import{S as at,i as et,s as tt,e as p,k as r,w as R,t as n,Y as b,M as nt,c as o,d as a,m as h,a as m,x as J,h as l,Z as _,b as c,N as re,G as e,g as i,y as U,L as lt,q as Y,o as Z,B as K,v as it}from"../chunks/vendor-hf-doc-builder.js";import{I as he}from"../chunks/IconCopyLink-hf-doc-builder.js";import{C as ce}from"../chunks/CodeBlock-hf-doc-builder.js";import{D as pt}from"../chunks/DocNotebookDropdown-hf-doc-builder.js";function ot(de){let k,ks,P,q,os,A,ya,ms,xa,Ps,S,zs,$,ba,Q,_a,ka,Ts,v,Pa,qs,Xe='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>=</mo><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo separator="true">,</mo><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><mo>\u2026</mo><mo separator="true">,</mo><msub><mi>x</mi><mi>t</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">X = (x_0, x_1, \\dots, x_t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">\u2026</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>',$s,Es,Re='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span></span></span></span>',Ms,js,Je='<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>PPL</mtext><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mi>exp</mi><mo>\u2061</mo><mrow><mo fence="true">{</mo><mrow><mo>\u2212</mo><mfrac><mn>1</mn><mi>t</mi></mfrac><munderover><mo>\u2211</mo><mi>i</mi><mi>t</mi></munderover><mi>log</mi><mo>\u2061</mo><msub><mi>p</mi><mi>\u03B8</mi></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mi mathvariant="normal">\u2223</mi><msub><mi>x</mi><mrow><mo>&lt;</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">\\text{PPL}(X) = \\exp \\left\\{ {-\\frac{1}{t}\\sum_i^t \\log p_\\theta (x_i|x_{&lt;i}) } \\right\\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">PPL</span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3.0582em;vertical-align:-1.2777em;"></span><span class="mop">exp</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mord">\u2212</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7806em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">\u2211</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">\u03B8</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">\u2223</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">&lt;</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size4">}</span></span></span></span></span></span></span>',Ls,y,za,Cs,Ue='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>log</mi><mo>\u2061</mo><msub><mi>p</mi><mi>\u03B8</mi></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mi mathvariant="normal">\u2223</mi><msub><mi>x</mi><mrow><mo>&lt;</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\\log p_\\theta (x_i|x_{&lt;i})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">\u03B8</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">\u2223</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">&lt;</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>',Gs,Is,Ye='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mo>&lt;</mo><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">x_{&lt;i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6079em;vertical-align:-0.1774em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">&lt;</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span></span></span></span>',Ws,As,E,Ta,B,qa,$a,Ss,z,M,rs,D,Ea,hs,Ma,Bs,V,ja,Ds,j,ge,Ns,u,La,ss,Ca,Ga,Os,Ze='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>\u03B8</mi></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mi>t</mi></msub><mi mathvariant="normal">\u2223</mi><msub><mi>x</mi><mrow><mo>&lt;</mo><mi>t</mi></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p_\\theta(x_t|x_{&lt;t})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">\u03B8</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">\u2223</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">&lt;</span><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>',Fs,Hs,Ke='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span></span></span></span>',Xs,Rs,f,Ia,Js,Qe='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span>',Us,Ys,Ve='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">x_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">\u200B</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>',Zs,Ks,st='<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>\u2212</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">k-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">\u2212</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span>',Qs,Vs,L,ue,sa,as,Wa,aa,es,Aa,ea,C,fe,ta,ts,Sa,na,T,G,cs,N,Ba,ds,Da,la,ns,Na,ia,O,pa,ls,Oa,oa,F,ma,g,Fa,gs,Ha,Xa,us,Ra,Ja,fs,Ua,Ya,ws,Za,Ka,ra,H,ha,is,Qa,ca,d,Va,vs,se,ae,ys,ee,te,xs,ne,le,bs,ie,pe,_s,oe,me,da;return A=new he({}),S=new pt({props:{classNames:"absolute z-10 right-0 top-0",options:[{label:"Mixed",value:"https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/perplexity.ipynb"},{label:"PyTorch",value:"https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/pytorch/perplexity.ipynb"},{label:"TensorFlow",value:"https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/tensorflow/perplexity.ipynb"},{label:"Mixed",value:"https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/perplexity.ipynb"},{label:"PyTorch",value:"https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/pytorch/perplexity.ipynb"},{label:"TensorFlow",value:"https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/tensorflow/perplexity.ipynb"}]}}),D=new he({}),N=new he({}),O=new ce({props:{code:`from transformers import GPT2LMHeadModel, GPT2TokenizerFast

device = "cuda"
model_id = "gpt2-large"
model = GPT2LMHeadModel.from_pretrained(model_id).to(device)
tokenizer = GPT2TokenizerFast.from_pretrained(model_id)`,highlighted:`<span class="hljs-keyword">from</span> transformers <span class="hljs-keyword">import</span> GPT2LMHeadModel, GPT2TokenizerFast

device = <span class="hljs-string">&quot;cuda&quot;</span>
model_id = <span class="hljs-string">&quot;gpt2-large&quot;</span>
model = GPT2LMHeadModel.from_pretrained(model_id).to(device)
tokenizer = GPT2TokenizerFast.from_pretrained(model_id)`}}),F=new ce({props:{code:`from datasets import load_dataset

test = load_dataset("wikitext", "wikitext-2-raw-v1", split="test")
encodings = tokenizer("\\n\\n".join(test["text"]), return_tensors="pt")`,highlighted:`<span class="hljs-keyword">from</span> datasets <span class="hljs-keyword">import</span> load_dataset

test = load_dataset(<span class="hljs-string">&quot;wikitext&quot;</span>, <span class="hljs-string">&quot;wikitext-2-raw-v1&quot;</span>, split=<span class="hljs-string">&quot;test&quot;</span>)
encodings = tokenizer(<span class="hljs-string">&quot;\\n\\n&quot;</span>.join(test[<span class="hljs-string">&quot;text&quot;</span>]), return_tensors=<span class="hljs-string">&quot;pt&quot;</span>)`}}),H=new ce({props:{code:`import torch
from tqdm import tqdm

max_length = model.config.n_positions
stride = 512

nlls = []
for i in tqdm(range(0, encodings.input_ids.size(1), stride)):
    begin_loc = max(i + stride - max_length, 0)
    end_loc = min(i + stride, encodings.input_ids.size(1))
    trg_len = end_loc - i  # may be different from stride on last loop
    input_ids = encodings.input_ids[:, begin_loc:end_loc].to(device)
    target_ids = input_ids.clone()
    target_ids[:, :-trg_len] = -100

    with torch.no_grad():
        outputs = model(input_ids, labels=target_ids)
        neg_log_likelihood = outputs[0] * trg_len

    nlls.append(neg_log_likelihood)

ppl = torch.exp(torch.stack(nlls).sum() / end_loc)`,highlighted:`<span class="hljs-keyword">import</span> torch
<span class="hljs-keyword">from</span> tqdm <span class="hljs-keyword">import</span> tqdm

max_length = model.config.n_positions
stride = <span class="hljs-number">512</span>

nlls = []
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> tqdm(<span class="hljs-built_in">range</span>(<span class="hljs-number">0</span>, encodings.input_ids.size(<span class="hljs-number">1</span>), stride)):
    begin_loc = <span class="hljs-built_in">max</span>(i + stride - max_length, <span class="hljs-number">0</span>)
    end_loc = <span class="hljs-built_in">min</span>(i + stride, encodings.input_ids.size(<span class="hljs-number">1</span>))
    trg_len = end_loc - i  <span class="hljs-comment"># may be different from stride on last loop</span>
    input_ids = encodings.input_ids[:, begin_loc:end_loc].to(device)
    target_ids = input_ids.clone()
    target_ids[:, :-trg_len] = -<span class="hljs-number">100</span>

    <span class="hljs-keyword">with</span> torch.no_grad():
        outputs = model(input_ids, labels=target_ids)
        neg_log_likelihood = outputs[<span class="hljs-number">0</span>] * trg_len

    nlls.append(neg_log_likelihood)

ppl = torch.exp(torch.stack(nlls).<span class="hljs-built_in">sum</span>() / end_loc)`}}),{c(){k=p("meta"),ks=r(),P=p("h1"),q=p("a"),os=p("span"),R(A.$$.fragment),ya=r(),ms=p("span"),xa=n("Perplexity of fixed-length models"),Ps=r(),R(S.$$.fragment),zs=r(),$=p("p"),ba=n(`Perplexity (PPL) is one of the most common metrics for evaluating language models. Before diving in, we should note
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log-likelihoods of each segment independently.`),Vs=r(),L=p("img"),sa=r(),as=p("p"),Wa=n(`This is quick to compute since the perplexity of each segment can be computed in one forward pass, but serves as a poor
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have less context at most of the prediction steps.`),aa=r(),es=p("p"),Aa=n(`Instead, the PPL of fixed-length models should be evaluated with a sliding-window strategy. This involves repeatedly
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practical compromise is to employ a strided sliding window, moving the context by larger strides rather than sliding by
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predictions at each step.`),na=r(),T=p("h2"),G=p("a"),cs=p("span"),R(N.$$.fragment),Ba=r(),ds=p("span"),Da=n("Example: Calculating perplexity with GPT-2 in \u{1F917} Transformers"),la=r(),ns=p("p"),Na=n("Let\u2019s demonstrate this process with GPT-2."),ia=r(),R(O.$$.fragment),pa=r(),ls=p("p"),Oa=n(`We\u2019ll load in the WikiText-2 dataset and evaluate the perplexity using a few different sliding-window strategies. Since
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