Feature Extraction
sentence-transformers
Safetensors
French
modernbert
splade
sparse
retrieval
sentence-similarity
text-embeddings-inference
🇪🇺 Region: EU
Instructions to use alphaedge-ai/sparseup-fr-v0 with libraries, inference providers, notebooks, and local apps. Follow these links to get started.
- Libraries
- sentence-transformers
How to use alphaedge-ai/sparseup-fr-v0 with sentence-transformers:
from sentence_transformers import SentenceTransformer model = SentenceTransformer("alphaedge-ai/sparseup-fr-v0") sentences = [ "The weather is lovely today.", "It's so sunny outside!", "He drove to the stadium." ] embeddings = model.encode(sentences) similarities = model.similarity(embeddings, embeddings) print(similarities.shape) # [3, 3] - Notebooks
- Google Colab
- Kaggle
File size: 25,864 Bytes
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Architecture: MLM → log1p(ReLU(x − θ)) → per-position top-k → max-pool
→ case / space-marker folding. The ``[Q] `` / ``[D] `` prefixes
are expected by the backbone but excluded from pooling.
References:
- https://huggingface.co/Linkup-Platform/linkup-sparseup-embed-v1
- https://www.linkup.so/blog/sparseup
"""
from __future__ import annotations
import html as html_lib
import json
import logging
import os
import re
from collections import defaultdict
from pathlib import Path
from typing import Any
import torch
from sentence_transformers.base.modules.module import Module
logger = logging.getLogger(__name__)
QUERY_PREFIX = "[Q] "
DOCUMENT_PREFIX = "[D] "
# ---------------------------------------------------------------------------
# Vocab fold (ingredient #3)
# ---------------------------------------------------------------------------
def _surface_body(token: str) -> str | None:
"""Lowercase body of a BPE token, without the space marker ``Ġ`` / ``▁``."""
if not token or token.startswith(("[", "<", "Ġ[", "▁[")):
return None
body = token[1:] if token[:1] in {"Ġ", "▁"} else token
body = body.lower()
return body or None
def _fold_rank(token: str, body: str) -> tuple[int, str]:
"""Prefer the lowercase form with a word-space marker, then the bare form."""
stripped = token[1:] if token[:1] in {"Ġ", "▁"} else token
space = token[:1] if token[:1] in {"Ġ", "▁"} else ""
if space == "▁" and stripped == body:
return (0, token)
if space == "Ġ" and stripped == body:
return (1, token)
if token == body:
return (2, token)
if stripped.lower() == body:
return (3, token)
return (4, token)
def build_case_space_fold(tokenizer) -> torch.Tensor:
"""Map each id to a canonical id (lowercase + space marker)."""
vocab = tokenizer.get_vocab()
size = max(len(tokenizer), max(vocab.values(), default=-1) + 1)
fold = torch.arange(size, dtype=torch.long)
groups: dict[str, list[tuple[str, int]]] = defaultdict(list)
for token, idx in vocab.items():
if idx < 0 or idx >= size:
continue
body = _surface_body(token)
if body is None:
continue
groups[body].append((token, int(idx)))
n_merged = 0
for body, members in groups.items():
if len(members) < 2:
continue
members.sort(key=lambda item: _fold_rank(item[0], body))
canon = members[0][1]
for _, idx in members:
fold[idx] = canon
n_merged += len(members) - 1
logger.info(
"vocab_fold case_space: %s ids → ~%s canonical (%s merged)",
f"{size:,}",
f"{size - n_merged:,}",
f"{n_merged:,}",
)
return fold
def prefix_token_ids(tokenizer, prefixes: tuple[str, ...] = (QUERY_PREFIX, DOCUMENT_PREFIX)) -> list[list[int]]:
ids = []
for prefix in prefixes:
enc = tokenizer(prefix, add_special_tokens=False)["input_ids"]
if enc:
ids.append([int(x) for x in enc])
return ids
def pooling_mask(
input_ids: torch.Tensor,
attention_mask: torch.Tensor,
prefix_ids: list[list[int]] | None,
special_ids: list[int] | None,
) -> torch.Tensor:
"""Pooling mask: drop specials + prefix at the start of the sequence."""
mask = attention_mask.clone()
if special_ids:
special = torch.tensor(special_ids, device=input_ids.device, dtype=input_ids.dtype)
mask = mask.masked_fill(torch.isin(input_ids, special), 0)
if not prefix_ids:
return mask
# If the first token is an already-masked special, the prefix starts at 1.
starts_with_special = mask[:, 0] == 0
for pref in prefix_ids:
n = len(pref)
if n == 0 or n >= input_ids.size(1):
continue
pref_t = torch.tensor(pref, device=input_ids.device, dtype=input_ids.dtype)
head0 = input_ids[:, :n]
head1 = input_ids[:, 1 : 1 + n]
match0 = (head0 == pref_t).all(dim=1) & ~starts_with_special
match1 = (head1 == pref_t).all(dim=1) & starts_with_special
if bool(match0.any()):
mask[match0, :n] = 0
if bool(match1.any()):
mask[match1, 1 : 1 + n] = 0
return mask
# ---------------------------------------------------------------------------
# SPARSEUP pooling
# ---------------------------------------------------------------------------
def _pair_mean_pool(weights: torch.Tensor, mask: torch.Tensor, factor: int) -> tuple[torch.Tensor, torch.Tensor]:
"""Average ``factor`` adjacent tokens (cheap hpool). Ward is not applicable in vocab dim."""
if factor <= 1:
return weights, mask
batch, length, vocab = weights.shape
pad = (factor - length % factor) % factor
if pad:
weights = torch.nn.functional.pad(weights, (0, 0, 0, pad))
mask = torch.nn.functional.pad(mask, (0, pad))
groups = weights.size(1) // factor
w = weights.view(batch, groups, factor, vocab)
m = mask.view(batch, groups, factor, 1)
denom = m.sum(dim=2).clamp_min(1.0)
pooled = (w * m).sum(dim=2) / denom
new_mask = (m.sum(dim=2).squeeze(-1) > 0).to(dtype=mask.dtype)
return pooled, new_mask
class SparseUpPooling(Module):
"""log1p(ReLU(logits − θ)) + per-position top-k + max-pool + vocab fold.
``pool_factor`` > 1: average adjacent tokens **before** max-pool
(hpool documents, like KURE / LI). Queries: leave at 1.
"""
config_keys = [
"logit_shift",
"position_top_k",
"vocab_fold",
"chunk_size",
"prefix_token_ids",
"special_token_ids",
"embedding_dimension",
"pool_factor",
]
def __init__(
self,
logit_shift: float = 15.0,
position_top_k: int | None = 12,
vocab_fold: str | None = "case_space",
chunk_size: int | None = 32,
prefix_token_ids: list[list[int]] | None = None,
special_token_ids: list[int] | None = None,
embedding_dimension: int | None = None,
vocab_fold_index: torch.Tensor | None = None,
pool_factor: int = 1,
) -> None:
super().__init__()
self.logit_shift = float(logit_shift)
self.position_top_k = int(position_top_k) if position_top_k else None
self.vocab_fold = vocab_fold
self.chunk_size = chunk_size
self.prefix_token_ids = prefix_token_ids or []
self.special_token_ids = special_token_ids or []
self.embedding_dimension = embedding_dimension
self.pool_factor = max(1, int(pool_factor))
self._hpool_enabled = False
if vocab_fold_index is None:
n = embedding_dimension or 1
vocab_fold_index = torch.arange(n, dtype=torch.long)
self.register_buffer("vocab_fold_index", vocab_fold_index.long(), persistent=True)
def get_embedding_dimension(self) -> int | None:
return self.embedding_dimension
def _activate(self, logits: torch.Tensor) -> torch.Tensor:
weights = torch.log1p(torch.relu(logits - self.logit_shift))
k = self.position_top_k
if k is not None and 0 < k < weights.size(-1):
cutoff = weights.topk(k, dim=-1).values[..., -1:]
weights = weights * (weights >= cutoff)
return weights
def _fold(self, sparse: torch.Tensor) -> torch.Tensor:
if self.vocab_fold is None or self.vocab_fold_index.numel() != sparse.size(-1):
return sparse
index = self.vocab_fold_index.to(device=sparse.device, dtype=torch.long)
if torch.equal(index, torch.arange(index.numel(), device=index.device)):
return sparse
index = index.unsqueeze(0).expand_as(sparse)
return torch.zeros_like(sparse).scatter_reduce(1, index, sparse, reduce="amax", include_self=False)
def _pool_mask(self, features: dict[str, torch.Tensor], length: int, device) -> torch.Tensor:
attn = features.get("attention_mask")
ids = features.get("input_ids")
if attn is None:
return torch.ones(ids.size(0), length, device=device) if ids is not None else None
if ids is None:
return attn
return pooling_mask(ids, attn, self.prefix_token_ids, self.special_token_ids)
def forward(self, features: dict[str, torch.Tensor], **kwargs) -> dict[str, torch.Tensor]:
if "cu_seq_lens_q" in features:
return self._forward_flattened(features)
logits = features["token_embeddings"]
batch, seq_len, vocab = logits.shape
device = logits.device
mask = self._pool_mask(features, seq_len, device)
if mask is None:
mask = torch.ones(batch, seq_len, device=device, dtype=logits.dtype)
mask = mask.to(device=device, dtype=logits.dtype)
pooled = torch.full((batch, vocab), float("-inf"), dtype=logits.dtype, device=device)
factor = self.pool_factor if self._hpool_enabled else 1
step = seq_len if not self.chunk_size else max(1, int(self.chunk_size))
for start in range(0, seq_len, step):
chunk = logits[:, start : start + step]
chunk_mask = mask[:, start : start + step]
weights = self._activate(chunk) * chunk_mask.unsqueeze(-1)
if factor > 1:
weights, chunk_mask = _pair_mean_pool(weights, chunk_mask, factor)
weights = weights * chunk_mask.unsqueeze(-1)
pooled = torch.maximum(pooled, weights.max(dim=1).values)
pooled = torch.where(torch.isfinite(pooled), pooled, torch.zeros_like(pooled))
pooled = self._fold(pooled)
if self.embedding_dimension is None:
self.embedding_dimension = pooled.size(1)
features["sentence_embedding"] = pooled
return features
def _forward_flattened(self, features: dict[str, torch.Tensor]) -> dict[str, torch.Tensor]:
flat = features["token_embeddings"].squeeze(0)
cu = features["cu_seq_lens_q"].tolist()
ids = features.get("input_ids")
attn = features.get("attention_mask")
rows = []
for i, (start, end) in enumerate(zip(cu[:-1], cu[1:])):
weights = self._activate(flat[start:end])
if ids is not None and attn is not None:
row_ids = ids[i : i + 1, : end - start]
row_attn = attn[i : i + 1, : end - start]
# Unpadded tensors often don't have the padded shape; keep everything.
_ = (row_ids, row_attn)
if self._hpool_enabled and self.pool_factor > 1 and weights.dim() == 2:
w = weights.unsqueeze(0)
m = torch.ones(1, w.size(1), device=w.device, dtype=w.dtype)
w, _ = _pair_mean_pool(w, m, self.pool_factor)
weights = w.squeeze(0)
rows.append(weights.max(dim=0).values)
pooled = self._fold(torch.stack(rows))
if self.embedding_dimension is None:
self.embedding_dimension = pooled.size(1)
features["sentence_embedding"] = pooled
return features
def save(self, output_path: str, *args, safe_serialization: bool = True, **kwargs) -> None:
os.makedirs(output_path, exist_ok=True)
self.save_config(output_path)
self.save_torch_weights(output_path, safe_serialization=safe_serialization)
@classmethod
def load(cls, model_name_or_path: str, subfolder: str = "", **kwargs):
# Sentence Transformers passes trust_remote_code here; load_config does not accept it.
config = cls.load_config(
model_name_or_path,
subfolder=subfolder,
token=kwargs.get("token"),
cache_folder=kwargs.get("cache_folder"),
revision=kwargs.get("revision"),
local_files_only=kwargs.get("local_files_only", False),
)
module = cls(**config)
try:
cls.load_torch_weights(
model_name_or_path,
subfolder=subfolder,
model=module,
token=kwargs.get("token"),
cache_folder=kwargs.get("cache_folder"),
revision=kwargs.get("revision"),
local_files_only=kwargs.get("local_files_only", False),
)
except ValueError:
logger.warning("No SparseUpPooling weights (identity fold).")
return module
def __repr__(self) -> str:
return f"SparseUpPooling({self.get_config_dict()})"
class hpool_documents:
"""Enable hpool only for ``encode_document`` (queries untouched)."""
def __init__(self, module: SparseUpPooling | None):
self.module = module
self._prev = False
def __enter__(self):
if self.module is not None:
self._prev = self.module._hpool_enabled
self.module._hpool_enabled = True
return self
def __exit__(self, *exc):
if self.module is not None:
self.module._hpool_enabled = self._prev
return False
def build_pooling(
tokenizer,
logit_shift: float = 15.0,
position_top_k: int | None = 12,
vocab_fold: str | None = "case_space",
chunk_size: int | None = 32,
) -> SparseUpPooling:
fold = build_case_space_fold(tokenizer) if vocab_fold == "case_space" else None
specials = sorted({int(i) for i in tokenizer.all_special_ids})
dim = int(len(tokenizer))
if fold is not None and fold.numel() < dim:
padded = torch.arange(dim, dtype=torch.long)
padded[: fold.numel()] = fold
fold = padded
elif fold is not None:
dim = int(fold.numel())
return SparseUpPooling(
logit_shift=logit_shift,
position_top_k=position_top_k,
vocab_fold=vocab_fold,
chunk_size=chunk_size,
prefix_token_ids=prefix_token_ids(tokenizer),
special_token_ids=specials,
embedding_dimension=dim,
vocab_fold_index=fold,
)
# ---------------------------------------------------------------------------
# Grafting the MLM head (backbone ingredient)
# ---------------------------------------------------------------------------
def _encoder_module(model):
if hasattr(model, "model") and hasattr(model.model, "embeddings"):
return model.model
if hasattr(model, "embeddings"):
return model
raise TypeError(f"Encoder not found on {type(model)}")
def _copy_matching(dst: torch.nn.Module, src: torch.nn.Module) -> tuple[int, int]:
dst_sd = dst.state_dict()
src_sd = src.state_dict()
merged = dict(dst_sd)
n_full = n_partial = 0
for key, src_t in src_sd.items():
if key not in dst_sd:
continue
dst_t = dst_sd[key]
if dst_t.shape == src_t.shape:
merged[key] = src_t
n_full += 1
continue
if dst_t.ndim != src_t.ndim:
continue
sl = tuple(slice(0, min(a, b)) for a, b in zip(dst_t.shape, src_t.shape))
cloned = dst_t.clone()
cloned[sl] = src_t[sl]
merged[key] = cloned
n_partial += 1
dst.load_state_dict(merged, strict=False)
return n_full, n_partial
def _ensure_qd_tokens(tokenizer, model) -> int:
"""Add ``[Q] `` / ``[D] `` if missing (like LateOn / mLateOn)."""
extra = [QUERY_PREFIX, DOCUMENT_PREFIX]
existing = set(tokenizer.all_special_tokens)
to_add = [t for t in extra if t not in existing]
if not to_add:
return 0
n = tokenizer.add_special_tokens({"additional_special_tokens": to_add})
if n:
model.resize_token_embeddings(len(tokenizer))
logger.info("Added tokens: %s (vocab %s)", to_add, len(tokenizer))
return n
def prepare_bare_mlm(mlm_name: str, output_dir: str | Path) -> Path:
"""MLM checkpoint + ``[Q] `` / ``[D] `` prefixes, without the LateOn encoder."""
from transformers import AutoModelForMaskedLM, AutoTokenizer
output_dir = Path(output_dir)
marker = output_dir / "graft_meta.json"
if marker.exists() and (output_dir / "config.json").exists():
meta = json.loads(marker.read_text())
if meta.get("late") is None and meta.get("mlm") == mlm_name:
logger.info("MLM cache already present: %s", output_dir)
return output_dir
logger.info("Loading bare MLM %s", mlm_name)
tokenizer = AutoTokenizer.from_pretrained(mlm_name)
mlm = AutoModelForMaskedLM.from_pretrained(mlm_name, torch_dtype=torch.float32)
_ensure_qd_tokens(tokenizer, mlm)
if hasattr(mlm, "tie_weights"):
mlm.tie_weights()
output_dir.mkdir(parents=True, exist_ok=True)
mlm.config.architectures = [mlm.__class__.__name__]
mlm.save_pretrained(output_dir)
tokenizer.save_pretrained(output_dir)
marker.write_text(
json.dumps({"late": None, "mlm": mlm_name, "vocab_size": int(mlm.config.vocab_size)}, indent=2)
)
logger.info("Bare MLM → %s (vocab %s)", output_dir, mlm.config.vocab_size)
del mlm
return output_dir
def graft_mlm_head(
late_name: str,
mlm_name: str,
output_dir: str | Path,
model_kwargs: dict[str, Any] | None = None,
) -> Path:
"""Graft the ``mlm_name`` MLM head onto the ``late_name`` LateOn encoder.
``decoder.weight`` stays tied to the LateOn embeddings (like SPARSEUP).
``head`` + ``decoder.bias`` come from the original MLM checkpoint.
Both checkpoints must share the same tokenizer (up to the ``[Q]`` / ``[D]``
tokens). An mmBERT ↔ modernCamemBERT graft is rejected: 256k vs 32k.
"""
from sentence_transformers import MultiVectorEncoder
from transformers import AutoModelForMaskedLM
output_dir = Path(output_dir)
marker = output_dir / "graft_meta.json"
if marker.exists() and (output_dir / "config.json").exists():
meta = json.loads(marker.read_text())
if meta.get("late") == late_name and meta.get("mlm") == mlm_name:
logger.info("Graft cache already present: %s", output_dir)
return output_dir
logger.info("Loading LateOn %s", late_name)
late = MultiVectorEncoder(late_name, model_kwargs=model_kwargs or {"torch_dtype": "float32"})
late_enc = _encoder_module(late[0].auto_model)
tokenizer = late[0].tokenizer
late_vocab = int(late_enc.config.vocab_size)
logger.info("Loading MLM head %s", mlm_name)
mlm = AutoModelForMaskedLM.from_pretrained(mlm_name, torch_dtype=torch.float32)
mlm_vocab = int(mlm.config.vocab_size)
extra = late_vocab - mlm_vocab
if extra < 0 or extra > 16:
raise ValueError(
f"Incompatible vocabularies for a SPARSEUP graft: "
f"encoder {late_vocab} vs MLM head {mlm_vocab} ({mlm_name}). "
"The head must come from the same tokenizer as the encoder "
"(mmBERT-base with mLateOn, modernCamemBERT with a modernCamemBERT PFT). "
"We do not graft a 32k head onto a 256k encoder: the ids no longer make sense."
)
if late_vocab != mlm_vocab:
logger.info("resize_token_embeddings %s → %s ([Q]/[D])", mlm_vocab, late_vocab)
mlm.resize_token_embeddings(late_vocab)
if hasattr(mlm, "decoder") and getattr(mlm.decoder, "bias", None) is not None:
with torch.no_grad():
mlm.decoder.bias[mlm_vocab:] = 0.0
n_full, n_partial = _copy_matching(_encoder_module(mlm), late_enc)
if hasattr(mlm, "tie_weights"):
mlm.tie_weights()
output_dir.mkdir(parents=True, exist_ok=True)
mlm.config.architectures = [mlm.__class__.__name__]
mlm.save_pretrained(output_dir)
tokenizer.save_pretrained(output_dir)
marker.write_text(
json.dumps(
{
"late": late_name,
"mlm": mlm_name,
"copied_full": n_full,
"copied_partial": n_partial,
"vocab_size": late_vocab,
},
indent=2,
)
)
logger.info("Graft OK (%s full tensors, %s partial) → %s", n_full, n_partial, output_dir)
del late, mlm
return output_dir
def build_sparseup_encoder(
init_dir: str | Path,
*,
logit_shift: float = 15.0,
position_top_k: int | None = 12,
vocab_fold: str | None = "case_space",
chunk_size: int | None = 32,
query_length: int = 128,
document_length: int = 512,
model_kwargs: dict[str, Any] | None = None,
):
from sentence_transformers.base.modules.transformer import Transformer
from sentence_transformers.sparse_encoder import SparseEncoder
from sentence_transformers.sparse_encoder.model_card import SparseEncoderModelCardData
init_dir = str(init_dir)
transformer = Transformer(
init_dir,
transformer_task="fill-mask",
query_length=query_length,
document_length=document_length,
model_kwargs=model_kwargs or {"torch_dtype": "float32"},
)
pooling = build_pooling(
transformer.tokenizer,
logit_shift=logit_shift,
position_top_k=position_top_k,
vocab_fold=vocab_fold,
chunk_size=chunk_size,
)
model = SparseEncoder(
modules=[transformer, pooling],
prompts={"query": QUERY_PREFIX, "document": DOCUMENT_PREFIX},
similarity_fn_name="dot",
model_card_data=SparseEncoderModelCardData(
language=["fr"],
license="apache-2.0",
model_name="SPARSEUP-style French sparse encoder",
),
)
return model
# ---------------------------------------------------------------------------
# Probes and reading bags
# ---------------------------------------------------------------------------
@torch.inference_mode()
def probe_logits(
model,
texts: list[str],
batch_size: int = 1,
max_length: int = 64,
max_tokens: int = 48,
max_values: int = 400_000,
) -> dict[str, float]:
"""Percentiles of the MLM logits (before shift) to calibrate θ.
We don't materialize the whole vocabulary: a
``[B, L, 256k]`` float32 tensor is enough to saturate RAM/GPU and freeze the cell.
"""
transformer = model[0]
tokenizer = transformer.tokenizer
device = next(transformer.parameters()).device
cap = min(max_length, transformer.document_length or max_length)
chunks: list[torch.Tensor] = []
n_seen = 0
print(f"Probing {len(texts)} texts (max_length={cap}, batch={batch_size})…", flush=True)
for start in range(0, len(texts), batch_size):
batch = texts[start : start + batch_size]
enc = tokenizer(
[DOCUMENT_PREFIX + t for t in batch],
padding=True,
truncation=True,
max_length=cap,
return_tensors="pt",
)
enc = {k: v.to(device) for k, v in enc.items() if torch.is_tensor(v)}
logits = transformer.auto_model(**enc).logits
flat = logits[enc["attention_mask"].bool()].float()
if flat.size(0) > max_tokens:
pick = torch.randperm(flat.size(0), device=flat.device)[:max_tokens]
flat = flat[pick]
chunks.append(flat.reshape(-1).cpu())
n_seen += int(flat.size(0))
print(f" batch {start // batch_size + 1}: {flat.size(0)} tokens, vocab={logits.size(-1)}", flush=True)
del logits, flat
values = torch.cat(chunks)
if values.numel() > max_values:
values = values[torch.randperm(values.numel())[:max_values]]
qs = torch.quantile(values, torch.tensor([0.01, 0.05, 0.25, 0.50, 0.75, 0.95, 0.99]))
return {
"n_tokens": n_seen,
"n_sample": int(values.numel()),
"min": float(values.min()),
"p1": float(qs[0]),
"p5": float(qs[1]),
"p25": float(qs[2]),
"median": float(qs[3]),
"p75": float(qs[4]),
"p95": float(qs[5]),
"p99": float(qs[6]),
"max": float(values.max()),
"frac>0": float((values > 0).float().mean()),
"frac>15": float((values > 15).float().mean()),
}
def l0(embeddings: torch.Tensor) -> torch.Tensor:
if embeddings.is_sparse:
embeddings = embeddings.to_dense()
return (embeddings > 0).sum(dim=-1).float()
def format_bag(pairs: list[tuple[str, float]], top_k: int = 20) -> str:
if not pairs:
return " (empty bag — lower LOGIT_SHIFT or check the pooling)"
peak = max(pairs[0][1], 1e-6)
lines = []
for token, weight in pairs[:top_k]:
shown = token[1:] if token[:1] in {"Ġ", "▁"} else token
bar = "█" * max(1, int(round(10 * weight / peak)))
lines.append(f" {shown:20s} {weight:6.2f} {bar}")
return "\n".join(lines)
_WORD = re.compile(r"\S+")
def highlight_html(text: str, bag: list[tuple[str, float]]) -> str:
"""Highlight the document words that (approximately) appear in the bag."""
weights = {}
for token, weight in bag:
body = _surface_body(token) or token.lower()
weights[body] = max(weights.get(body, 0.0), float(weight))
peak = max(weights.values()) if weights else 1.0
parts = []
last = 0
for match in _WORD.finditer(text):
parts.append(html_lib.escape(text[last : match.start()]))
word = match.group()
key = word.lower().strip(".,;:!?()[]\"'«»")
w = weights.get(key, 0.0)
safe = html_lib.escape(word)
if w <= 0:
parts.append(f"<span>{safe}</span>")
else:
alpha = min(0.85, 0.18 + 0.67 * (w / peak))
parts.append(
f'<span style="background:rgba(53,159,171,{alpha:.2f});padding:1px 3px;'
f'border-radius:3px" title="{w:.2f}">{safe}</span>'
)
last = match.end()
parts.append(html_lib.escape(text[last:]))
return "<p style='line-height:1.8;font-family:sans-serif'>" + "".join(parts) + "</p>"
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