---
kind: concept
slug: conditional-random-field
title: Conditional random field
summary: >-
  A CRF scores a whole label sequence from emission and transition terms and decodes with Viterbi. On BERT it beats a softmax head by only 0.35 F1 (LAPTOP) and 0.84 (REST). A neural CRF beats a log-linear CRF on high-resource targets, and on low-resource ones only with a related source language. Dense depth models reuse the name for windowed refinement.
tags: [sequence-labeling, structured-prediction, decoding]
papers: ["1910.00883", "2010.11683", "2203.01502", "2404.09383", "1910.11470", "1707.09861", "2104.05919", "2606.26485", "2109.15290"]
related: [sequence-labeling, named-entity-recognition, transfer-learning, recurrent-neural-network, language-model-pretraining, domain-adaptation, constrained-decoding, data-augmentation, monocular-depth-estimation, self-attention, vision-transformer, prototype-learning, zero-shot-learning]
status: draft
updated_at: 2026-11-01
---

## Overview

A conditional random field (CRF) puts one score on a whole structured output,
not one score per item. The score is built from a term for each item and a
pairwise term for each linked pair. The model normalises over all possible
outputs, is trained by maximising the likelihood of the gold output, and
predicts the highest-scoring one.

The cards use the name in two ways. In sequence labelling, the items are tokens
and the pairs are neighbouring tags. This covers NER, keyphrase tagging and
event trigger detection. The emission term scores each token's tag,
the transition term scores each pair of neighbouring tags, and Viterbi search
gives the best sequence [arxiv:1910.00883 §2.2] [arxiv:1910.00883 eq. 7]
[arxiv:1910.00883 eq. 8] [arxiv:2404.09383 eq. 1]. In dense vision, the items
are pixels and the pairs are pixel links. A deep network refines a depth map
with these links, and the link weights are learned with attention instead of a
probability model [arxiv:2203.01502 §3.1] [arxiv:2203.01502 §3.3].

Within sequence labelling, the invariant all variants share is that the output
is a sequence, and the tag at one position is scored together with the tags
around it. Where a card states the objective, it is a likelihood over whole
sequences [arxiv:1910.00883 eq. 7] [arxiv:2104.05919 eq. 9]. Where a card names
a decoder, it is Viterbi [arxiv:1910.00883 eq. 8] [arxiv:2404.09383 eq. 1]. The
event-trigger and keyphrase cards do not name a decoder. The cross-lingual model adds a source-language term to
the objective [arxiv:2404.09383 eq. 7]. What changes is how the emission and
transition scores are computed: from hand-built sparse features, from prototype
distances, or from a neural encoder such as BERT or a character-plus-word BiLSTM. The dense-vision
variant shares only the idea of pairwise links; it does not share the objective
or the decoder.

## Variants

### Linear-chain CRF head on BERT

A single CRF layer over BERT token states, with 13 BIEOS-style tags for
end-to-end aspect-based sentiment analysis. The emissions come from a linear map
of the encoder states, and the transitions form a learned 13 by 13 matrix
[arxiv:1910.00883 §2.2] [arxiv:1910.00883 eq. 7]. Reported F1: 60.78 on LAPTOP
and 74.06 on REST, against 60.43 and 73.22 for the linear head on the same
encoder [arxiv:1910.00883 tab. 2]. The paper's SAN head scores 74.72 on REST,
the best in its table [arxiv:1910.00883 tab. 2]. Card:
[Exploiting BERT for End-to-End Aspect-based Sentiment Analysis](/papers/1910.00883).

The paper does not restrict transitions, and the released code keeps the
constraint mask at all ones. Viterbi can therefore output tag sequences that
break the BIEOS scheme, and the span rebuild silently drops or repairs them
[arxiv:1910.00883 §2] [code: absa_layer.py#L127].

### CRF head on a domain-pretrained encoder

MatSciBERT tests three output layers on one encoder: a softmax (LM-Linear), a
CRF on the encoder states (LM-CRF), and a 2-layer BiLSTM with hidden size 300
followed by a CRF (LM-BiLSTM-CRF). Each word takes the output at its first
WordPiece [arxiv:2109.15290 §2.4.1] [arxiv:2109.15290 §2.4.4]. On the test
sets, LM-CRF has a higher Macro-F1 than LM-Linear in all three NER tables: 65.00
against 63.63 on SOFC-Slot, 81.92 against 81.56 on SOFC, and 86.30 against 85.56
on Matscholar [arxiv:2109.15290 tab. 2] [arxiv:2109.15290 tab. 3]
[arxiv:2109.15290 tab. 5]. The same holds for Micro-F1 and for the SciBERT
encoder. Across these twelve test cells the gain runs from 0.36 to 1.83 points.
The paper reports means over three seeds with no spread, so gaps near one point
are hard to judge [arxiv:2109.15290 tab. 2].

The BiLSTM layer helps on the two SOFC sets. On SOFC-Slot, LM-BiLSTM-CRF is
0.92 above LM-CRF in Macro-F1, and on SOFC it is 0.15 above. On Matscholar it is
0.64 below in Macro-F1 and 0.70 below in Micro-F1 [arxiv:2109.15290 tab. 2]
[arxiv:2109.15290 tab. 3] [arxiv:2109.15290 tab. 5]. Card:
[MatSciBERT: A Materials Domain Language Model for Text Mining and Information Extraction](/papers/2109.15290).

### CRF output layer under data augmentation

A CRF over BIO tags sits on two taggers, a BiLSTM with GloVe embeddings and
SciBERT, in a study of simple token-level augmentation for NER
[arxiv:2010.11683 §4.2] [arxiv:2010.11683 tab. 3]. The paper studies the
augmentation, not the output layer. It does not compare the CRF with a softmax
head, so its numbers say nothing about whether the CRF helps.

With all four augmentations combined, the mean gain over the no-augmentation
baseline is +3.3 F1 for the LSTM tagger and +1.8 F1 for SciBERT, averaged over
eight columns [arxiv:2010.11683 tab. 3]. The gain is largest on the smallest set:
with 50 sentences, SciBERT rises from 68.1 to 71.2 on MaSciP and from 35.1 to
41.5 on i2b2-2010 [arxiv:2010.11683 tab. 3]. On the full training set the
effect is flat or negative in several cells; for SciBERT on i2b2-2010 it goes
from 87.8 to 87.2 [arxiv:2010.11683 tab. 3]. The text says all methods improve
on the baseline [arxiv:2010.11683 §4.4], which the full-set column does not
support. Card:
[An Analysis of Simple Data Augmentation for Named Entity Recognition](/papers/2010.11683).

The paper does not state transition constraints for its CRF. The released
code trains with an unconstrained transition matrix and decodes with
constraints [code: models.py#L186-L203] [code: models.py#L131-L137]. Those two
choices can give different outputs, so check which one your decoder uses.

### Log-linear CRF with hand-built features

Each pairwise potential is the exponential of a dot product between a weight
vector and a sparse feature vector. The features are built from the two tags,
the sentence and the position. The paper uses the standard NER templates of
Sha and Pereira, which it does not list [arxiv:2404.09383 eq. 2]
[arxiv:2404.09383 §2.2]. The objective is convex, and training uses L-BFGS
until convergence with the CRFsuite toolkit [arxiv:2404.09383 §2.2]
[arxiv:2404.09383 §5.2]. With 100 target sentences, monolingual F1 runs from
42.76 (Marathi) to 62.71 (West Frisian) [arxiv:2404.09383 tab. 2]. Card:
[Low-Resource Named Entity Recognition with Cross-Lingual, Character-Level Neural Conditional Random Fields](/papers/2404.09383).

A survey lists CRFs with hand-built features among the classic supervised NER
systems [arxiv:1910.11470 §6.3]. Its CoNLL table has a CRF system of Passos et
al. (2014) at 90.90 F1 on English, which uses a gazetteer [arxiv:1910.11470
tab. 1]. The survey copies that number and does not re-run it. It is on CoNLL
2003 English, not on the cross-lingual data above, so the two sets of numbers
are not comparable. Card:
[A Survey on Recent Advances in Named Entity Recognition from Deep Learning models](/papers/1910.11470).

For cross-lingual transfer, the same paper adds an atomic language-ID feature
and conjoins it with every template, which doubles the template count
[arxiv:2404.09383 §3.1]. With Spanish as a source, Galician rises from 57.64
to 71.46 F1 [arxiv:2404.09383 tab. 2].

### CRF output layer on a BiLSTM tagger, compared with softmax across seeds

The tagger reads pre-trained word embeddings, with optional casing and
character features, then one to three stacked BiLSTM layers, then a softmax or
a CRF output [arxiv:1707.09861 §4.1] [arxiv:1707.09861 §4.2]. The paper
compares the two outputs over sampled configurations and many seeds, not on one
hand-tuned setup [arxiv:1707.09861 §5]. On 232 NER configurations the CRF gave
the higher score in 90.5% of them, with a median difference of −0.66 F1 points.
The paper defines the difference as softmax minus CRF, so the sign favours the
CRF [arxiv:1707.09861 §5] [arxiv:1707.09861 tab. 3]. The CRF also had a smaller
spread on NER, σ = 0.0060 against 0.0082 for softmax (Brown-Forsythe
p < 10⁻³) [arxiv:1707.09861 §5]. The CRF won on four of the five tasks. It did
not win on Events, where softmax was better in 61.9% of configurations
[arxiv:1707.09861 tab. 3] [arxiv:1707.09861 §6.1]. A softmax output gained more
from extra stacked LSTM layers than a CRF did [arxiv:1707.09861 §6.1] [fig. 3].
Card:
[Score spreads of LSTM sequence taggers, softmax against CRF output](/papers/1707.09861).

### Neural CRF with a character-plus-word BiLSTM

The word input is the final state of a character LSTM over the word's
characters, concatenated with a word embedding. A sentence-level BiLSTM runs
over these inputs, and each tag-pair potential is the exponential of a
transition weight plus a tag output vector times the hidden state at that
position [arxiv:2404.09383 eq. 3] [arxiv:2404.09383 eq. 4]
[arxiv:2404.09383 eq. 5] [arxiv:2404.09383 §2.3]. With 10,000 target sentences
it beats the log-linear CRF on all five monolingual targets, by 0.61 to 4.79
F1 [arxiv:2404.09383 tab. 2]. With 100 target sentences it loses on all five,
by 0.75 to 8.45 F1 [arxiv:2404.09383 tab. 2]. Card:
[Low-Resource Named Entity Recognition with Cross-Lingual, Character-Level Neural Conditional Random Fields](/papers/2404.09383).

### Cross-lingual neural CRF with shared parameters

The character LSTM, the sentence BiLSTM, the transition weights, the projection
and the tag output vectors are shared across languages. Word embeddings and a
learned language vector are language-specific, and the language vector is fed
into the projection [arxiv:2404.09383 §3.1] [arxiv:2404.09383 eq. 6]. Training
maximises the target log-likelihood plus μ times the source log-likelihood,
with μ > 0 [arxiv:2404.09383 eq. 7]. The paper does not report a value for μ.
With 100 target sentences, this model beats the log-linear CRF with the same
source in all ten transfer pairs, by 3.97 to 9.80 F1
[arxiv:2404.09383 tab. 2]. For Galician, the neural CRF goes from 49.19
(monolingual) to 68.02 with French, while the log-linear CRF goes from 57.64
to 58.22 [arxiv:2404.09383 tab. 2]. The choice of source matters: Spanish gives
76.40 for the neural CRF [arxiv:2404.09383 tab. 2].

### Prototype-emission linear-chain CRF for zero-shot trigger detection

The trigger model scores a tag sequence with a linear-chain CRF, but its
emissions come from distances to class prototypes, not from a learned linear
map. Emissions use a TapNet-style projection, solved in closed form from the
class vectors and a set of reference vectors [arxiv:2104.05919 §2.2] [arxiv:2104.05919 eq. 6]
[arxiv:2104.05919 eq. 7]. The transitions are two diagonal matrices, one for
staying in the same event type and one for steps involving O, not a full
matrix [arxiv:2104.05919 eq. 8]. Training minimises the negative
log-probability of the tag sequences, plus a term that keeps the reference
vectors close to orthonormal [arxiv:2104.05919 eq. 9]. For zero-shot use, the
model first trains on pseudo-labels from cosine similarity between tokens and
class vectors, and marks uncertain tokens as unknown [arxiv:2104.05919 §2.2].

The paper's trigger results are for whole systems. TapKey, the trigger model,
reaches 55.19 trigger identification F1 with no seen event types, against 3.19
for prototype networks [arxiv:2104.05919 tab. 8]. The table does not isolate the
CRF layer, so these numbers do not show what the CRF adds. With 10 frequent seen
types, TapKey plus the generator reaches 72.31 trigger identification F1 [arxiv:2104.05919 tab. 8].
The released repository contains argument extraction only, not the trigger
model, so these zero-shot results cannot be reproduced from it. Card:
[Document-Level Event Argument Extraction by Conditional Generation](/papers/2104.05919).

### BiLSTM+CRF keyphrase tagger with cognitive features

Keyphrase extraction on tweets is tagged with B, I, E, S and O [code:
config.py#L14-L15]. Baselines are a BiLSTM and a BiLSTM+CRF [arxiv:2606.26485
§3.2.1] [arxiv:2606.26485 fig. 2]. The attention variants add a soft-attention
or self-attention layer on top, with or without the CRF [arxiv:2606.26485 §3.2.2]
[arxiv:2606.26485 fig. 3]. The cognitive features are per-word averages of EEG
and eye-tracking values from the ZuCo corpus, not per-reader values at
inference [arxiv:2606.26485 §3.1.3].

On General-Twitter, the paper's plain Bi-LSTM scores 70.67 F1, and its
SATT-BiLSTM+CRF with all EEG features scores 82.46 [arxiv:2606.26485 tab. 4].
Its BiLSTM+CRF with no cognitive features scores 81.63 on the same set, and
SATT-BiLSTM+CRF without features scores 81.74 [arxiv:2606.26485 tab. 4]. Read this way, most of the gain
over the plain BiLSTM on this set comes with the CRF output, and the EEG
features add 0.72 F1 over the no-feature SATT model. These figures come from the
card's reading of tab. 4; check that table before relying on the split. On
Election-Trec the plain BiLSTM to SATT-BiLSTM+CRF gap is 61.67 to 67.82
[arxiv:2606.26485 tab. 4]. The
hyperparameters were tuned on each test set and the best test epoch is kept,
so these F1 values are optimistic [arxiv:2606.26485 §4.1] [code: models/SATT_BILSTMCRF.py#L217-L223].
The released SATT-BiLSTM+CRF does not build as written
[code: models/SATT_BILSTMCRF.py#L132]. Card:
[Utilizing Cognitive Signals Generated during Human Reading to Enhance Keyphrase Extraction from Microblogs](/papers/2606.26485).

### Windowed attention CRF for monocular depth (not a sequence model)

NeW CRFs use a decoder whose refinement step is a fully connected CRF energy,
computed only inside non-overlapping windows of 7 by 7 patches. A second step
uses windows shifted by half a window, so information crosses window borders
[arxiv:2203.01502 §3.2] [arxiv:2203.01502 §3.4]. The pairwise weights come from
multi-head attention with a relative position term, not from a fixed colour
and position kernel [arxiv:2203.01502 §3.3] [arxiv:2203.01502 eq. 9]. The
output is a depth map, trained with a scale-invariant log loss rather than a
likelihood [arxiv:2203.01502 eq. 11]. Nothing here is a tag sequence, and no
Viterbi search is used.

The pairwise cost per iteration is hw(N² − 1) for N × N windows, against
hw(hw − 1) for a full CRF over h × w nodes [arxiv:2203.01502 eq. 3]. On the
Eigen split, adding the neural CRFs to a UNet-style baseline lowers Abs Rel
from 0.069 to 0.055, and the full model reaches 0.052 [arxiv:2203.01502 tab. 5].
In a separate study on 352 × 352 crops, window size trades accuracy for cost:
Abs Rel goes from 0.061 at window 2 to 0.054 at window 32, while decoder time
goes from 121 ms to 192 ms; window 48 runs out of memory in training
[arxiv:2203.01502 tab. 6]. Card:
[NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](/papers/2203.01502).

## When to use which

| Situation | Use | Why |
|---|---|---|
| Sequence labelling on a pretrained encoder, you want a sequence-level score, and a sequential Viterbi decode is affordable | Linear-chain CRF head | The gain over softmax is small, 0.35 F1 on LAPTOP and 0.84 on REST [arxiv:1910.00883 tab. 2]. Transitions are learned but not constrained, so invalid BIEOS sequences can still come out [code: absa_layer.py#L127] |
| Sequence tagger on a BiLSTM you train from scratch, and you want the output layer that gives the more stable result across seeds and settings | CRF output layer | On NER it was the better choice in 90.5% of 232 configurations, with a smaller spread (σ 0.0060 against 0.0082) [arxiv:1707.09861 §5] [arxiv:1707.09861 tab. 3]. It did not win on Events [arxiv:1707.09861 tab. 3] |
| Simple setup, or per-token cost matters more than the last fraction of F1 | Per-token linear softmax head | It reaches 60.43 and 73.22 F1, within 0.84 of the CRF on each dataset [arxiv:1910.00883 tab. 2] and decodes each token independently [arxiv:1910.00883 eq. 2] |
| You need a per-token probability for each label | Linear softmax head | The paper's CRF defines a probability over whole sequences [arxiv:1910.00883 eq. 7]. It reports no per-token marginals, so getting them from a CRF is extra work the paper does not describe |
| NER with a small labelled set and a CRF tagger you already use | Add augmentation on top of the CRF | With all four augmentations the gain is largest at 50 sentences, +3.3 F1 (LSTM) and +1.8 (SciBERT) on average [arxiv:2010.11683 tab. 3]. The paper does not compare with a softmax head, so the CRF choice itself is not tested there |
| Low-resource target (about 100 labelled sentences) with no labelled related language | Log-linear CRF with hand-built features | It wins on all five monolingual low-resource targets, by 0.75 to 8.45 F1 [arxiv:2404.09383 tab. 2] |
| Low-resource target and a related language with 10,000 labelled sentences that you can train on jointly | Cross-lingual neural CRF | It wins on all ten low-resource transfer pairs, by 3.97 to 9.80 F1 over the log-linear CRF with the same source [arxiv:2404.09383 tab. 2]. You must pick μ on your own validation data [arxiv:2404.09383 eq. 7] |
| High-resource target (10,000 sentences), no transfer | Neural CRF with a BiLSTM encoder | It beats the log-linear CRF on all five targets, by 0.61 to 4.79 F1 [arxiv:2404.09383 tab. 2] |
| Domain NER on a domain-pretrained encoder, and you want a CRF output | CRF on the encoder, without a BiLSTM | LM-CRF beats LM-Linear on all three NER test sets, by 0.36 to 1.37 Macro-F1 on MatSciBERT [arxiv:2109.15290 tab. 2] [arxiv:2109.15290 tab. 5]. The extra BiLSTM helped on SOFC-Slot but lowered Matscholar Macro-F1 by 0.64 [arxiv:2109.15290 tab. 5] |
| Per-pixel prediction (for example depth), and you want refinement with learned pairwise links inside the network | Windowed attention CRF | It lowers Abs Rel on the Eigen split from 0.069 to 0.055 over a UNet-style baseline [arxiv:2203.01502 tab. 5]. Pick the window size against cost, since larger windows cost more time and memory [arxiv:2203.01502 tab. 6] |
| Event trigger detection for event types with few or no labelled examples | Prototype-emission linear-chain CRF | Reports 55.19 trigger F1 with no seen types, against 3.19 for prototype networks [arxiv:2104.05919 tab. 8]. The released code has no trigger model, so you must rebuild it from §2.2 and the appendix hyperparameters |
| Keyphrase tagging on tweets, with a BiLSTM+CRF tagger you already run | BiLSTM+CRF, no cognitive features | The CRF output carries most of the reported gain on General-Twitter [arxiv:2606.26485 tab. 4]. Per-word EEG features add an author-reported 0.72 F1 to the attention variant with no features (81.74 to 82.46) [arxiv:2606.26485 tab. 4]. The features are per word type, not per reader [arxiv:2606.26485 §3.1.3] |

The gaps in this table come from author-reported numbers. The BiLSTM rows of
[arxiv:2404.09383 tab. 2] come from single runs with no variance. The keyphrase
row tunes on the test set, and the event-trigger row reports whole systems
[arxiv:2606.26485 §4.1] [arxiv:2104.05919 tab. 8]. The CRF row for
BiLSTM taggers [arxiv:1707.09861 tab. 3] is a distribution over configurations,
not a single run, so its spread can be compared with the other rows. The BERT rows [arxiv:1910.00883 tab. 2]
are on two review datasets, and the BiLSTM rows are on a 15-language NER set
[arxiv:2404.09383 §5.1]. The augmentation rows [arxiv:2010.11683 tab. 3] use
five seeds, but the paper's own text overstates the full-set gains. Treat the
choice as open until you have run your own comparison.

## Implementation sketch

Language-agnostic pseudocode of the common core of the sequence variants. The
BERT head, the BiLSTM variants and the prototype variant differ in how
`emissions` is computed, and the prototype variant also uses diagonal
transitions. See the comment at the end.

```pseudocode
# Linear-chain CRF over token emissions  [arxiv:1910.00883 eq. 7]
# emissions: (T, 13) per-token scores from a linear map of the encoder states
# transitions: (13, 13) learned score for each tag-to-tag step

def sequence_score(emissions, transitions, tags):
    # Sum of emission scores at the chosen tag of each token  [eq. 7]
    total = sum(emissions[t, tags[t]] for t in range(T))
    # Plus the transition score for each pair of neighbouring tags  [eq. 7]
    total += sum(transitions[tags[t], tags[t + 1]] for t in range(T - 1))
    return total

def training_loss(emissions, transitions, gold_tags):
    # Negative log-likelihood of the gold sequence  [§2.2] [eq. 7]
    # The normaliser sums over every possible tag sequence  [eq. 7]
    return logsumexp_over_all_sequences(...) - sequence_score(...)

def decode(emissions, transitions):
    # Highest-scoring tag sequence, found by Viterbi search  [eq. 8]
    return viterbi(emissions, transitions)    # (T,)

# BiLSTM variant: emissions[t] = u[tag] @ hidden_t, where hidden_t is the
# BiLSTM state at position t  [arxiv:2404.09383 eq. 3]. Log-linear variant:
# emissions come from a sparse feature dot product  [arxiv:2404.09383 eq. 2].
# Prototype variant: emissions come from distances to class prototypes, and
# transitions are two diagonal matrices instead of one full matrix
# [arxiv:2104.05919 eq. 6-8]. sequence_score, the loss and decode stay the same
# in the sketch; the prototype paper's own loss adds an orthonormality term
# [arxiv:2104.05919 eq. 9].
```

The paper's score sums from t = 0 [arxiv:1910.00883 eq. 7] and does not spell
out start or end terms, so an implementation has to decide whether to add them
[arxiv:1910.00883 eq. 7]. The released BERT code has none
[code: absa_layer.py#L428].

The windowed depth variant is not a sequence model and does not use this
sketch. Its refinement step is a windowed attention block over pixel features
[arxiv:2203.01502 §3.2] [arxiv:2203.01502 §3.3].

## Contradictions

No direct disagreement on a shared setting. The papers measure different things,
on different encoders. [arxiv:1910.00883 tab. 2] compares a CRF head with a
softmax head on BERT, and finds a gain of 0.35 F1 on LAPTOP and 0.84 on REST.
[arxiv:2606.26485 tab. 4] reports a larger gap on General-Twitter, 70.67 for a plain Bi-LSTM against 81.63 for a BiLSTM+CRF with no features. That baseline has no CRF, and the task is tweet keyphrase tagging, so it is not directly comparable with the BERT head above. [arxiv:1707.09861 tab. 3] compares a CRF with a softmax output on BiLSTM taggers
over many configurations, and reports a larger CRF advantage on NER, with a
median difference of 0.66 F1 points. Both point the same way. The magnitudes are
not comparable: the first is a single-setting comparison on BERT, and the second
is a median over sampled configurations of a different encoder. The MatSciBERT
gains of 0.36 to 1.83 test points [arxiv:2109.15290 tab. 2] [arxiv:2109.15290 tab. 5]
overlap the BERT gains above, but the encoders, tasks and seed counts differ. The paper's
Events result goes the other way [arxiv:1707.09861 tab. 3]. [arxiv:2404.09383 tab. 2] compares a neural CRF with a
log-linear CRF on a BiLSTM. The second paper reports that the neural CRF loses
to the log-linear CRF in the monolingual low-resource setting [arxiv:2404.09383
tab. 2], so the advantage of a neural CRF depends on how much labelled data you
have. [arxiv:2010.11683 tab. 3] does not compare CRF with softmax, so it does not
add a conflicting number. [arxiv:2203.01502 tab. 5] compares its decoder with a
UNet-style baseline, not with any sequence CRF; the shared name does not make the
numbers comparable.

## Papers

- [Exploiting BERT for End-to-End Aspect-based Sentiment Analysis](/papers/1910.00883): uses a linear-chain CRF as one of five task layers over BERT-base for joint aspect extraction and sentiment tagging, and compares it with linear, GRU, self-attention and transformer heads.
- [An Analysis of Simple Data Augmentation for Named Entity Recognition](/papers/2010.11683): tests four token-level augmentations for NER on a BiLSTM and a SciBERT tagger, both with a CRF output layer, on two specialist data sets.
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](/papers/2203.01502): a depth decoder whose refinement step is a fully connected CRF energy inside shifted 7 by 7 patch windows, with learned attention weights.
- [Low-Resource Named Entity Recognition with Cross-Lingual, Character-Level Neural Conditional Random Fields](/papers/2404.09383): compares a log-linear CRF with a character-plus-word BiLSTM CRF, monolingual and cross-lingual, on low-resource NER.
- [A Survey on Recent Advances in Named Entity Recognition from Deep Learning models](/papers/1910.11470): a survey that groups NER systems into families and copies CoNLL and DrugNER scores from the cited papers; it places CRF among the feature-engineered systems.
- [Score spreads of LSTM sequence taggers, softmax against CRF output](/papers/1707.09861): compares softmax and CRF output layers on BiLSTM taggers across sampled configurations and seeds, and reports the score spread for each choice.
- [MatSciBERT: A Materials Domain Language Model for Text Mining and Information Extraction](/papers/2109.15290): compares linear, CRF and BiLSTM-CRF heads on a materials-domain BERT and on SciBERT for three NER sets, reporting test F1 averaged over three seeds.
- [Document-Level Event Argument Extraction by Conditional Generation](/papers/2104.05919): its trigger model is a prototype-emission linear-chain CRF for zero-shot event detection; the released code covers argument extraction only.
- [Utilizing Cognitive Signals Generated during Human Reading to Enhance Keyphrase Extraction from Microblogs](/papers/2606.26485): BiLSTM and BiLSTM+CRF keyphrase taggers on tweets, with per-word EEG and eye-tracking features added at three points.