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Speculative_Decoding_Implementation.ipynb
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speculative_decoding_implementation.ipynb
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},
"source": [
"<a href=\"https://colab.research.google.com/gist/staghado/7a84347154c39e934b559b72a7357c14/speculative_decoding_implementation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"# Speculative Decoding"
],
"metadata": {
"id": "niLCFiiLOfNq"
}
},
{
"cell_type": "markdown",
"source": [
"The objective of this Notebook is to implement the Speculative Decoding algorithm from the **[paper](https://arxiv.org/pdf/2211.17192.pdf)** : Fast Inference from Transformers via Speculative Decoding."
],
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"id": "ixTaO5N7N87_"
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},
{
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"source": [
"Speculative Decoding works by considering two models $M_p$ and $M_q$ where $M_p$ represents the target model(slow or expensive to evaluate) and $M_q$ is a more efficient model for the same task(what would happen if it's not the same task?). The conditional probability $p(x_t|x_{<t}) = p(x)$ is what we get when we run a prefix/context $x_{<t}$ through the model $M_p$. We have the same thing for q.\n",
"\n",
"\n",
"The algorithm is divided into three steps:\n",
"\n",
"\n",
"1. Use $M_q$ to autoregressively generate $\\gamma$ guesses\n",
"2. Use $M_p$ to evaluate all the guesses and their probabilities in *parallel* and accept those that give the same distribution\n",
"3. Sample an additional token from an adjusted distribution to fix the first rejected token or to add an additional one if they are all accepeted\n",
"\n",
"Each time the target model is run in parallel, a token is either accepted or generated thus even in the worst case(all completions generated by $M_q$ are rejected), the number of serial runs of the target model can not be larger than that of the simple autoregressive method. But it can generate up to $\\gamma + 1$ new tokens depending on how well is $M_q$ an approximaton of $M_p$. This means that choosing $\\gamma$ is crucial.\n",
"\n",
"## Speculative Sampling\n",
"\n",
"To sample a token $x$ from $p(x)$, we sample $x$ from $q(x)$. If the acceptance rate $r = \\frac{p(x)}{q(x)}$ is bigger than 1 we accept $x$ else we reject it with a probability equal to $1 - r$ and sample x again from an adjusted distribution defined as $p'(x) = norm(max(0, p(x) - q(x))) = \\frac{p(x)-min(q(x), p(x))}{\\sum_{x'}p(x')-min(q(x'), p(x'))}$.\n",
"\n",
"This ensures that each sample $x$ is indeed from $p(x)$."
],
"metadata": {
"id": "1HOc2aoCTsLv"
}
},
{
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"source": [
"I am going to implement this algorithm in Python and illustrate its effectiveness using the GPT2 model."
],
"metadata": {
"id": "4ZM0xneAjKOZ"
}
},
{
"cell_type": "markdown",
"source": [
"# Implementation"
],
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"id": "xHy4pafXbBOH"
}
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"outputId": "074c0353-e7eb-42c3-94b1-685c843dfb16"
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{
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"name": "stderr",
"text": [
"/usr/local/lib/python3.10/dist-packages/huggingface_hub/utils/_token.py:88: UserWarning: \n",
"The secret `HF_TOKEN` does not exist in your Colab secrets.\n",
"To authenticate with the Hugging Face Hub, create a token in your settings tab (https://huggingface.co/settings/tokens), set it as secret in your Google Colab and restart your session.\n",
"You will be able to reuse this secret in all of your notebooks.\n",
"Please note that authentication is recommended but still optional to access public models or datasets.\n",
" warnings.warn(\n"
]
},
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"source": [
"import torch\n",
"import torch.nn.functional as F\n",
"import numpy as np\n",
"from transformers import GPT2LMHeadModel, GPT2Tokenizer\n",
"\n",
"\n",
"device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
"\n",
"# Load model and tokenizer\n",
"small_model = GPT2LMHeadModel.from_pretrained('gpt2')\n",
"tokenizer = GPT2Tokenizer.from_pretrained('gpt2')\n",
"small_model.eval()\n",
"\n",
"big_model = GPT2LMHeadModel.from_pretrained('gpt2-medium')\n",
"# tokenizer = GPT2Tokenizer.from_pretrained('gpt2-base')\n",
"big_model.eval();"
]
},
{
"cell_type": "code",
"source": [
"def normalize_probability(p, q):\n",
" # calculate max(0, p - q)\n",
" max_p_q = np.maximum(0, p - q)\n",
"\n",
" # sum of max(0, p - q)\n",
" sum_max_p_q = np.sum(max_p_q)\n",
"\n",
" return max_p_q / sum_max_p_q\n",
"\n",
"@torch.inference_mode()\n",
"def speculative_decoding(big_model, small_model, tokenizer, context, gamma, max_len, device='cpu'):\n",
" big_model.to(device)\n",
" small_model.to(device)\n",
"\n",
" # Prepare for generation\n",
" input_ids = tokenizer.encode(context, return_tensors='pt').to(device)\n",
" output_tokens = input_ids.squeeze(0).tolist()\n",
" print(f\"prefix : {output_tokens}\")\n",
" seq_len = len(output_tokens)\n",
" T = seq_len + max_len\n",
"\n",
" while len(output_tokens) < T:\n",
" print(\"\\n\")\n",
" input_ids = torch.tensor(output_tokens, device=device).unsqueeze(0)\n",
" print(input_ids)\n",
"\n",
" # Autoregressive prediction using the small model\n",
" qs = []\n",
" for _ in range(gamma):\n",
" # Keep only the last gamma tokens\n",
" if input_ids.size(1) > gamma:\n",
" current_input_ids = input_ids[:, -gamma:]\n",
" else:\n",
" current_input_ids = input_ids\n",
"\n",
" logits = small_model(current_input_ids).logits\n",
" q = F.softmax(logits, dim=-1)\n",
" token_id = torch.argmax(q[:, -1, :], dim=1)\n",
" qs.append(q[torch.arange(q.size(0)), -1, token_id].item())\n",
"\n",
" input_ids = torch.cat([input_ids, token_id.unsqueeze(-1)], dim=1)\n",
"\n",
" #print(input_ids)\n",
" print(f\"qs : {qs}\")\n",
" #print(f\"q : {q.shape}\")\n",
"\n",
" # Parallel prediction using the big model for all gamma tokens\n",
" sequences = []\n",
" for i in range(0, gamma):\n",
" flattened_slice = input_ids[0, :seq_len+i+1].tolist()\n",
" sequence = [tokenizer.eos_token_id] * (gamma + 1 - i) + flattened_slice\n",
" sequences.append(sequence)\n",
"\n",
" big_model_input_ids = torch.tensor(sequences, device=device)\n",
" #print(f\"sequences : \\n {big_model_input_ids}\")\n",
" logits = big_model(big_model_input_ids).logits\n",
" p = F.softmax(logits, dim=-1)\n",
" max_indices = torch.argmax(p[:, -1, :], dim=1)\n",
" ps = p[torch.arange(p.size(0)), -1, max_indices].tolist()\n",
"\n",
" print(f\"ps : {ps}\")\n",
" #print(f\"p : {p.shape}\")\n",
"\n",
" # Rejection sampling (is this the term?)\n",
" for i in range(gamma):\n",
" r = np.random.rand()\n",
" if r < min(1, ps[i] / qs[i]):\n",
" print(f\"Accept token --- {r=}\")\n",
" output_tokens.append(input_ids[0, i].item())\n",
" else:\n",
" print(f\"Reject token --- {r=}\")\n",
" # Resample from modified distribution (p - q)+\n",
" p_values = p[i, -1].cpu().numpy() # Mp(x|prefix + [x1, ..., xi])\n",
" q_values = q[0, i].cpu().numpy() # Mq(x|prefix + [x1, ..., xi])\n",
" modified_dist = normalize_probability(p_values, q_values)\n",
" resampled_token = np.argmax(modified_dist)\n",
" output_tokens.append(resampled_token)\n",
" break\n",
"\n",
" if len(output_tokens) >= T:\n",
" break\n",
"\n",
" return tokenizer.decode(output_tokens)"
],
"metadata": {
"id": "EIivAKNxwUcf"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"speculative_decoding(big_model, small_model, tokenizer, context=\"?\", gamma=10, max_len=20, device='cpu')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "Gt8oCZarwWm7",
"outputId": "27767a5e-bcbe-4406-d7be-f7c406a2f228"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"prefix : [30]\n",
"\n",
"\n",
"tensor([[30]])\n",
"qs : [0.19046689569950104, 0.9974822402000427, 0.04046527296304703, 0.014151415787637234, 0.17853666841983795, 0.24155157804489136, 0.1434582620859146, 0.35640135407447815, 0.46105727553367615, 0.2116636484861374]\n",
"ps : [0.9997956156730652, 0.04178453981876373, 0.009618090465664864, 0.07049383968114853, 0.28149107098579407, 0.12991298735141754, 0.3220902383327484, 0.31611168384552, 0.21645575761795044, 0.005884469486773014]\n",
"Accept token --- r=0.7949574078488768\n",
"Reject token --- r=0.9867005161530952\n",
"\n",
"\n",
"tensor([[ 30, 30, 464]])\n",
"qs : [0.017411954700946808, 0.5770674347877502, 0.15108421444892883, 0.3730606436729431, 0.190965935587883, 0.13193561136722565, 0.3160296678543091, 0.27728918194770813, 0.07303090393543243, 0.06415461748838425]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.4111337661743164, 0.2350817173719406, 0.4014590084552765, 0.19441832602024078, 0.17333969473838806, 0.37568894028663635, 0.4460189640522003, 0.08329732716083527]\n",
"Accept token --- r=0.9124535407715543\n",
"Reject token --- r=0.1485821175199964\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471]])\n",
"qs : [0.09757586568593979, 0.3589145243167877, 0.08827701210975647, 0.16411790251731873, 0.1429288387298584, 0.34841737151145935, 0.24378572404384613, 0.23079589009284973, 0.3766885995864868, 0.3927386403083801]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.3080926239490509, 0.12946657836437225, 0.14953801035881042, 0.11066985875368118, 0.324092298746109, 0.274862676858902]\n",
"Accept token --- r=0.2584475772707704\n",
"Reject token --- r=0.4002190391692598\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471]])\n",
"qs : [0.23126403987407684, 0.20943371951580048, 0.6963736414909363, 0.3198361098766327, 0.8611474633216858, 0.7109270691871643, 0.918040931224823, 0.7878872752189636, 0.918040931224823, 0.7878872752189636]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.04369279369711876, 0.601730227470398, 0.1389172524213791, 0.7183928489685059]\n",
"Reject token --- r=0.5812715698616406\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198]])\n",
"qs : [0.9983175992965698, 0.039442963898181915, 0.08644590526819229, 0.2016361951828003, 0.33566009998321533, 0.999723494052887, 0.12391902506351471, 0.3279598355293274, 0.8937756419181824, 0.5827931761741638]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.17599572241306305, 0.09412114322185516, 0.3690154552459717]\n",
"Reject token --- r=0.33250058623219925\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317]])\n",
"qs : [0.07126375287771225, 0.16335107386112213, 0.17992806434631348, 0.96848464012146, 0.139245867729187, 0.16008779406547546, 0.9997510313987732, 0.4954289495944977, 0.7942255139350891, 0.9997485280036926]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.2301088571548462]\n",
"Accept token --- r=0.8550008414400189\n",
"Reject token --- r=0.4859357257031437\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717]])\n",
"qs : [0.06684976816177368, 0.08340673893690109, 0.09082558751106262, 0.2181549370288849, 0.24584779143333435, 0.13503772020339966, 0.12941280007362366, 0.11891001462936401, 0.2181248664855957, 0.5539020895957947]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Accept token --- r=0.2566709926371308\n",
"Reject token --- r=0.2608691919724604\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471]])\n",
"qs : [0.1881367415189743, 0.9962267875671387, 0.09159476310014725, 0.32305991649627686, 0.9997047781944275, 0.6163424253463745, 0.8433228135108948, 0.9997914433479309, 0.8690729737281799, 0.924921989440918]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Reject token --- r=0.8588050024973333\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471, 198]])\n",
"qs : [0.9962267875671387, 0.09159476310014725, 0.32305991649627686, 0.9997047781944275, 0.6163424253463745, 0.8433228135108948, 0.9997914433479309, 0.8690729737281799, 0.924921989440918, 0.9997794032096863]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Accept token --- r=0.015186309015798094\n",
"Reject token --- r=0.5741618338963972\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471, 198,\n",
" 30, 471]])\n",
"qs : [0.3230714797973633, 0.9677258729934692, 0.13142770528793335, 0.5596310496330261, 0.6324248909950256, 0.9996699094772339, 0.7634159922599792, 0.9043468236923218, 0.8917067050933838, 0.9997115731239319]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Reject token --- r=0.5911273052527936\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471, 198,\n",
" 30, 471, 198]])\n",
"qs : [0.9677258729934692, 0.13142770528793335, 0.5596310496330261, 0.6324248909950256, 0.9996699094772339, 0.7634159922599792, 0.9043468236923218, 0.8917067050933838, 0.9997115731239319, 0.8051623702049255]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Accept token --- r=0.11129868971047663\n",
"Reject token --- r=0.3525345294785772\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471, 198,\n",
" 30, 471, 198, 30, 471]])\n",
"qs : [0.6963173747062683, 0.831706702709198, 0.7058556079864502, 0.8536752462387085, 0.8859078288078308, 0.9996699094772339, 0.7634159922599792, 0.9043468236923218, 0.8917067050933838, 0.9997115731239319]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Reject token --- r=0.6918611788359988\n",
"\n",
"\n",
"tensor([[ 30, 30, 464, 30, 471, 30, 471, 198, 317, 30, 717, 30, 471, 198,\n",
" 30, 471, 198, 30, 471, 198]])\n",
"qs : [0.831706702709198, 0.7058556079864502, 0.8536752462387085, 0.8859078288078308, 0.9996699094772339, 0.7634159922599792, 0.9043468236923218, 0.8917067050933838, 0.9997115731239319, 0.8051623702049255]\n",
"ps : [0.12164535373449326, 0.00834901537746191, 0.03454000502824783, 0.490310937166214, 0.0907512679696083, 0.3403111398220062, 0.9992044568061829, 0.2770899832248688, 0.12410762161016464, 0.039666011929512024]\n",
"Reject token --- r=0.7882347905816853\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"'??The? U? U\\n A? first? U\\n? U\\n? U\\n A'"
],
"application/vnd.google.colaboratory.intrinsic+json": {
"type": "string"
}
},
"metadata": {},
"execution_count": 119
}
]
},
{
"cell_type": "markdown",
"source": [
"We can see that there is a problem of repetition which is due to the argmax sapmling(greedy decoding). We can use other sampling methods like beam search, topk, topp(nucleus), etc"
],
"metadata": {
"id": "DOqcUDzX-4_I"
}
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "gEKtOMdy-sVd"
},
"execution_count": null,
"outputs": []
}
]
}
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