---
kind: concept
slug: multi-label-classification
title: Multi-label classification
summary: >-
  Predict a set of labels for one input, where labels are not mutually exclusive. The default is one sigmoid per label with binary cross-entropy. Variants handle uncertain targets, weight noisy candidate labels, use known labels at test time, change the loss, or give one softmax per hierarchy depth. Trade-off: more compute, and for one token per label, cost that grows with the label count.
tags: [multi-label, image-classification, label-dependencies, partial-labels, binary-cross-entropy, uncertain-labels, label-noise, asymmetric-loss, semantic-softmax, logic-constraints]
papers: ["2011.14027", "2203.00962", "1901.07031", "2610.17635", "2104.10972", "2012.13635", "2007.10937"]
related: [self-attention, masked-language-modeling, feature-attribution, semantic-segmentation, noisy-labels, calibration, transfer-learning, knowledge-distillation, partial-label-learning, neural-symbolic-integration, differentiable-fuzzy-logic]
status: draft
updated_at: 2026-11-01
---

## Overview

A multi-label input carries several correct labels at once, so the target is a
binary vector rather than one class. The usual setup gives each label its own
logit and sigmoid, trained with binary cross-entropy. Each label is scored on
its own, so the model cannot use the fact that some labels co-occur and others
rarely appear together [arxiv:2011.14027 §1].

The cards in this wiki change that default in different places. Some models
add label dependencies, some handle targets that are uncertain, some down-weight
candidate labels that may be wrong, and one keeps the sigmoid classifier as the
first stage of weakly supervised segmentation, because a softmax over classes
is not valid when an image has several true classes at once
[arxiv:2203.00962 §1] [arxiv:2203.00962 §5.2]. Two more cards change the loss
or the head: one uses an asymmetric loss on the sigmoid outputs, and one splits
the classes by WordNet depth and puts a softmax on each depth
[arxiv:2104.10972 §3.2] [arxiv:2104.10972 §3.3]. A last route writes the label
rules as first-order logic and trains the sigmoid outputs so that those rules
hold. Logic Tensor Networks need explicit exclusion rules for this, because a
sigmoid head does not stop two labels from both being on [arxiv:2012.13635 §4.3].

"Partial" means two different things in these cards. In C-Tran, some target
labels are known at test time. In PML-CD, the training labels are candidates
that may include wrong positives. The two settings are separate and are named
separately below.

## Variants

### Independent per-label sigmoid head (BCE)

Shared image features feed one linear output per label. The loss is binary
cross-entropy over all labels, and each label's sigmoid is read on its own
[arxiv:2203.00962 §4.1 eq. 1, eq. 4]. ReCAM's first stage is this model, with
global average pooling in front of the head [arxiv:2203.00962 §3]. C-Tran
reports a plain ResNet-101 row for reference: 77.3 mAP on COCO-80 and 30.9 on
VG-500 [arxiv:2011.14027 tab. 1] [arxiv:2011.14027 tab. 2]. The card does not
describe that baseline's head beyond the row, so use it as a reference point
only. Card: [General Multi-label Image Classification with Transformers](/papers/2011.14027).

MovieNet uses binary cross-entropy for its 21-genre task, scored with a 0.5
threshold for its precision and recall figures [arxiv:2007.10937 §4.1]
[arxiv:2007.10937 app. C.1]. The author-reported mAP is 46.88 for a ResNet-50 on
1.6M photos and 45.23 for a TRN-R50 on trailers, against 43.70 for TSN-R50
[arxiv:2007.10937 tab. 3]. The inputs differ between rows, so these figures do
not compare losses. The same card also tags actions and places per clip as a
multi-label task. The best action result is SlowFast at 23.52 mAP, and the best
place result is TSN at 8.33 mAP [arxiv:2007.10937 §4.4] [arxiv:2007.10937 tab. 8].
Card: [MovieNet: A Holistic Dataset for Movie Understanding](/papers/2007.10937).

### Asymmetric loss on the sigmoid head (ASL)

The head is still one sigmoid per class. The change is in the binary loss,
which the paper calls asymmetric. Its multi-label pretraining uses a focusing
parameter of 4 on negatives and 0 on positives [arxiv:2104.10972 §3.2]
[arxiv:2104.10972 app. B]. The appendix says several negative-focusing values
were tried to maximise mAP [arxiv:2104.10972 app. B].

On the pretraining data, ASL reaches 48.5 micro mAP and 74.7 macro mAP. Cross-
entropy reaches 47.3 and 73.9, and focal loss 47.4 and 74.1
[arxiv:2104.10972 tab. 6]. With multi-label pretraining, ASL beats cross-entropy
on all seven downstream datasets, by 0.3 to 1.6 points
[arxiv:2104.10972 tab. 7]. The gains are the paper's own, and the caveats below
apply. Card: [ImageNet-21K Pretraining for the Masses](/papers/2104.10972).

### One softmax per hierarchy depth (semantic softmax)

Use this when each image carries labels at several levels of a class hierarchy,
such as the WordNet ancestors of its class. The classes are grouped by depth,
and each group gets its own softmax. An image labelled at depth d also trains
the softmaxes at depths 0 to d, which see its ancestor labels
[arxiv:2104.10972 §2.2] [arxiv:2104.10972 §3.3]. The per-depth losses are summed
with weights [arxiv:2104.10972 eq. 3]. The paper uses 11 depths on
ImageNet-21K-P [arxiv:2104.10972 §2.2].

Compared with the single-label softmax, semantic softmax is higher on all seven
transfer datasets. Compared with sigmoid multi-label pretraining, it is higher
on six; the exception is CIFAR-100 [arxiv:2104.10972 tab. 2]. Examples: ImageNet-1K
top-1 is 81.4 against 81.1 and 81.0, MS-COCO mAP is 81.3 against 80.8 and 80.6,
and Pascal-VOC mAP is 89.7 against 88.1 and 87.9 [arxiv:2104.10972 tab. 2].
These are transfer results after pretraining. Adding a semantic distillation
term raises every column further, but that term is not in the release (see
Caveats) [arxiv:2104.10972 tab. 2] [arxiv:2104.10972 §3.4]. Card:
[ImageNet-21K Pretraining for the Masses](/papers/2104.10972).

### Label-graph methods (named baselines only)

Earlier label-dependency methods that C-Tran compares against, ML-GCN, SSGRL and
KGGR, rely on label graphs built from co-occurrence statistics [arxiv:2011.14027 §5].
C-Tran's comparison table lists them at 83.0, 83.8 and 84.3 mAP on COCO-80
[arxiv:2011.14027 tab. 1]. C-Tran also states that such methods cannot take
partial evidence at test time [arxiv:2011.14027 §5].
No card on wikillm covers these methods, so the numbers above are only what
C-Tran reports for them.

### Label tokens in a Transformer with label-mask training

C-Tran gives each label a learned token and a state (unknown, negative or
positive). The label tokens and image grid tokens go through a Transformer
encoder together. Each label's output token then gets its own linear readout
[arxiv:2011.14027 §3.1] [arxiv:2011.14027 §3.2] [arxiv:2011.14027 §3.3].
During training, a random share of labels is hidden and the loss is taken only
on the hidden labels [arxiv:2011.14027 §3.4]. Without the image, mAP drops to
3.60 on COCO-80 at 0% known labels, so the image pathway carries most of the
signal when no labels are known [arxiv:2011.14027 tab. 5].

Reported results, mAP on the regular test split: 85.1 on COCO-80, 38.4 on
VG-500 and 34.3 on COCO-1000 [arxiv:2011.14027 tab. 1] [arxiv:2011.14027 tab. 2]
[arxiv:2011.14027 tab. 5]. Removing label-mask training costs 0.3 points on
COCO-80 and 0.1 on VG-500 at 0% known labels, but 1.6 points on VG-500 and 18.4
points on NEWS-500 at 50% known labels [arxiv:2011.14027 tab. 5]. These are
single runs with no variance reported [arxiv:2011.14027 §4].

### Using known labels at inference (partial and extra labels)

This is a setting rather than a separate model. Some target labels are known at
test time (partial labels), or related labels outside the target set are known
(extra labels). In C-Tran, known labels are given their state in the input and
the model returns predictions in one pass, with no iterative refinement
[arxiv:2011.14027 §4.2] [arxiv:2011.14027 §4.3].

Against Feedbackprop, the paper's only partial-label baseline, C-Tran's mAP
on unknown labels rises with the known share. On NEWS-500 it goes from 18.1 at
0% to 39.4 at 75%, against 14.7 and 25.9 for Feedbackprop [arxiv:2011.14027 tab. 3].
On COCO-80 the same comparison is 85.1 to 86.0 against 80.1 to 80.9
[arxiv:2011.14027 tab. 3]. The extra-label experiment uses CUB-312, a 200-class
task with extra label groups, so it is not a multi-label result [arxiv:2011.14027 §4.3]. The paper assumes known labels are correct and does not test noisy ones [arxiv:2011.14027 §2] [arxiv:2011.14027 §3.4].

### Uncertain targets: one state per label (CheXpert)

Each target here is yes, no or uncertain, for 14 observations per chest
radiograph. The labels were extracted from radiology reports by a rule-based
labeler, so "uncertain" marks hedged report wording rather than an annotator's
doubt [arxiv:1901.07031 § Method]. The paper compares five ways to train a
DenseNet121 on these targets [arxiv:1901.07031 § Uncertainty Approaches]:

- **U-Ignore:** binary cross-entropy summed over observations, skipping each
  uncertain entry.
- **U-Zeros and U-Ones:** map every uncertain entry to 0 or to 1, then apply
  ordinary binary cross-entropy.
- **U-SelfTrained:** train U-Ignore to convergence, then use its predicted
  probability as the target for each uncertain entry.
- **U-MultiClass:** a three-way softmax (negative, positive, uncertain) per
  observation. At test time the positive probability is taken after
  renormalising over negative and positive.

No approach wins on every observation. On the 200-study validation set, U-Ones
has the highest AUROC for Atelectasis (0.858) and U-MultiClass for
Cardiomegaly (0.854). Within each observation, the five approaches differ by
0.01 to 0.04 AUROC [arxiv:1901.07031 tab. 3]. The paper reports U-Ones beating U-Zeros on
Atelectasis (p = 0.03) and U-MultiClass beating U-Ignore on Cardiomegaly
(p < 0.01), with no significant difference for Consolidation, Edema or Pleural
Effusion [arxiv:1901.07031 § Results]. On the test set, each observation uses
the approach that scored best on validation: U-Ones for Atelectasis and Edema,
U-MultiClass for Cardiomegaly and Pleural Effusion, and U-SelfTrained for
Consolidation [arxiv:1901.07031 § Test Results]. Card: [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](/papers/1901.07031).

### Noisy candidate labels: calibrated per-entry weights (PML-CD)

Here each image carries candidate labels, and some candidate positives are
wrong. PML-CD keeps the BCE loss but weights each candidate positive by an
estimate of the chance that it is correct, given the model's confidence in it.
The paper argues that this optimal weight equals the calibrated probability of
the candidate being true [arxiv:2610.17635 §3] [arxiv:2610.17635 eq. 3–4]. Negatives
keep weight 1 [arxiv:2610.17635 alg. 1].

The weight comes from a small pre-trained calibrator. It maps a 20-bin histogram
of the confidences on candidate positives to a reliability per bin, and each
confidence gets a weight by interpolating between neighbouring bins
[arxiv:2610.17635 §4.1] [arxiv:2610.17635 eq. 7]. The calibrator was trained on
VOC 2007 at noise rates from 10% to 90%, then reused unchanged on other datasets
and noise rates [arxiv:2610.17635 §5.1] [arxiv:2610.17635 §5.2]. A second phase
adds a prototype-cosine loss on class embeddings [arxiv:2610.17635 §4.2]
[arxiv:2610.17635 eq. 13].

Author-reported mAP, at 20% and 80% noise. On VOC, PML-CD gets 88.83 and 71.70,
against 87.73 and 48.86 for BCE on the raw candidates and 64.46 for ML-Decoder
at 80% [arxiv:2610.17635 tab. 1]. On COCO at 80% noise, PML-CD gets 62.10
against 50.47 for BCE [arxiv:2610.17635 tab. 1]. The paper reports PML-CD as
best in 15 of 16 settings; the exception is VOC at 20% noise, where LL-R gets
88.99 [arxiv:2610.17635 §5.2]. In the ablation, the second-phase prototype loss
lifts VOC at 80% noise from 66.91 to 71.70 [arxiv:2610.17635 tab. 3]. The
noise in every reported setting is synthetic: each 0 is flipped to 1 with
probability ρ [arxiv:2610.17635 §5.1]. Card: [Calibrated Disambiguation for Partial Multi-label Learning](/papers/2610.17635).

### Logical rules as the training objective (LTN)

Logic Tensor Networks treat each formula as a fuzzy truth value in [0, 1], and
training maximises the satisfiability of a knowledge base built from those
formulas [arxiv:2012.13635 §2.2] [arxiv:2012.13635 §3.2]. For multi-label
data, the paper uses one sigmoid predicate P(x, l) over four labels: blue,
orange, male and female. It adds four axioms that mark the given positives, plus
two exclusion rules, one for each colour pair and one for each sex pair. No
negative examples are given [arxiv:2012.13635 §4.3]. The experiment uses a
200-example crabs dataset with 5 features [arxiv:2012.13635 §4.3].

The paper reports the multi-label case as a trend, not as an accuracy
comparison. The rule "blue implies not orange" rises towards true during
training, while "blue implies orange" and "blue implies male" fall towards false
[arxiv:2012.13635 §4.3] [arxiv:2012.13635 fig. 12]. The card's results give no
multi-label accuracy figure, although the paper defines accuracy as one minus
the Hamming loss at threshold 0.5 [arxiv:2012.13635 §4.3]. Card:
[Logic Tensor Networks](/papers/2012.13635).

### BCE plus softmax on isolated class features (localisation)

Classification is not the goal here. The goal is better class activation maps
for pixel masks. ReCAM keeps BCE on the classifier and adds a second softmax
term. Each class's feature map is first masked by that class's activation map,
so the second term sees one class per feature [arxiv:2203.00962 §4.1 eq. 5–8].
Softmax alone on the full multi-label target is worse: on VOC seed masks it
gives 44.6 mIoU against 48.8 for BCE alone, and 27.9 against 33.1 on MS COCO
[arxiv:2203.00962 tab. 1]. The best variant reaches 54.8 mIoU on VOC seeds
[arxiv:2203.00962 tab. 2]. The paper reports only segmentation mIoU, so
classification mAP is not measured. Card: [Class Re-Activation Maps for Weakly-Supervised Semantic Segmentation](/papers/2203.00962).

## When to use which

| Situation | Use | Why |
|---|---|---|
| Labels are needed, no known relations, no extra signal | Independent sigmoid head with BCE | Simplest; the reference row in the comparisons, 77.3 mAP on COCO-80 for C-Tran's ResNet-101 [arxiv:2011.14027 tab. 1] |
| Multi-label loss needed over many classes, no other constraint | Asymmetric loss on the sigmoid head | Beats cross-entropy on all seven downstream sets, by 0.3 to 1.6 points [arxiv:2104.10972 tab. 7]; about 1.1 micro-mAP points above focal loss on the pretraining data [arxiv:2104.10972 tab. 6]. The gains come from one paper and the caveats below apply |
| Labels nest in a hierarchy and each image carries several levels | One softmax per depth (semantic softmax) | Higher than the single-label baseline on all seven transfer sets and than sigmoid pretraining on six [arxiv:2104.10972 tab. 2]. Its depth weights differ between paper and code, and its KD variant is not reproducible from the release (see Caveats) |
| Label co-occurrence matters and there is compute for attention over image and label tokens | Label tokens in a Transformer (C-Tran style) | Highest reported mAP among the compared methods on COCO-80 and VG-500 [arxiv:2011.14027 tab. 1] [arxiv:2011.14027 tab. 2] |
| Very large label sets | Not settled by these cards | Attention cost grows with the label count; the paper estimates a practical limit near 2,000 labels on four GPUs, and suggests efficiency changes it does not implement [arxiv:2011.14027 §4.4]. No card here measures graph methods' cost on the same task |
| Some labels are known at test time | Label tokens with label-mask training | Gains grow with the known share, one pass at inference [arxiv:2011.14027 tab. 3] [arxiv:2011.14027 §4.2] |
| Known labels may be wrong | Not established | The paper does not test noisy known labels [arxiv:2011.14027 §2] |
| Targets carry an "uncertain" state | One of the U-approaches; pick by validation per observation | Best approach differs by observation, and most pairwise gaps are not significant [arxiv:1901.07031 tab. 3] [arxiv:1901.07031 § Results]. Dropping uncertain entries discards a lot when they are common: Consolidation has 12.78% uncertain and 6.78% positive in training [arxiv:1901.07031 tab. 1] |
| Candidate labels may include wrong positives, noise rate unknown | Calibrated per-entry weights on BCE (PML-CD) | Gains over BCE grow with the noise rate, but only under synthetic noise; at 20% the gap is small, 87.73 to 88.83 mAP on VOC [arxiv:2610.17635 tab. 1] [arxiv:2610.17635 §5.1] |
| Exactly one true class per input | Softmax cross-entropy | Pretraining on single-label data shows small gaps in both directions: ImageNet-1K top-1 is 81.1 for softmax and 81.0 for sigmoid, while CIFAR-100 is 89.5 for softmax and 90.6 for sigmoid [arxiv:2104.10972 tab. 2]. ReCAM's softmax term on single-label images gives 49.4 against 48.8 mIoU on VOC seeds, a single-run gap [arxiv:2203.00962 tab. 1] |
| Labels obey logical rules, such as exclusions, and no negative examples are available | Logical rules as the training objective (LTN) | The one multi-label experiment has no negatives and uses exclusion axioms; its result is a qualitative trend, not an accuracy gain [arxiv:2012.13635 §4.3] [arxiv:2012.13635 fig. 12]. Operator choice matters: the stable product configuration needs a small constant the paper does not state, and the gradients of standard fuzzy operators can vanish or explode [arxiv:2012.13635 §2.4] |
| Need pixel masks from a multi-label classifier | Keep BCE and add the isolated-feature softmax term | 48.8 to 54.8 mIoU on VOC seeds, at about 1.9 times the seed cost of plain CAM [arxiv:2203.00962 tab. 2] |

## Implementation sketch

Common core: one logit per label, binary cross-entropy, sigmoid at inference.
The label-token variant replaces the head with the Transformer described above.

```pseudocode
# Common core for multi-label training
# [arxiv:2203.00962 §4.1] [arxiv:2011.14027 §3.4]
# Input:  image (3, H, W); targets y (L,) with 0 or 1
# Output: scalar loss

def multilabel_loss(image, y, backbone, head):
    # Shared image features, pooled to one vector  [arxiv:2203.00962 §4.1]
    feat = backbone(image)                       # (d,)
    # One logit per label; no softmax across labels  [arxiv:2203.00962 §1]
    logits = head(feat)                          # (L,)
    # Binary cross-entropy per label  [arxiv:2011.14027 §3.4]
    # The paper does not state how the terms are reduced
    return bce_with_logits(logits, y)

# Inference  [arxiv:2011.14027 §4.1]
def predict(image, backbone, head):
    # Sigmoid per label, then a fixed threshold
    probs = sigmoid(head(backbone(image)))       # (L,)
    return probs >= 0.5                          # threshold 0.5 as in C-Tran
```

Notes:
- Label-token variant: replace `head(feat)` with a Transformer over image grid
  tokens and label tokens, where each label token carries a state embedding
  (unknown, negative or positive). Mask random labels during training and take the
  loss on the hidden ones only [arxiv:2011.14027 §3.1] [arxiv:2011.14027 §3.4].
- Known labels at test time: set their states in the input and keep the rest
  unknown, then run one forward pass [arxiv:2011.14027 §4.2].
- Localisation variant: the softmax term is computed on per-class masked
  features, and the BCE term stays on the classifier [arxiv:2203.00962 §4.1].
- Uncertain targets: before the loss, mask the entry (U-Ignore), set it to 0 or
  1 (U-Zeros, U-Ones), replace it with the teacher's probability (U-SelfTrained),
  or switch the observation to a three-way softmax (U-MultiClass)
  [arxiv:1901.07031 § Uncertainty Approaches].
- Candidate weights: multiply the BCE term of each candidate positive by its
  calibrated weight, and keep negatives at weight 1 [arxiv:2610.17635 alg. 1]
  [arxiv:2610.17635 eq. 1]. The official code applies a further rescaling of the
  weights; see Caveats.
- Asymmetric loss: replace the `bce_with_logits` term with the asymmetric loss,
  using a focusing parameter of 4 on negatives and 0 on positives
  [arxiv:2104.10972 app. B]. This sketch does not restate the formula; use the
  paper's definition [arxiv:2104.10972 §3.2].
- Semantic softmax: replace the head with one softmax per depth, and train each
  image at depths 0 to the depth of its own label [arxiv:2104.10972 §3.3]. Take
  the depth weights from the released code, not from eq. 2 (see Caveats).
- Logical rules: keep one sigmoid output per label, then replace the BCE term
  with a loss of one minus the satisfiability of the rules. Each rule is a fuzzy
  formula, using the stable product operators and a p-mean for the universal
  quantifier [arxiv:2012.13635 §2.4] [arxiv:2012.13635 §3.2]. Each exclusion rule
  is a universal over the instances, and the rule's truth is that of the negated
  conjunction of the two labels [arxiv:2012.13635 §4.3].

## Caveats

- C-Tran and ReCAM report single runs with no variance [arxiv:2011.14027 §4]
  [arxiv:2203.00962 §5.1]. PML-CD does not state its run count [arxiv:2610.17635 §5.1].
  CheXpert's AUROC intervals are DeLong intervals on the validation set, which
  reflect sampling error in that set, not variation across training runs
  [arxiv:1901.07031 tab. 3].
  Differences of a few tenths of a point are not established as real.
- The semantic-softmax paper gives 3 runs for downstream datasets under 150,000
  images [arxiv:2104.10972 app. D]. The card states no run count for its
  pretraining tables [arxiv:2104.10972 tab. 2] [arxiv:2104.10972 tab. 6]
  [arxiv:2104.10972 tab. 7].
- The ASL comparison may not be like for like. The paper tried several
  negative-focusing values to maximise mAP [arxiv:2104.10972 app. B], and the
  card does not say whether the cross-entropy baseline got the same tuning.
- The multi-label pretraining baseline is not fully specified. The card does not
  say whether ancestor labels are positives in the sigmoid baseline, so
  semantic softmax and sigmoid pretraining may not use the same targets
  [arxiv:2104.10972 §3.2].
- Semantic KD is not usable as described. The teacher is not named, the weight
  between KD and classification losses is not stated, and the rule for teacher
  confidence is ambiguous [arxiv:2104.10972 §3.4] [arxiv:2104.10972 app. F].
  The released code has the KD helper but no training script that calls it
  (see the card). Treat the KD column of tab. 2 as author-reported only
  [arxiv:2104.10972 tab. 2].
- The depth weights in eq. 2 and eq. 3 do not match the released code, and
  eq. 2 is undefined at depth 0 as printed. Pick one version and state it
  [arxiv:2104.10972 eq. 2] [arxiv:2104.10972 eq. 3].
- ImageNet-21K-P is derived from ImageNet-21K. The paper states no separate
  dataset licence, and the release says its use is subject to image-net.org
  terms. Check those terms before you redistribute derived data
  [arxiv:2104.10972 §2.1].
- C-Tran's released training masks are off for VG-500 and NEWS-500 in the
  shipped code, while the paper describes label-mask training for all datasets
  [arxiv:2011.14027 §3.4]. The paper does not explain this, so the VG-500 and
  NEWS-500 rows of its tables may not match the method as described.
- Attention in C-Tran runs over 324 image tokens plus one token per label
  [arxiv:2011.14027 §3.2]. Its experiments use up to 1000 labels
  [arxiv:2011.14027 tab. 5]; the roughly 2,000-label limit is an estimate, not a
  tested maximum [arxiv:2011.14027 §4.4].
- CheXpert's labels come from a rule-based labeler, not from annotators, and its
  uncertainty comparison uses one hospital's data [arxiv:1901.07031 § Dataset].
  The radiologist comparison has no statistical test [arxiv:1901.07031 § Limitations].
  The paper's CC BY 4.0 licence covers its text and figures, not the dataset
  [arxiv:1901.07031 § Pitfalls].
- PML-CD's official code rescales the weights after the calibrator, uses a hard
  threshold of 0.7 where the paper says 0.6, and runs early stopping on a loader
  built from the test split [arxiv:2610.17635 § Paper vs code]. The paper's
  "optimal" weighting uses true labels, so it is an upper bound, not a method
  you can deploy [arxiv:2610.17635 tab. 2].
- LTN's multi-label evidence is one qualitative trend on a small crabs dataset,
  with no accuracy comparison against a baseline [arxiv:2012.13635 §4.3]. The
  paper's only numeric baseline comparison is MNIST addition, which is not a
  multi-label task [arxiv:2012.13635 tab. 2].
- LTN's stable operators need a small positive constant the paper does not state
  [arxiv:2012.13635 §2.4]. Set it yourself and record the value.
- PML-CD's two tables disagree on the VOC prototype ablation: 71.70 at 80% matches,
  but the 20% to 60% values differ between the ablation and the main table
  [arxiv:2610.17635 tab. 1] [arxiv:2610.17635 tab. 3].
- MovieNet's paper licence (CC BY 4.0) covers its text, not the films, trailers,
  photos or labels. The project page describes access under a user agreement, and
  the card records a 60K vs 68K trailer-count conflict. Check the data terms
  before any commercial use [arxiv:2007.10937 § Pitfalls].

## Contradictions

Most results do not conflict across the cards, because they measure different
things: classification mAP for C-Tran, PML-CD and CheXpert, top-1 and mAP
after pretraining for the semantic-softmax paper, and seed-mask mIoU for ReCAM.
Three points still sit uneasily together.

ReCAM finds a softmax over the full multi-label target worse than BCE, 44.6
against 48.8 mIoU on VOC seeds [arxiv:2203.00962 tab. 1]. The semantic-softmax
paper finds one softmax per hierarchy depth better than sigmoid pretraining on
six of seven transfer datasets [arxiv:2104.10972 tab. 2]. These differ in target
(the full multi-label set against ancestor labels), in stage (segmentation seeds
against pretraining), and in measure, so neither refutes the other.

CheXpert's U-MultiClass, which uses a three-way softmax per observation, beats
U-Ignore on Cardiomegaly [arxiv:1901.07031 § Results]. That is a different
setting again, and it does not settle the ReCAM point either.

The LTN card adds no number that conflicts with these, because its only
multi-label result is a qualitative trend [arxiv:2012.13635 §4.3].

## Papers

- [General Multi-label Image Classification with Transformers](/papers/2011.14027): label tokens with a state embedding in a Transformer, label-mask training, and inference with partial and extra labels.
- [Class Re-Activation Maps for Weakly-Supervised Semantic Segmentation](/papers/2203.00962): keeps BCE on a multi-label classifier and adds a softmax term on isolated class features to improve pseudo masks.
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](/papers/1901.07031): five ways to train on uncertain labels, compared on validation AUROC for five observations.
- [Calibrated Disambiguation for Partial Multi-label Learning](/papers/2610.17635): calibrated per-entry weights for candidate positives, plus a prototype-cosine loss, tested under synthetic label noise.
- [ImageNet-21K Pretraining for the Masses](/papers/2104.10972): semantic softmax over WordNet depths, and asymmetric loss for multi-label pretraining, with transfer results on seven datasets.
- [Logic Tensor Networks](/papers/2012.13635): first-order rules as a differentiable training objective, with a multi-label crabs experiment that uses exclusion axioms and no negatives.
- [MovieNet: A Holistic Dataset for Movie Understanding](/papers/2007.10937): a film dataset with a 21-genre multi-label task trained with BCE, plus multi-label action and place tagging per clip; results are author-reported.