $A_i < 0$ then $\\overline{A} \\approx 0$ and $\\overline{B} = \\Delta B$, and so $h_t \\approx \\Delta B x_t$ and so the state is reset.\n",
    "\n",
    "We can see here that the distribution of $\\Delta$ across hidden dimensions changes over time (here the tokens)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a3a6c9a3-bcb5-4aad-804f-4c7fc5d71da7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(delta.size(1)):\n",
    "    plt.hist(delta[0,i].cpu(), bins=50, alpha=0.7,\n",
    "             label=f\"t={i}, {tokenizer.decode(input_ids[0,i])}\")\n",
    "plt.xlabel(\"delta\")\n",
    "plt.ylabel(\"freq\")\n",
    "plt.legend(loc=\"upper right\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c9ab74d-1885-42fc-b84f-2b258fd17a82",
   "metadata": {},
   "source": [
    "The values of $A$ indicate how much state to keep for each embedding dimension: very negative values correspond to forgetting state, values close to 0 correspond to keeping state.\n",
    "\n",
    "Note that the majority of values are very close to 0 (keeping state) but it varies by channel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "94bb3eab-eca6-45bd-a94e-127ce2d577cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x1000 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(4, 4, figsize=(15,10)) \n",
    "\n",
    "for i in range(4):\n",
    "    for j in range(4):\n",
    "        ax[i,j].hist(A[:, i*4+j].cpu().exp(), bins=50)\n",
    "        \n",
    "\n",
    "fig.suptitle(\"Distribution of exp(A), each subplot is different dimension\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ab30744-b953-4edd-9b2e-39b67fcec1f5",
   "metadata": {},
   "source": [
    "B is applied uniformly across channel (and so its impact by channel is controlled by $\\Delta$), but varies over time by dimension.\n",
    "\n",
    "In particular when $B \\approx 0$ the input is ignored for that hidden dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5c059a56-bbae-4035-9735-6d275c518f35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x1000 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(4, 4, figsize=(15,10)) \n",
    "\n",
    "for i in range(4):\n",
    "    for j in range(4):\n",
    "        ax[i,j].bar(range(B.size(1)), B[0, :, 4*i+j].cpu())\n",
    "        ax[i,j]\n",
    "\n",
    "fig.suptitle('B over time; each subplot is a different hidden dimension');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab883661-864c-45e7-afab-e3af1ecfbaaa",
   "metadata": {},
   "source": [
    "# Reconstructing the model\n",
    "\n",
    "Now we've taken the model apart top-to-bottom let's put it back together again bottom-to-top using elementary PyTorch.\n",
    "In particular we will focus on an *iterative inference* scenario for generating text, rather than the parallel scan for training.\n",
    "\n",
    "## Implementing Discrete SSM\n",
    "\n",
    "The Discrete State Space model is straightforward to implement, being careful about dimensions:\n",
    "\n",
    "$$\\begin{align}\n",
    "h_0 &= 0 \\\\\n",
    "h_{t} &= \\overline{A} h_{t-1} + \\overline{B} x_{t} \\\\\n",
    "y_{t} &= C h_t + D x_t\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "49ae63ce-38d4-4a14-9fac-0b6d6db6d8de",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ssm(A_bar, # (B, D, N)\n",
    "        B_bar, # (B, D, N)\n",
    "        C,     # (B, N)\n",
    "        D,     # (D)\n",
    "        x,     # (B, D)\n",
    "        h=None, # (B,D,N)\n",
    "       ): #-> y=(B, D), h=(B,D,N)\n",
    "    if h is None:\n",
    "        h = torch.zeros_like(A_bar)\n",
    "    #   (B,D,N) * (B,D,N)   (B,D,N) * (B,D,1)\n",
    "    h =  A_bar  *    h    + B_bar   * x.unsqueeze(-1)\n",
    "    #                                           (D) * (B, D)\n",
    "    y = torch.einsum(\"b n, b d n -> b d\", C, h) + D * x\n",
    "\n",
    "    return y, h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "39183fc3-db47-4e96-b2d0-4fc35d7d91a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ssm(A_bar, # (B, D, N)\n",
    "        B_bar, # (B, D, N)\n",
    "        C,     # (B, N)\n",
    "        D,     # (D)\n",
    "        x,     # (B, D)\n",
    "        h=None, # (B,D,N)\n",
    "       ): #-> y=(B, D), h=(B,D,N)\n",
    "    if h is None:\n",
    "        h = torch.zeros_like(A_bar)\n",
    "    #   (B,D,N) * (B,D,N)   (B,D,N) * (B,D,1)\n",
    "    h =  A_bar  *    h    + B_bar   * x.unsqueeze(-1)\n",
    "    #    (B, 1, N)    (B,D,N) => (B,D)    (D) * (B, D)\n",
    "    y = (C.unsqueeze(1) * h).sum(axis=-1) + D * x\n",
    "\n",
    "    return y, h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05021028-5842-48ef-81cd-8b01bc7879f6",
   "metadata": {},
   "source": [
    "We can then get the same output as before by stepping through the model token by token:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "3ff001a7-b1e6-4b5a-b37c-3d5df3e374c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    h = None\n",
    "    l = A_bar.size(1)\n",
    "    ys = [None] * l\n",
    "    for i in range(l):\n",
    "        ys[i], h = ssm(A_bar[:, i], B_bar[:, i],\n",
    "                       C[:, i].float(), mixer.D, x[:, i], h)\n",
    "\n",
    "assert torch.allclose(y_t, torch.stack(ys, axis=1))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2c0255ab-2741-45c8-be7d-089cdef61ca3",
   "metadata": {},
   "source": [
    "## S6 (S4 with Selection)\n",
    "\n",
    "We run a modified version of algorithm 2 from the paper, where the time step L=1 is omitted since we advance 1 step at a time:\n",
    "\n",
    "```\n",
    "Input: 𝑥 ∶ (𝙱, 𝙳)\n",
    "Output: 𝑦 ∶ (𝙱, 𝙳)\n",
    "1: A ∶ (𝙳, 𝙽) ← 𝖯𝖺𝗋𝖺𝗆𝖾𝗍𝖾𝗋 (Diagonal NxN matrix)\n",
    "2: B ∶ (𝙱, 𝙽) ← 𝑠_𝐵 (𝑥)\n",
    "3: C ∶ (𝙱, 𝙽) ← 𝑠_𝐶 (𝑥)\n",
    "4: D : (1,N)  ← 𝖯𝖺𝗋𝖺𝗆𝖾𝗍𝖾𝗋\n",
    "4: ∆ ∶ (𝙱, 𝙳) ← 𝜏∆(𝖯𝖺𝗋𝖺𝗆𝖾𝗍𝖾𝗋+𝑠∆(𝑥))\n",
    "5: A_bar, B_bar ∶ (𝙱, 𝙳, 𝙽) ← 𝖽𝗂𝗌𝖼𝗋𝖾𝗍𝗂𝗓𝖾(∆, A, B)\n",
    "6: 𝑦 ← 𝖲𝖲𝖬(A, B, C, D)(𝑥)\n",
    "7: return 𝑦\n",
    "```\n",
    "\n",
    "One particular detail is $s_\\Delta$ is produced via a lower rank factorization $s_\\Delta = U_\\Delta V_\\Delta$, where the two matrices have a lower rank, here 32 times smaller.\n",
    "\n",
    "We can apply this in a straightforward manner (again being careful with dimensions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "226f5fd5-957d-4658-a39a-85303bfdfa1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def s6(x,          # (B,D)\n",
    "       A,          # (D,N)\n",
    "       s_B,        # (D, N)\n",
    "       s_C,        # (D, N)\n",
    "       U_Δ,  # (D, R)\n",
    "       V_Δ,  # (R, D)\n",
    "       bias_Δ, # (1, D)\n",
    "       D,          # (D)\n",
    "       # Softplus\n",
    "       t_Δ = lambda x: torch.log(1+torch.exp(x)),\n",
    "       h = None,  # (B,D,N)\n",
    "      ):\n",
    "    \n",
    "    B = x @ s_B  # (B, N)\n",
    "    C = x @ s_C  # (B, N)\n",
    "\n",
    "    Δ = t_Δ((x @ U_Δ) @ V_Δ + bias_Δ).unsqueeze(-1) # (B, D, 1)\n",
    "    \n",
    "\n",
    "    # Discretize    \n",
    "                     #(B,D,1) (D,N)\n",
    "    A_bar = torch.exp(Δ      *  A)  # (B,D,N)\n",
    "          #(B,D,1)  (B, 1, N)\n",
    "    B_bar = Δ *      B.unsqueeze(1) # (B,D,N)\n",
    "\n",
    "    # Apply SSM\n",
    "    return ssm(A_bar, B_bar, C.float(), D, x, h)    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a70723c9-85cb-4163-a6af-e0e45fe64e54",
   "metadata": {},
   "source": [
    "To run this we need to be able to extract the parameter matrices out from a mixer.\n",
    "The $U_\\Delta, s_B, s_C$ matrices are stored together for computational efficiency, so we separate out the weights for clarity based on dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "970a7c53-4e62-4c69-9648-2f0d0b299246",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_s6_params(mixer):\n",
    "    A = -torch.exp(mixer.A_log)\n",
    "    n = A.size(-1)\n",
    "\n",
    "    return dict(\n",
    "        A = A,\n",
    "        U_Δ = mixer.x_proj.weight[:-2*n].T,\n",
    "        s_B = mixer.x_proj.weight[-2*n:-n].T,\n",
    "        s_C = mixer.x_proj.weight[-n:].T,\n",
    "        V_Δ = mixer.dt_proj.weight.T,\n",
    "        bias_Δ =  mixer.dt_proj.bias,\n",
    "        D = mixer.D\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4a3aaca-9368-4490-bd1d-3ec6110f7f91",
   "metadata": {},
   "source": [
    "Then the S6 model can be run token by token, keeping track of the state `hs`, to get a similar output `y_t` as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "6da78496-aeec-4132-bb71-4c78ded05968",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hs = None\n",
    "outs = []\n",
    "with torch.inference_mode():\n",
    "    for x_i in [x[:, i] for i in range(pre_x.size(1))]:\n",
    "        out, hs = s6(x_i, **get_s6_params(mixer), h=hs)\n",
    "        outs.append(out)\n",
    "\n",
    "plot_diff(y_t, torch.stack(outs, axis=1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90ae1389-429b-4124-a9e1-b3ebee7fe365",
   "metadata": {},
   "source": [
    "## Iterative convolution\n",
    "\n",
    "The convolution looks back the input kernel_length steps, and as we progress iteratively through the sequence we need to store the state of that convolution.\n",
    "If we have those inputs we can pass it through the convolution layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "99f6c569-4448-4a36-84f7-96a068a2ea70",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    conv_output = rearrange(\n",
    "        mixer.conv1d(rearrange(pre_x, 'b l d -> b d l')),\n",
    "        'b d l -> b l d')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "928dcdc1-82f6-4418-af7d-f03ec2c03d7e",
   "metadata": {},
   "source": [
    "The convolution consists of weights (for each dimension, across the kernel) and a bias (for each dimension)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "1e4f01f8-4786-40cf-828c-c1caa9c4a383",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1536, 1, 4]), torch.Size([1536]))"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv_weight = mixer.conv1d.weight  # (D, 1, kernel_size)\n",
    "conv_bias = mixer.conv1d.bias      # (D)\n",
    "\n",
    "conv_weight.shape, conv_bias.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39dda08a-25b8-44e6-bf53-3fe8788ccfb8",
   "metadata": {},
   "source": [
    "The [convolution](https://en.wikipedia.org/wiki/Convolution) works by sliding the weights over the embeddings and performing a multiply and add.\n",
    "It can be calculated by:\n",
    "\n",
    "* left padding the input with zeros\n",
    "* for each time step in the convolution\n",
    "    - get the next convolution weight\n",
    "    - shift the input 1 place left\n",
    "    - multiply together and add to the result\n",
    "* add the convolution bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "10fc7ca8-23aa-4d6a-881a-dd5f430e8ce6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0014514923095703125"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel_size = conv_weight.size(-1)\n",
    "\n",
    "b, l, d = pre_x.size()\n",
    "pad_sz = mixer.conv1d.padding[0]\n",
    "\n",
    "with torch.inference_mode():\n",
    "    # Left pad the input with zeros\n",
    "    pad_x = torch.zeros(b, l+pad_sz, d, device=conv_weight.device)\n",
    "    pad_x[:,-l:,:] = pre_x\n",
    "\n",
    "    result = torch.zeros_like(pad_x)\n",
    "    # for each time step\n",
    "    for i in range(kernel_size):\n",
    "        shifted_input = torch.roll(pad_x, shifts=-i, dims=1)\n",
    "      # add to result: convolution weight * input shifted left\n",
    "        result += conv_weight[:, 0, i] * shifted_input\n",
    "    # add the bias\n",
    "    result += conv_bias\n",
    "\n",
    "plot_diff(conv_output, result)\n",
    "max_diff(conv_output, result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc23691b-3fb1-4aa8-878d-0a9a3d09c40c",
   "metadata": {},
   "source": [
    "Note that we drop the padding on the right (since those items aren't fully convolved)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "fa31f985-1815-4820-870b-966f3af51123",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 5, 1536])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_unpad = result[:, :-pad_sz]\n",
    "result_unpad.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "361a80e7-65c9-4ab8-b27f-22cc0fe1e6d8",
   "metadata": {},
   "source": [
    "This is how we obtained x from x_pre before, by applying the activation which gives relatively similar results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "f6d9ba2a-1475-4f88-a0f2-6428c584b79f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diff(x, mixer.act(result_unpad));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b531eda-852c-4927-a923-adda949dbe7d",
   "metadata": {},
   "source": [
    "Note that in particular the last value is just obtained by a dot product of the convolution weights with the last `kernel_size` (here 4) elements of the input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "f237407b-e7c3-4c5e-8b17-d20887933f52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0013649463653564453"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    convolution_end = torch.einsum('b k d, d k -> b d',\n",
    "                                   pre_x[:,-kernel_size:,:],\n",
    "                                   conv_weight.squeeze(1)\n",
    "                                  ) + conv_bias\n",
    "\n",
    "plot_diff(result_unpad[:,-1], convolution_end)\n",
    "max_diff(result_unpad[:,-1], convolution_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1931e8d8-6cf5-4068-b75a-4316e89837bb",
   "metadata": {},
   "source": [
    "So if we store the last `kernel_size` elements of x, for each dimension and batch item, we can perform the convolution at each step with a simple multiplication:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "220586e6-1539-43c8-bce6-9dc3a41fe114",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "conv_state = torch.zeros(b, kernel_size, d, device=pre_x.device).half()\n",
    "\n",
    "with torch.inference_mode():\n",
    "    conv_output = []\n",
    "    for pre_x_i in [pre_x[:, i] for i in range(pre_x.size(1))]:\n",
    "        # Move the convolution state back\n",
    "        conv_state = conv_state.roll(shifts=-1, dims=1)\n",
    "        conv_state[:, -1] = pre_x_i\n",
    "        conv_output.append(\n",
    "            torch.einsum('b k d, d k -> b d', \n",
    "                         conv_state,\n",
    "                         conv_weight.squeeze(1)) \n",
    "            + conv_bias)\n",
    "\n",
    "plot_diff(result_unpad, torch.stack(conv_output, dim=1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee40116-0456-4b4e-b523-081fa9216221",
   "metadata": {},
   "source": [
    "## Mixer\n",
    "\n",
    "With the iterative convolution we can now go back and implement the Mixer block step by step\n",
    "\n",
    "<img src=\"./mamba_architecture.png\" alt=\"Illustration of Mamba Mixer Block\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "2166b4a6-b7e3-404c-90c4-d051115c92b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mixer_step(\n",
    "          x,      # (B,D)\n",
    "          left_proj, # (D, E*D)\n",
    "          right_proj, # (D, E*D)\n",
    "          conv_weight, # (E*D, K)\n",
    "          conv_bias,   # (E*D)\n",
    "          out_proj,   # (E*D,D)\n",
    "          s6_params,\n",
    "          σ=lambda x: x/(1+torch.exp(-x)), # SiLU\n",
    "          h=None,       # (B,E*D,N)\n",
    "          conv_state=None, # (B, E*D, K)\n",
    "         ): # -> y, h, conv_state\n",
    "    \n",
    "    # Left branch\n",
    "    left_input = x @ left_proj   #(B, E*D)\n",
    "\n",
    "    # Initialise convolution state to 0\n",
    "    if conv_state is None:\n",
    "        b = x.size(0)\n",
    "        ed, k = conv_weight.shape\n",
    "        conv_state = torch.zeros((b,ed,k),\n",
    "                                 dtype=x.dtype,\n",
    "                                 device=x.device,\n",
    "                                 requires_grad=x.requires_grad)\n",
    "\n",
    "    # Conv, σ\n",
    "    conv_state = conv_state.roll(shifts=-1, dims=-1)\n",
    "    conv_state[..., -1] = left_input\n",
    "    conv_output = σ( (conv_state * conv_weight).sum(axis=-1) + \n",
    "                      conv_bias) # (B, E*D)\n",
    "\n",
    "    # SSM\n",
    "    ssm_output, h = s6(conv_output, **s6_params, h=h)\n",
    "\n",
    "    # Multiplication\n",
    "    block_act = ssm_output * σ(x @ right_proj)  # (B, E*D)\n",
    "\n",
    "    # Output\n",
    "    return block_act.to(out_proj.dtype) @ out_proj, h, conv_state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e716c89-79bb-4d01-bcc2-0e7556961ab5",
   "metadata": {},
   "source": [
    "As before we need to extract the matrices from the Mixer, in particular breaking `in_proj` apart for clarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f88b0967-4b61-474e-937b-72e64ad3a023",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mixer_params(mixer):\n",
    "    ed = mixer.in_proj.out_features // 2\n",
    "\n",
    "    return dict(\n",
    "      left_proj=mixer.in_proj.weight[:ed].T,\n",
    "      right_proj=mixer.in_proj.weight[ed:].T,\n",
    "      conv_weight=mixer.conv1d.weight.squeeze(1),\n",
    "      conv_bias=mixer.conv1d.bias,\n",
    "      out_proj=mixer.out_proj.weight.T,\n",
    "      s6_params=get_s6_params(mixer),\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83a766b0-21e9-4dd9-b494-8c132c95dff9",
   "metadata": {},
   "source": [
    "Running our version gets similar results to running the Mixer directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "87eb3197-c57e-4a94-bb3f-2f704d22f92a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = None\n",
    "conv_state = None\n",
    "outputs = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for hs_i in [hidden_states[:, i] for i in range(hidden_states.size(1))]:\n",
    "        output, h, conv_state = mixer_step(hs_i,\n",
    "                                           **get_mixer_params(mixer),\n",
    "                                           h=h, conv_state=conv_state)\n",
    "        outputs.append(output)\n",
    "\n",
    "plot_diff(mixer(hidden_states), torch.stack(outputs, axis=1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e8021f8-0e73-40fd-8cd2-8ffac4622749",
   "metadata": {},
   "source": [
    "For simplicity we can pass the mixer into the function to extract all the parameters for mixer_step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "758d68c9-88c2-4780-b89c-18704d891f1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_mixer(mixer, x, h=None, conv_state=None):\n",
    "    return mixer_step(x, **get_mixer_params(mixer), h=h, conv_state=conv_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a2fa257-1b54-463b-95a0-9e2d13f24e6f",
   "metadata": {},
   "source": [
    "We can then call it as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "7f7c0115-ef34-4ce0-b880-8772824c9ed1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = None\n",
    "conv_state = None\n",
    "outputs = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for hs_i in [hidden_states[:, i] for i in range(hidden_states.size(1))]:\n",
    "        output, h, conv_state = my_mixer(mixer, hs_i, h=h, conv_state=conv_state)\n",
    "        outputs.append(output)\n",
    "\n",
    "plot_diff(mixer(hidden_states), torch.stack(outputs, axis=1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c5875d4-c37a-4f24-ba04-2b2e189be5a8",
   "metadata": {},
   "source": [
    "## Connecting the blocks\n",
    "\n",
    "Recall that before we walked through the mixers, keeping the neural network hidden state (hs) and the unnormed residual (rs):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "b6f5ed9d-24c8-4105-91f9-f6137cd487b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.inference_mode():\n",
    "    hs0, rs0 = embedding(input_ids), None\n",
    "    hs1, rs1 = mixers[0](hs0, rs0)\n",
    "    hs2, rs2 = mixers[1](hs1, rs1)\n",
    "    #..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fe65bc4-6fe2-4147-a663-d44d80ade706",
   "metadata": {},
   "source": [
    "We can reproduce this using MyMixer by keeping track of the hidden states and convolutions in each layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "ab67ed1a-cd05-4a28-8983-3259bf19d43f",
   "metadata": {},
   "outputs": [],
   "source": [
    "hs1_ = []\n",
    "hs2_ = []\n",
    "\n",
    "with torch.inference_mode():\n",
    "    hs1_h, hs1_conv = None, None\n",
    "    hs2_h, hs2_conv = None, None\n",
    "    # ...\n",
    "    for token in [input_ids[:,i] for i in range(input_ids.size(1))]:\n",
    "        hs0_i = embedding(token)\n",
    "        rs0_i = torch.zeros_like(hs0_i)\n",
    "\n",
    "        rs1_i = (hs0_i + rs0_i).float()\n",
    "        rs1_i_norm = rms_norm(rs1_i.half(), mixers[0].norm.weight)\n",
    "        hs1_i, hs1_h, hs1_conv = my_mixer(mixers[0].mixer, rs1_i_norm,\n",
    "                                          h=hs1_h, conv_state=hs1_conv)\n",
    "        hs1_.append(hs1_i)\n",
    "\n",
    "        rs2_i = (hs1_i + rs1_i).float()\n",
    "        rs2_i_norm = rms_norm(rs2_i.half(), mixers[1].norm.weight)\n",
    "        hs2_i, hs2_h, hs2_conv = my_mixer(mixers[1].mixer, rs2_i_norm,\n",
    "                                          h=hs2_h, conv_state=hs2_conv)\n",
    "        hs2_.append(hs2_i)\n",
    "\n",
    "        #..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "693ffdfd-4ac3-4793-a2c8-7e7c6fffef16",
   "metadata": {},
   "source": [
    "This gives a relatively similar result to running it directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2332062b-9045-4e7f-8b85-48e8d7214b9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diff(hs1, torch.stack(hs1_, axis=1))\n",
    "plot_diff(hs2, torch.stack(hs2_, axis=1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68df6375-56e8-47c8-a5b3-5010662a2ac3",
   "metadata": {},
   "source": [
    "## Going through all the layers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "214a67b4-d23a-4304-a8c6-5e6349a5a658",
   "metadata": {},
   "source": [
    "We can write this programatically using the backbone layers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "9997c01c-fe31-4b46-aad4-c8fbcf69125a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModuleList(\n",
       "  (0-23): 24 x Block(\n",
       "    (mixer): Mamba(\n",
       "      (in_proj): Linear(in_features=768, out_features=3072, bias=False)\n",
       "      (conv1d): Conv1d(1536, 1536, kernel_size=(4,), stride=(1,), padding=(3,), groups=1536)\n",
       "      (act): SiLU()\n",
       "      (x_proj): Linear(in_features=1536, out_features=80, bias=False)\n",
       "      (dt_proj): Linear(in_features=48, out_features=1536, bias=True)\n",
       "      (out_proj): Linear(in_features=1536, out_features=768, bias=False)\n",
       "    )\n",
       "    (norm): RMSNorm()\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backbone.layers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19223822-5f12-447c-b3ad-0544c8e07a8b",
   "metadata": {},
   "source": [
    "Our implementation isn't as numerically stable so let's convert everything to float (removing the fp16):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "e6b6303e-c169-4fde-a12f-b674c2edcb45",
   "metadata": {},
   "outputs": [],
   "source": [
    "batckbone = backbone.float()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85654e89-86f5-4c19-b1ca-6e27466965a4",
   "metadata": {},
   "source": [
    "We need to keep an SSM state and convolution state for each block separately to proceed token by token."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "f8df9308-cab3-4c2f-a3af-a64b249fb0ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "hs = [None] * len(backbone.layers)\n",
    "conv_state = [None] * len(backbone.layers)\n",
    "\n",
    "with torch.inference_mode():\n",
    "    for token in [input_ids[:,i] for i in range(input_ids.size(1))]:\n",
    "        hsi = embedding(token)\n",
    "        rsi = torch.zeros_like(hsi)\n",
    "\n",
    "        for i, layer in enumerate(backbone.layers):\n",
    "            rsi = (hsi + rsi)\n",
    "            rsi_norm = rms_norm(rsi, layer.norm.weight)\n",
    "            hsi, hs[i], conv_state[i] = my_mixer(layer.mixer, rsi_norm,\n",
    "                                                 h=hs[i], conv_state=conv_state[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7bb7818-f0a5-4b91-915e-1cf754a1db0f",
   "metadata": {},
   "source": [
    "As before we can RMS normalise the last layers output and pass it through the language modelling head to get the logits (which have a small relative difference to the actual values):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "21bc2a99-1c30-4e59-92bf-18079b32806c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_prelogits = rms_norm(hsi + rsi, weight=norm_f.weight)\n",
    "my_logits = my_prelogits @ lm_head.weight.T\n",
    "\n",
    "plot_diff(logits[:,-1], my_logits);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d015d06-7d7b-4f81-8307-84f661001d48",
   "metadata": {},
   "source": [
    "This gives reasoanbly similar probabilities for common tokens:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "c6fea0bf-80f5-4ef1-9fcd-05b18a38f08e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Input value', ylabel='Difference in output'>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_probs = my_logits.softmax(dim=-1)\n",
    "\n",
    "plot_diff(probs, my_probs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68fcdd8-2c1a-4687-b6ed-527976473be8",
   "metadata": {},
   "source": [
    "## Aside: Size of the state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7d6638b-d3eb-4baa-a9f0-06f943b189cf",
   "metadata": {},
   "source": [
    "Note that the each convolution state has size `(B, E*D, K)` (where `K` is the kernel dimension), and each SSM hidden state has dimension `(B, E*D, N)`.\n",
    "So the total number of parameters to track per block is $BED(N+K)$ which is typically a small fraction of the roughly $3ED^2$ parameters per block"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "250335e6-a5a6-4fae-8fe3-af436162a1a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'The state is 1.4% of the parameters per item in batch'"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b, ed, k = conv_state[0].shape \n",
    "b, ed, k = hs[0].shape\n",
    "\n",
    "# E=2 here\n",
    "d = ed/2\n",
    "\n",
    "f'The state is {ed*(n+k) / (3*ed*d):0.1%} of the parameters per item in batch'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ebaf9e1-7147-4817-8885-86bcd9a3838d",
   "metadata": {},
   "source": [
    "We can check the parameters per model really is roughly $3ED^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "d622a372-7ed8-4192-a93f-4b26884d6376",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0657552083333333"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum([len(x.flatten()) for x in backbone.layers[0].parameters()]) / (3*ed*d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "132078d3-069e-43bf-ac2e-4b7136b6845e",
   "metadata": {},
   "source": [
    "## Greedy decoding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d6acac-65a2-4c9c-ba5b-8d8f79d2d75e",
   "metadata": {},
   "source": [
    "Now that we have the state we can iteratively continue token by token to generate the text:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "059aed56-1ebc-498c-8ae1-0b2d333084ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "output_tokens = [my_logits.argmax(dim=-1)]\n",
    "num_tokens = 11-1\n",
    "\n",
    "\n",
    "with torch.inference_mode():\n",
    "    for _ in range(num_tokens):\n",
    "        # Embedding\n",
    "        hsi = embedding(output_tokens[-1]).float()\n",
    "        rsi = torch.zeros_like(hsi)\n",
    "\n",
    "        # Backbone\n",
    "        for i, layer in enumerate(backbone.layers):\n",
    "            rsi = (hsi + rsi)\n",
    "            rsi_norm = rms_norm(rsi, layer.norm.weight)\n",
    "            hsi, hs[i], conv_state[i] = my_mixer(layer.mixer, rsi_norm,\n",
    "                                                 h=hs[i], conv_state=conv_state[i])\n",
    "\n",
    "        # LM Head\n",
    "        my_prelogits = rms_norm(hsi + rsi, weight=norm_f.weight)\n",
    "        my_logits = my_prelogits @ lm_head.weight.T\n",
    "\n",
    "        output_tokens.append(my_logits.argmax(dim=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "4f1c1268-6b3f-4758-9e15-84a9e2cac7d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " feel like I was a part of the team. I\n"
     ]
    }
   ],
   "source": [
    "for result in tokenizer.batch_decode(torch.stack(output_tokens, axis=-1)):\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd4891c2-0ccd-4c0f-907a-6c3a0d2bc3b9",
   "metadata": {},
   "source": [
    "Which generates exactly the same result as the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "16b67b75-6848-4da1-8a65-d67657c1883e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "So I was made to feel like I was a part of the team. I\n"
     ]
    }
   ],
   "source": [
    "with torch.inference_mode():\n",
    "    preds = model.generate(input_ids, len(input_tokens[0]) + 11)\n",
    "    \n",
    "for result in tokenizer.batch_decode(preds):\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22639b97-97ba-49c0-96b5-c521f2941c85",
   "metadata": {},
   "source": [
    "Note there is nothing special about greedy decoding here; we could equally use sampling or beam search in a similar way."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dcaa371-4191-42c0-940d-38b400bc4f1d",
   "metadata": {},
   "source": [
    "# What next?\n",
    "\n",
    "Mamba is a really promising alternative direction to Transformers, especially for very long texts (as an alternative of techniques to increase the size of the context window such as [LongRoPE](https://arxiv.org/abs/2402.13753)).\n",
    "Given the recent history of Large Language Models there are some obvious things to try with Mamba (such as scaling up the model size and training, instruction tuning, RHLF or DPO), which are straightforward but require compute and work on making the training more stable and adapting parameter efficient techniques such as LoRA.\n",
    "There are also potentially straightforward architecture optimisations; there have been many detailed studies on the transformer achitecture (such as in [the T5 paper](https://arxiv.org/abs/1910.10683)) that have helped make it better, these remain to be explored for Mamba.\n",
    "Because the model is straightforward and works on many long inputs (such as audio and DNA), there's also a lot of potential in multimodal models and other applications such as code generation.\n",
    "There are also some more speculative questions I find interesting overcoming the issues I have had using encoder transformers in long documents:\n",
    "\n",
    "* can this produce good representations for retrieval in large documents (such as dense vector embeddings, or in techniques like SPLADE or ColBERT)?\n",
    "* how can this be used for span classification for long documents (e.g. extracting relevant text from HTML pages)?\n",
    "* for document understanding does it make sense to use bidirectional Mamba models (in analogy to bidirectional LSTMs)? How does it compare with BERT?\n",
    "\n",
    "Mamba also opens new research for understanding and interpreting high performing language models, which have been solely concentrated on transformers.\n",
    "State selection gives an insight into understanding the hidden states, it would be interesting to understand how this interacts with representations of underlying features of the text (such as grammar) through the layers of the model.\n",
    "I look forward to seeing the new research to come on Mamba."
   ]
  }
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