A language mannequin is a chance distribution over sequences of tokens. If you practice a language mannequin, you need to measure how precisely it predicts human language use. This can be a tough process, and also you want a metric to guage the mannequin. On this article, you’ll study concerning the perplexity metric. Particularly, you’ll study:
- What’s perplexity, and tips on how to compute it
- How one can consider the perplexity of a language mannequin with pattern knowledge
Let’s get began.
Evaluating Perplexity on Language Fashions
Photograph by Lucas Davis. Some rights reserved.
Overview
This text is split into two components; they’re:
- What Is Perplexity and How one can Compute It
- Consider the Perplexity of a Language Mannequin with HellaSwag Dataset
What Is Perplexity and How one can Compute It
Perplexity is a measure of how nicely a language mannequin predicts a pattern of textual content. It’s outlined because the inverse of the geometric imply of the chances of the tokens within the pattern. Mathematically, perplexity is outlined as:
$$
PPL(x_{1:L}) = prod_{i=1}^L p(x_i)^{-1/L} = expbig(-frac{1}{L} sum_{i=1}^L log p(x_i)massive)
$$
Perplexity is a perform of a selected sequence of tokens. In follow, it’s extra handy to compute perplexity because the imply of the log possibilities, as proven within the formulation above.
Perplexity is a metric that quantifies how a lot a language mannequin hesitates concerning the subsequent token on common. If the language mannequin is totally sure, the perplexity is 1. If the language mannequin is totally unsure, then each token within the vocabulary is equally doubtless; the perplexity is the same as the vocabulary dimension. You shouldn’t anticipate perplexity to transcend this vary.
Consider the Perplexity of a Language Mannequin with HellaSwag Dataset
Perplexity is a dataset-dependent metric. One dataset you need to use is HellaSwag. It’s a dataset with practice, take a look at, and validation splits. It’s obtainable on the Hugging Face hub, and you may load it with the next code:
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import datasets
dataset = datasets.load_dataset(“HuggingFaceFW/hellaswag”) print(dataset)
for pattern in dataset[“validation”]: print(pattern) break |
Working this code will print the next:
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DatasetDict({ practice: Dataset({ options: [‘ind’, ‘activity_label’, ‘ctx_a’, ‘ctx_b’, ‘ctx’, ‘endings’, ‘source_id’, ‘split’, ‘split_type’, ‘label’], num_rows: 39905 }) take a look at: Dataset({ options: [‘ind’, ‘activity_label’, ‘ctx_a’, ‘ctx_b’, ‘ctx’, ‘endings’, ‘source_id’, ‘split’, ‘split_type’, ‘label’], num_rows: 10003 }) validation: Dataset({ options: [‘ind’, ‘activity_label’, ‘ctx_a’, ‘ctx_b’, ‘ctx’, ‘endings’, ‘source_id’, ‘split’, ‘split_type’, ‘label’], num_rows: 10042 }) }) {‘ind’: 24, ‘activity_label’: ‘Roof shingle removing’, ‘ctx_a’: ‘A person is sitting on a roof.’, ‘ctx_b’: ‘he’, ‘ctx’: ‘A person is sitting on a roof. he’, ‘endings’: [ ‘is using wrap to wrap a pair of skis.’, ‘is ripping level tiles off.’, “is holding a rubik’s cube.”, ‘starts pulling up roofing on a roof.’ ], ‘source_id’: ‘activitynet~v_-JhWjGDPHMY’, ‘cut up’: ‘val’, ‘split_type’: ‘indomain’, ‘label’: ‘3’} |
You’ll be able to see that the validation cut up has 10,042 samples. That is the dataset you’ll use on this article. Every pattern is a dictionary. The important thing "activity_label" describes the exercise class, and the important thing "ctx" gives the context that must be accomplished. The mannequin is anticipated to finish the sequence by choosing one of many 4 endings. The important thing "label", with values 0 to three, signifies which ending is right.
With this, you possibly can write a brief code to guage your personal language mannequin. Let’s use a small mannequin from Hugging Face for instance:
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import datasets import torch import torch.nn.practical as F import tqdm import transformers
mannequin = “openai-community/gpt2”
# Load the mannequin torch.set_default_device(“cuda” if torch.cuda.is_available() else “cpu”) tokenizer = transformers.AutoTokenizer.from_pretrained(mannequin) mannequin = transformers.AutoModelForCausalLM.from_pretrained(mannequin)
# Load the dataset: HellaSwag has practice, take a look at, and validation splits dataset = datasets.load_dataset(“hellaswag”, cut up=“validation”)
# Consider the mannequin: Compute the perplexity of every ending num_correct = 0 for pattern in tqdm.tqdm(dataset): # tokenize textual content from the pattern textual content = tokenizer.encode(” “ + pattern[“activity_label”] + “. “ + pattern[“ctx”]) endings = [tokenizer.encode(” “ + x) for x in sample[“endings”]] # 4 endings groundtruth = int(pattern[“label”]) # integer, 0 to three # generate logits for every ending perplexities = [0.0] * 4 for i, ending in enumerate(endings): # run your complete enter and ending to the mannequin input_ids = torch.tensor(textual content + ending).unsqueeze(0) output = mannequin(input_ids).logits # extract the logits for every token within the ending logits = output[0, len(text)–1:, :] token_probs = F.log_softmax(logits, dim=–1) # accumulate the chance of producing the ending log_prob = 0.0 for j, token in enumerate(ending): log_prob += token_probs[j, token] # convert the sum of log possibilities to perplexity perplexities[i] = torch.exp(–log_prob / len(ending)) # print the perplexity of every ending print(pattern[“activity_label”] + “. “ + pattern[“ctx”]) right = perplexities[groundtruth] == min(perplexities) for i, p in enumerate(perplexities): if i == groundtruth: image = ‘(O)’ if right else ‘(!)’ elif p == min(perplexities): image = ‘(X)’ else: image = ‘ ‘ print(f“Ending {i}: {p:.4g} {image} – {pattern[‘endings’][i]}”) if right: num_correct += 1
print(f“Accuracy: {num_correct}/{len(dataset)} = {num_correct / len(dataset):.4f}”) |
This code hundreds the smallest GPT-2 mannequin from the Hugging Face Hub. It’s a 124M-parameter mannequin which you can simply run on a low-profile pc. The mannequin and tokenizer are loaded utilizing the Hugging Face transformers library. You additionally load the HellaSwag validation dataset.
Within the for-loop, you tokenize the exercise label and the context. You additionally tokenize every of the 4 endings. Observe that tokenizer.encode() is the strategy for utilizing the tokenizer from the transformers library. It’s totally different from the tokenizer object you used within the earlier article.
Subsequent, for every ending, you run the concatenated enter and ending to the mannequin. The input_ids tensor is a 2D tensor of integer token IDs with the batch dimension 1. The mannequin returns an object, through which you extract the output logits tensor. That is totally different from the mannequin you constructed within the earlier article as this can be a mannequin object from the transformers library. You’ll be able to simply swap it together with your educated mannequin object with minor modifications.
GPT-2 is a decoder-only transformer mannequin. It processes the enter with a causal masks. For an enter tensor of form $(1, L)$, the output logits tensor has form $(1, L, V)$, the place $V$ is the vocabulary dimension. The output at place $p$ corresponds to the mannequin’s estimate of the token at place $p+1$, relying on the enter at positions 1 to $p$. Subsequently, you extract the logits beginning at offset $n-1$, the place $n$ is the size of the mixed exercise label and context. You then convert the logits to log possibilities and compute the common over the size of every ending.
The worth token_probs[j, token] is the log chance at place j for the token with ID token. The imply log-probability of every token within the ending is used to compute the perplexity. An excellent mannequin is anticipated to determine the proper ending with the bottom perplexity. You’ll be able to consider a mannequin by counting the variety of right predictions over your complete HellaSwag validation dataset. If you run this code, you will note the next:
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… Finance and Enterprise. [header] How one can purchase a peridot Evaluating Perplexity on Language Fashions Have a look at a wide range of stones… Ending 0: 13.02 (X) – It would be best to watch a number of of the gem stones, significantly eme… Ending 1: 30.19 – Not solely are they among the many delicates amongst them, however they are often… Ending 2: 34.96 (!) – Familiarize your self with the totally different shades that it is available in, … Ending 3: 28.85 – Neither peridot nor many different jade or allekite stones are necess… Household Life. [header] How one can inform in case your teen is being abused Evaluating Perplexity on Language Fashions Take note of… Ending 0: 16.58 – Attempt to determine why they’re dressing one thing that’s frowned… Ending 1: 22.01 – Learn the next as a rule for figuring out your teen’s behaviou… Ending 2: 15.21 (O) – [substeps] For example, your teen might attempt to conceal the indicators of a… Ending 3: 23.91 – [substeps] Ask your teen if they’ve black tights (with stripper… Accuracy: 3041/10042 = 0.3028 |
The code prints the perplexity of every ending and marks the proper reply with (O) or (!) and the mannequin’s mistaken prediction with (X). You’ll be able to see that GPT-2 has a perplexity of 10 to twenty, even for an accurate reply. Superior LLMs can obtain perplexity under 10, even with a a lot bigger vocabulary dimension than GPT-2. Extra essential is whether or not the mannequin can determine the proper ending: the one which naturally completes the sentence. It needs to be the one with the bottom perplexity; in any other case, the mannequin can’t generate the proper ending. GPT-2 achieves solely 30% accuracy on this dataset.
You may as well repeat the code with a unique mannequin. Listed here are the outcomes:
- mannequin
openai-community/gpt2: That is the smallest GPT-2 mannequin with 124M parameters, used within the code above. The accuracy is 3041/10042 or 30.28% - mannequin
openai-community/gpt2-medium: That is the bigger GPT-2 mannequin with 355M parameters. The accuracy is 3901/10042 or 38.85% - mannequin
meta-llama/Llama-3.2-1B: That is the smallest mannequin within the Llama household with 1B parameters. The accuracy is 5731/10042 or 57.07%
Subsequently, it’s pure to see increased accuracy with bigger fashions.
Observe that you shouldn’t evaluate perplexities throughout fashions with vastly totally different architectures. Since perplexity is a metric within the vary of 1 to the vocabulary dimension, it extremely is dependent upon the tokenizer. You’ll be able to see the rationale whenever you evaluate the perplexity within the code above after changing GPT-2 with Llama 3.2 1B: The perplexity is an order of magnitude increased for Llama 3, however the accuracy is certainly higher. It’s because GPT-2 has a vocabulary dimension of solely 50,257, whereas Llama 3.2 1B has a vocabulary dimension of 128,256.
Additional Readings
Under are some assets that you could be discover helpful:
Abstract
On this article, you realized concerning the perplexity metric and tips on how to consider the perplexity of a language mannequin with the HellaSwag dataset. Particularly, you realized:
- Perplexity measures how a lot a mannequin hesitates concerning the subsequent token on common.
- Perplexity is a metric delicate to vocabulary dimension.
- Computing perplexity means computing the geometric imply of the chances of the tokens within the pattern.
