Multimodal Classification via Total Correlation Maximization
Authors: Feng Yu
Xiangyu Wu
Yang Yang
Jianfeng Lu
Venue: ICLR 2026 Poster (2026)
Keywords: Multimodal Learning; Modality Imbalance; Multimodal Classification;
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: We train the multimodal classification model by maximizing the lower bound of the Total Correlation among multimodal features and labels.

Abstract: Multimodal learning integrates data from diverse sensors to effectively harness information from different modalities. However, recent studies reveal that joint learning often overfits certain modalities while neglecting others, leading to performance inferior to that of unimodal learning. Although previous efforts have sought to balance modal contributions or combine joint and unimodal learning—thereby mitigating the degradation of weaker modalities with promising outcomes—few have examined the relationship between joint and unimodal learning from an information-theoretic perspective.
    In this paper, we theoretically analyze modality competition and propose a method for multimodal classification by maximizing the total correlation between multimodal features and labels. By maximizing this objective, our approach alleviates modality competition while capturing inter-modal interactions via feature alignment. Building on Mutual Information Neural Estimation (MINE), we introduce **T**otal **C**orrelation **N**eural **E**stimation (**TCNE**) to derive a lower bound for total correlation. Subsequently, we present TCMax, a hyperparameter-free loss function that maximizes total correlation through variational bound optimization. Extensive experiments demonstrate that TCMax outperforms state-of-the-art joint and unimodal learning approaches. Our code is available at https://anonymous.4open.science/r/TCMax_Experiments.

Published as a conference paper at ICLR 2026
MULTIMODAL CLASSIFICATION VIA TOTAL CORRELA- TION MAXIMIZATION
Feng Yu" Xiangyu Wu' Yang Yang' Jianfeng Lu Nanjing University of Science and Technology
ABSTRACT
Multimodal learning integrates data from diverse sensors to effectively harness information from different modalities. However, recent studies reveal that joint learning often overfits certain modalities while neglecting others, leading to perfor- mance inferior that unimodal learning. Although previous efforts have sought to balance modal contributions or combine joint and unimodal learning-thereby mitigating the degradation of weaker modalities with promising outcomes- few have examined the relationship between joint and unimodal learning from an information-theorett perspective. this paper, we theoretically analyze modality competition and propose method for multimodal classification by maximizing the total correlation between multimodal features and labels. By maximizing this ob- jective, approach alleviates modality competition while capturing inter-modal interactions via feature alignment. Building on Mutual Information Neural Esti- mation (MINE), introduce Total Correlation Neural Estimation (TCNE) derive a lower bound for total correlation. Subsequently, we present TCMax, a hyperparameter- free loss function that maximizes total correlation through varia- tional bound optimization. Extensive experiments demonstrate that TCMax out- performs ifate-of-the-ar joint and unimodal learning approaches. Our code is available at https: //gitttttb////////g com http//huaaa/TTee TCMax.
INTRODUCTION
Humans better perceive the world through diverse sensory inputs, i.e., text, audio, and vision. Likewise, multimodal fusion models Yang et al. (2021); Yao & Mihalcea (2022); Li et al. (2023b); Zhang et al. (2024); Wei et al. (2024); Zong et al. (2024), which integrate different modalities, are expected to learn more robust and generalized representations than unimodal counterparts. However, recent studies Wang et al. (2020); Huang et al. (2022); Peng et al. (2022) uncover an intriguing phenomenon in multimodal classification: the best-performing unimodal network surpasses the joint learning network, which can be attributed to the differences in convergence and generalization rates among modalities. In such inconsistent convergence states cases, some dominant modalities are adequately overfitted to the training data, causing the multimodal model to overly rely on dominant modalities while neglecting others, ultimately resulting suboptimal performance.
To address it, several studies Peng et al. (2022); Xu et al. (2023); Li et al. (2023a); Fan et al. (2023); Wei et al. (2024) are committed to balancing multimodal joint learning. Representatively. OGM-GE Peng al. (2022) modulates the gradient of modality-specific encoders according to their contribution to prediction, inhibiting modalities that converge faster. AGM Li et al. (2023a) dynamically adjusts the gradient contributions from different modalities. However, modality competi- tion Huang et al. (2022) points out that despite joint learning allowing for modality interaction, easily causes the model to saturate dominant modalities prematurely, neglecting unimodal features that are difficult to learn but conducive to generalization. Followed by some works are proposed to harness the benefits of the unimodal learning strategy, e.g., QMF Zhang al. (2023) explicitly incorporates unimodal loss and a regularization term, evaluating the quality of the truncated samples into the loss function. MLL Zhang et al. (2024) decomposes joint learning into alternating unimodal learning, with a lightweight shared head for modality interaction. MMPareto Wei & Hu (2024)
"quual contribution. Corresponding author.

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Published as a conference paper at ICLR 2026
considers both the direction and magnitude of gradients, ensuring that unimodal gradients do not interfere with multimodal training.
Despite significant progress in existing methods, current approaches still primarily rely on joint learning or a combination of joint learning and unimodal learning, with little consideration given to the inherent alignment properties of multimodal data. However, directly integrating joint learning loss, unimodal loss, and alignment loss (i.e., contrastive learning loss) with inherently conflict- ing optimization objectives requires introducing extra hyperparameters, additional structures, and algorithmic procedures to balance their contributions during training. In this paper, through an cormmation-thooretie analysis. we demonstrate that maximizing the total correlation between the features encoded by each modal encoder in the multimodal model and the labels avoids modality competition while learning inter-modal interactions and incorporating alignment between modalities.
Inspired by Mutual Information Neural Estimation Belghazi et al. (2018), we propose the TCMax loss, which employs Total Correlation Neural Estimation to estimate the lower bound of total correlation. By maximizing this lower bound, we enhance the total correlation between features and labels. We theoretically demonstrate that the output of the model optimized by the TCMax loss possesses the same mathematical significance method does not require the introduction of additional hyperparameter or structural modifications. Merely employing the TCMax loss during the training phase suffices to achieve favorable results. In summary, our contributions are as follows:
that of model trained using joint learning. Consequently, our
From an informmttion-hhoreette perspective, we elucidate the underlying causes of modality competition and propose that maximizing the total correlation between multimodal features and labels can amalgamate the advantages of joint learning and unimodal learning while incorporating inter-modal alignment
We introduce Total Correlation Neural Estimation and, based on this, propose the TCMax loss. Theoretically, we prove that optimizing the TCMax loss can increase total correlation and demonstrate that models utilizing TCMax capable of estimating the joint distribution of multimodal data and the label.
Comprehensive experiments showcase the considerable improvement over previous joint and unimodal learning methods on various multimodal datasets.
2 RELATED WORKS
Modality Imbalance Integrating information from multimodal data essential for comprehensively addressing and solving real-world problems Yu et al. (2025); Wu et al. (2025a;b). However, training a multimodal model using a joint learning strategy is challenging because different modalities often exhibit varying data distributions, require distinct network architectures, and have different convergence rates Wang et al. (2020). Simultaneously, joint learning makes all modalities contribute to one learning objective, causing weak modalities to be suppressed after strong modalities converge, resulting in modality competition Huang et al. (2022). Several works Peng et al. (2022); Zong al. (2024); Wei al. (2024); Xu et al. (2023); Li al. (2023a) have recently been suggested to balance modalities. Representatively, OGM-GE Peng et al. (2022) and AGM Li et al. (2023a) propose balanced multimodal learning methods that correct the contribution imbalance of different modalities by encouraging intensive gradient updating from suboptimal modalities. However, rebalance methods are not able to overcome modality laziness Du et al. (2023) and fail to exploit unimodal features efficiently. Some works Zhang et al. (2023); Wei et al. (2024); Zhang et al. (2024); Wei & Hu (2024) explicitly or implicitly incorporate unimodal loss into their loss functions to avoid modality laziness. Specifically, MLA Zhang et al. (2024) decomposes the conventional multimodal joint optimization scenario into an alternating unimodal learning scenario and exchanges information using shared head for different modalities. ReconBoost Hua et al. (2024) alternates between different modalities during the learning process, mitigating the issue of synchronous optimization limitations. MMPareto Wei & Hu (2024) balances the objectives of joint learning and unimodal learning using the Pareto method. By preventing modality laziness in multimodal learning, they achieve performance slightly higher than that of unimodal learning.
Information Theory with Multimodal Learning In information theory, mutual information quantifies the correlation between two variables in terms of their distribution. Recent works Belghazi
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et al. (2018); Hu et al. (2024) have leveraged neural networks to estimate mutual information, bridging the gap between deep learning and information theory. In contrastive learning, the InfoNCE Oord et al. (2018) loss serves as lower bound estimate of mutual information, providing solid theoretical foundation for its use. As more applications Chen et al. (2020b); Radford et al. (2021) demonstrate the effectiveness of the InfoNCE loss, the validity of the underlying mutual information theory has been further validated. For more than two variables, total correlation Watanabe (1 (1960) extends mutual information and serves as a measure of the interdependence among multiple variables. In Hwang et al. (2021), the authors applied total correlation in the Multi- View Representation Learning problem and achieved promising results, demonstrating the utility of total correlation in multi-variable scenarios.
METHOD
3.1 MOTIVATION AND PRELIMINARY
Problem Formulation. Consider multimodal data distribution (I(1), g ..... x ((A)) ,))
y where IP, "ex,..... "*.,....,00,,, denotes the joint probability distribution over the modalities and labels of the train set, (²()) represents the sample space of the m-th modality, ) corresponds to the label space. For each modality m, modality-specific encoder vee... (m) (mm) maps the in-
put space x(m) to its corresponding embedding space Z(m) = ( (z(m²) x(()) xx(m) }. The embeddings from all modalities are subsequently fed into prediction head fo zZ() x....X ( + R! to integrate information across different modalities and predict the probability distribution of labels p(O L) = Softmax (2()),, ,,,,,,((())), )),)))) where & denotes the predicted label and 9 represents the parameters of the prediction head.
Joint Learning. The objective of multimodal joint learning is to minimize the distance cross- entropy between the predicted distribution and the ground truth distribution:
Cjoint = E (2(1) (000... g) [e(v. 0) = (200) (M.
log p(y 2)),
(1)
where .(s-)) is the cross-entropy loss and Z (2 (AM) is the multimodal feature. As the distribution of ÿ is calculated by Z, [(y, v) in Equation 1 can be seen as the conditional cross- entropy under Z, denoted as I(y, Z). Boudiaf et al. (2020) shows minimizing the conditional cross-entropy [[,, Z) is equivalent to maximizing the mutual information [ 2). This implies, with joint learning strategies Peng et al. (2022); Li al. (2023a), the multimodal model is trained by maximizing the mutual information between the multimodal feature Z and the label
To explain the cause of modality imbalance from an information-theoretii perspective, we analyze the scenario involving two modalities (audio and visual) without loss of generality, where Z (2(a), 2())). Specifically, the mul- timodal model trained via joint learning aims to maximize the mutual information:
Mone
H(2!9)
Sjoint
(y; Z) [(;; 2(() 2())) Iwyi (()) 11y5 2 (0)
B6y
(2)
Kge 2/t))
Ky: giaty
The mutual information between any two variables is bounded by the entropy of either variable. Moreover, since I(y; (())2()))())) 2 O. it follows H (v) 2 I(y; 2(0), 2())) > [ (a)). When the encoder of one modality learns faster than the other, assuming 2(a) contains sufficient informa- tion to predict the label accurately on the train set, then T(y; z(01) in Equation 2 becomes close to Hyy) As T(y; (=)
Venn graph of an extreme case where the audio encoder has already been well-fitted. The visual component (blue) only needs to cover T(y; 200)| to achieve the training objective (Cjoiit zs 0), therefore ends up being unfitted.
Figure 1:
T(y; 2(0) 2(()) Tly; z(0)) S (v) - (g:; 2(a)) and z()) Rs H (y). the upper bound of [(2: =()))=(a)) tends to be quite small, making it challenging for the visual encoder to learn adequate features though maximizing
[y, (=)))))))) as it shows in Figure 1. This phenomenon of resource contention between modalities
termed modality competition Huang et al. (2022).
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Joint Learning
Alignment
TCMax
x(0)),(0),)))
1(2(0)2000)
TC(x(a), 200
1(2(()
H(2(0))
(y(()))
y(x()))
(((0)) 200
Unimodal Learning
H(y)
Figure 2:
An illustration of the relationship between joint learning, unimodal leaming, and learning through
maximizing the total correlation.
Unimodal Learning. In unimodal learning, each moddlltt--ppccifi model is trained independently and later combined into an ensemble model. Specifically, the logits of the unimodal ensemble model during prediction are equal to the sum of all modality-specifie models. For mathematical consistency, treat the unimodal ensemble model its prediction head can be decomposed into the sum modality-specific prediction heads, i.e., fo(Z) = Em 1om) (2(m)). The optimization objective of unimodal learning is:
single entity during training. However,
M log p (m) (y)
Lunimdda E (1())) (AA DNND
m==
where f(m) (y))) Softmax (2(m)) is the predicted distribution of the label the uni- modal model of the m-th modality. During training, the unimodal ensemble model maximizes the mutual information (y; (m)) separately for each modality m. For multimodal learning with two modalities, maximizes:
(fom)/
Tyy; 2(y; + T(y; (()))
As mentioned before, we assume the audio modality encoder converges faster, i.e., ((a) captures sufficient information earlier than 2(t), Since T(y; 2()) is independent of 2(*), it ensures that during the learning process of the visual modality, sufficient mutual information between features and labels can be learned. Although unimodal learning avoids modality competition, its independent training paradigm prevents the model from capturing cross-modal interactions.
While joint learning and unimodal learning focus on modality-label relationships (2)())) Y) mul- timodal datasets additionally encode cross-modal relationships (2) X.)) To this end, we aim fully utilize the prior information embedded in (x("),...,r,,,,,)) While mutual information [(f1: E2) effectively measures pairwise dependencies, its multivariate extension I :f:::..:: (.) has a limitation: yields negative values for synergistic interactions. In contrast, total correlation (TC) Watanabe (1960) is non-negative by definition, making it more suitable for measuring multivariate dependencies. Formally:
TC(E(1) (.,..,,((M)) =KL
... PPEG)
Σ m
(5)
H(( 5(2) ((M))
where is the entropy. To leverage the strengths of both joint and unimodal learning, we propose maximizing the TC across all modalities and the label. As Figure 2 shows, in the of two
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modalities, TC can be decomposed as:
(3:; 1 + 12
Joint learning
Alignment
[yy 2 + (y: 2 (1)) +
I I(2 (0)
Unimodal learning
Alignment
This decomposition reveals that TC simultaneously captures: (1) joint modality-label dependencies (joint learning), (2) moodality-mddaliiy alignment, and (3) unimodal label dependencies (unimodal learning). This ensures that the model leverages more prior information during training, thereby making the model more robust. In the following sections, we first propose a lower bound estimator for TC, then indirectly maximize TC by optimizing the TCMax loss, which is based the estimator.
3.2 TOTAL CORRELATION NEURAL. ESTIMATION
To maximize TC, we propose maximizing its lower bound. This requires a reliable estimator for the TC lower bound. We start from the lower-bound estimator for mutual information. Mutual Information Neural Estimation (MINE) Belghazi et al. (2018) provides a viable approach to estimate lower bound of mutual information.
Theorem (MINE Belghazi et al. (2018)) The mutual information between Z Z and y admits the following dual representation:
I(Z:y)
sup T:2xy=E
Er Er T - log (EezxBy (e"1)
(7)
where the supremum is taken over all functions T such that the two expectations are finite. As neural networks To with parameter E A compose family of functions which is a subset of Z R. we have:
1(Z:8) 2 sup Ep [To] log (Er, xFy [e" Age
Fortunately, MINE can be directly extended to Total Correlation Neural Estimation (TCNE). Note that for two variables, TC reduces to mutual information, making MINE a special case of TCNE.
Corollary (TCNE) The total correlation among M + variables (1)) E 2(1,, 2(),.... {M) E 2(M) and y E Y, admits the following dual representation:
TC(:11, ....,,,................... (MM) y) sup EE 200 T:Q--B
[T] - log EE g()) xux.......PPP. 2(1 xBy (e"]).
where the supremun is taken over all functions T such that the two expectations are finite and Q Z1 x x 2M V. As neural networks To with parameter e ① compose a family of functions which is subset of + R, we have:
TC(2(1) (M) N sup Er 2(M6 [Tol log (Ergan x. 200 xPy leT+ (10)
AE
See the supplement material for all proofs of corollaries and propositions.
3.3
TCMAX LOss
To align with the form in Corollary set (z(2 ,..., (M) .y) fo(2 ,.... (()), decom-
posing fe into D functions of the form (1)) x Z(M) + R. Based on Equation 10, we propose the TCMax loss:
CicMa = - EEp z(1 sa.....ee (M) [fo] + log
Ex (Bga))x- x.. g(ns x2y (efo))
(11)
-Ep +(1) x(.)) [Fe) + log
Ep (Bp ( x.. xP can xpy [eFo])
where (2)
((M) .y) = So (v0) (x()),
w (M) 0x
(M) (z(M))) is the multimodal model, θ =
(Oi,..., 0M, denotes all parameters of the multimodal model. From the above derivation,
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consider the prediction head TC estimator 21 X ZMs x V. Similarly, the multimodal model can be regarded as an estimator on 21 X ... x XM x y. Combine with Equation 10, we have following proposition:
Proposition 1 The TC between the imput data and labels, the TC between features and labels, and our proposed TCMax loss satisfy the following inequality:
(3d) TC(x 2..., (A)) 2 TC. .4) 2 LTCMax
(12)
Since LrcMax 2 -TC(2()) 2(M), v). minimizing LreMax pushes - -rcMax upward, thereby in- creasing the lower bound of TC .........MM))... (MM) y). Since the distribution of the dataset is determined, TC(x(),.... xM(M,, y) is fixed value and does not vary with model parameters. So far, we have not addressed the mathematical interpretation of the (CMax-trained model's 's output. Next, we prove that the output of this model possesses the same capability to predict the label distribution as multimodal model trained with joint learning.
Proposition 2 The supremim in in Equation 9 reaches its upper bound if and only if G. where the Gibbs distribution defined as dG EjerydQ and
P 2g (20))..,E(),)))
e"
Q = P=)) x .... PZM x Py.
Proposition indicates that when the TC estimator in TCNE is accurate, the estimator can also accurately estimate the joint probability distribution of all variables.
Proposition 3 The two inequalities in Equation 12 simultaneously hold as equalities if and only x G, where G is the Gibbs distribution defined dG Pxas X
_P
dQ and
Eale"o)
................................ .... Pran x Py.
No Modifications when Predicting. Proposition demonstrates that the lower bound of LreMas is -TC(x0)) (MM,, y). and when this lower bound is achieved, we have
ply. x(1)
(M)
(Fe(x!)) .... (M) M)
P(y (1)
(M)) Evey plk, (1), I (M))
ΣNEY (Fa( (k = py:
(13)
where p is the probability mass function of data distribution Fp. Equation 13 indicates that the model trained using the TCMax loss does not require additional operations modifications the model structure during prediction. The only difference between our proposed method and joint learning in practice replacing Cjint with LTCMax during training, yet yields more robust results.
3.4 COMPUTATIONAL COST
When training a multimodal model that includes both audio and visual modalities, direct implemen- tation of LTCMax mini-batch is:
exp So (6 (xt (a)) (v)
(2x())
Ve.
LTCMax
log
y1
log |3 [B/)) (14)
|
E E(kh/))BBBB2 exp
Vo (0)),
(0) (v)
(m)
SEB
where x (m) denotes the i-th sample of m-th modality. Notice that using LreMax requires forwarding the prediction head |B] M times. Although the parameter count of the prediction head is generally much smaller compared to the encoders, for large number of modalities M and large batch size, this can still introduce significant additional computational overhead. To mitigate this overhead, the computation can be optimized by sampling only certain number of negative samples (denominator) in the feature space, i.c., randomly sampling A C B B, where each (i, E N is sampled uniformly without replacement from B B. LrCMa with sampling is:
exp fo ( (z/
1. (2(())
LTCMax =
log
21
log [W[p)% (15)
B
Euiner EVEy exp fo Ve.
(a)
(z,
ve. (1) (1))
(0)
1EB

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((0) (2(x)), ) the denominator decouples into separate sums over modalities due to the identity exp(a exp(a) exp(b). LTMMa becomes:
For linear fusion ((=((1),(0))
[10 So.
exp (a) (w (a) (z, exp exp (10) (x.")))
1
LTCMax =
log
[
Ey'ey
(Eje exp 1/ (1/ (1) (EkeB exp So. (v) (xf )),
iEB
log BB (/)
(16)
In this way, only [B] forward passes of the prediction head are required, introducing almost no additional computational overhead with LreMax.
4 EXPERIMENTS
4.1 DATASETS
CREMA-D Cao et al. (2014) encompasses 442 audio-visual clips from 91 actors express- ing six emotions, with emotion labels determined by 2, 443 crowd-sourced raters. Kineties- Sounds (KS) Arandjelovic & Zisserman (2017), a subset of Kinetics Kay et al. (2017) dataset, includes 19, 000 10s videos across 31 human action labels, annotated manually through Mechan- ical Turk, AVE Tian et al. (2018) focuses on localizing audio-visual events in 4, 143 10s videos across 28 labels, sourced from YouTube with frame-level labeling for both audio and visual com- ponents. VGGSound Chen et al. (2020a) is a large dataset of 309 labels, with 10s videos that exhibit clear audio-visual correlations. It contains 152, 638 training videos and 13, 294 testing videos. UCF101 Soomro (2012) comprises 13, 320 videos from 101 action labels. The clips, ranging from 3s 10s, are split into a training set with 9, 537 clips and testing set with 3, 783 clips, utilizing the official train-test split. MVSA Niu et al. (2016) MMVSA-Singlle is multimodal sentiment analysis dataset that jointly leverages text and image data for classification.
4.2 IMPLEMENTATION DETAILS
Backbone and Hyperparameter For all audio-visual datasets, follow the same setting in the previous study Peng et al. (2022), selecting ResNet-18 18 He et al. (2016) as the encoder for both audio and visual modalities, and training it from scratch. For the audio modality, inputs converted into spectrograms McFee et al. (2015) of size 129 x 862 for the CREMA-D, AVE, and VGGSound datasets, and fbank Davis& & Mermelstein (1980) acoustic features for the Kinetics-Sounds dataset. For the visual modality, we extract images from videos at I fps and use 3 images as input for the CREMA-D, Kinetics-Sounds, and AVE datasets, and four images as input for the VGGSound dataset. For the UCF101 dataset, we extract frames and optical flow data from the videos at fps. using 3 RGB frames and 10 optical flow frames for each sample. We use ResNet- 18 as the backbone for both RGB and optical flow modalities and train ResNet- 18 from scratch as their backbone. We utilize SGD Robbins Monro (1951) with 0.9 momentum and 1 weight decay as the optimizer for all experiments. We set (learning rate, mini-batch size, epochs) to (le-3) 3, 32, 200) for CREMA-D and AVE, (le -Le-,, 3. 64, 200) for Kinetics-Sounds -3e-3, 64, 100) for VGGSound. and (le-3, 3, 32, 400) for UCF101. All of our experiments were performed on one NVIDIA Tesla V100 GPU.
4.3 COMPARISON WITH -HTE--FF-HEE-ATSS
Compared methods We conduct comprehensive comparisons of TCMax with several baselines and recent studies. (1) Baselines: concatenation (Concat), share predicted head (Share Head), unimodal fusion (Unimodal); (2) Recent studies: FiLM Perez et al. (2018), BiGated Kiela et al. (2018), OGM- GE Peng et al. (2022), OPM Wei et al. (2024), QMF Zhang al. (2023), AGM Li al. (2023a), MLA Zhang et al. (2024), MMPareto Wei & Hu (2024).
4.3.1 RESULTS OF TEST ACCURACY
Table 1 presents testing accuracy of using single modality and combining modalities (i.e., Multi). First, joint learning shows severe modality imbalance, with one modality significantly underperform- ing, and generally yields worse results than alternatives. Second, balanced joint learning methods
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Table 1: Results of the average test accuracy(%) of three random seeds on CREMA-D, Kinetics-
Sounds, AVE, VGGSound, and UCF101 datasets. Both the results of only using single modality ("Audio" and "Visual") and the results of combining all modalities ("Multi") are listed. The best results and second best results are bold and underlined, respectively.
Methods
CREMA-D
Kineties-Sound= Sounds Visual
AVE Visual
VGGSound Visual
UCF101
Audio
Visual Multi
Audio
Multi
Andio
Multi
Audio
Multi
RGB
OF
Multi
Concal
586
26.5
68.5
36.8
22.2
53.5
48.9
17.2
60.4
29.5
10.3
41.1
27.5
15.8
46.1
Share Head
63.0
29.5
68.3
38.7
29.1
53.7
19.7
22.1
61.1
30.9
13.0
11.8
31.2
20.2
16.0
58.8
44.7
BiGated Kiela et al. (2018)
64.7
49.1
59.3
38.3
46.7
OGM-GE Pang al. (2022)
55.8
15.8
75.2
35.7
25.6
55.4
39.5
19.3
61.3
28.7
13.2
12.5
25.3
16.6
11.2
(2023s)
46.0
Unimodal Ensemble
62.9
74.9
82.1
43.0
45.8
62.3
54.1
36.7
62.9
34.8
26.7
J6.3
39.2
29.2
51.8
QMP Zhong (2023)
65.5
74.3
$1.4
44.6
44..2
62.1
55.1
37.0
65.1
34.6
265.1
45.8
39.2
31.22
52.1
OPM Wei et al. (2024)
61.3
67.2
79.4
39.1 1
44.1
61.7
-8..8
36.2
63.1
31..2
233.5
15.9
38.
28.66.
26.6
50.8
DGM-GE OPM Wei et al. (2024)
58.3
69.8
80.3
37.6
11.1
62.5
08.2
35.3
63.3
31.6
23.5
45.5
38.6
26.9
48.3
MLA Zhang (2024)
63.5
75.6
$1.0
41.6
44.3
61.1
53.2
17.9
62.6
35-3
25.8
44.5
40.1
31.0
51.2
MMParcto Hu (2024)
65.4
75.7
74.4
44.8
02.7
54.0
41.1
63.1
35.5
27.5
46.2
42.4
33.0
56.9
Oursewaar
63.7
75.0
82.8
41.0
41.4
62.4
53.8
33.5
63.2
33.9
22.0
47.6
37.7
32.5
55.4
Our Hoad
63.0
73-6
52.7
40.4
63.5
54.2
36.7
64.5
36.3
47.5
41.0
37.2
56.0
Table 2: Results of Jensen-Shannon divergence between predictions of two modalities CREMA-D, Kinetics-Sound Sounds, AVE, VGGSound, and UCF101 datasets. The minima and second minima results bold and underlined, respectively.
Dataset
Concat Share Head OGM GE
AGM Unimodal
QMF
OPM
ML.A
MMPareto CoteetooOurrCcooooo CursConcal OursShare Head
CREMA-D
0.478
0.490
0.518
0.400
0.312
0.293
0.337 0.306
0.314
0.281
0.271
Kinetics Sounds
0.543
0.551
0.459
0.455 0.448 0.466
0.429
AVE
0.562
0.568
0.560
0.540
0.462
0.471
0.470 0.468
0.465
0.452
0.406
VGGSound
0.620
0.631
0.610
0.594
0.526
0.528
0.513 0.528
0.539
0.513
0.473
UCF101
0,581
0.579
0.589
0.586
0.463
0.531
0.473 0.457
0.485
0.427
0.366
(e.g., OGM-GE, AGM) improve the weaker modality but slightly degrade the stronger one, failing to consistently surpass unimodal-loss methods. Third, unimodal-basse methods prevent overfitting and sometimes outperform pure unimodal learning, while achieving the highest single-modal accuracy. Finally, TCMax achieves the best multimodal scores, but its single-modality performance matches other unimodal mnimodal-based methods- its gains stem from cross-modal synergy rather than individual improvements.
4.3.2 RESULTS OF JENSEN-SUIANNOX DIVERGENCE
To investigate the correlation of prediction outcomes across modalities, we calculate the average Jensen-Shanme Shannon divergence (JS (DS-divergence) between the prediction results of two separate modalities in Table 2. This metric quantifies the degree correlation in predictions between the two modalities, with lower JS-divergence signifying stronger correlation. As shown in the table, our TCMax consistently achieves the smallest JS-divergence for the single-modal predictions across all datasets, indicating that TCMax which is rooted in contrastive learning, facilitates the model to learn cross- modal representations, thereby enhancing the correlation of predictions.
4.4 FURTHER ANALYSIS
Number of Sampled Negative Pairs. We first explore the effect of sampling dif- ferent numbers of negative pairs, as men- tioned in Equation 15. Figure 3a shows that, for the CREMA-D dataset, the ac- curacy of TCMax rises with an increase in the number of negative pair samplings, achieving optimal performance at 1024. In contrast, the UCF101 dataset, the best performance is observed at the maximum sampling number 256.
0.60
6.80
0.55
0.30
67
6.60
Woul Mal
0:55
(a) CREMA-D, Batchsize 64 (b) UCF101, Batchsize 32
Figure 3: Accuracy on different numbers of sampled negative pairs.
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Concat Share Head Unimodal
OurSCoocat
UCFI0L CREMA-D
H(a)
0.369
0.184
0.320
0.575
warinng
H(v)
1.076
1.229
0.746
0.890
Ebech
p
2.913
6.674
2.331
1.549
(a) CREMA-D Loss
(b) CREMA-D Acc
((RGB)
1.245
0.630
0.921
2.000
H(OF)
2.244
1.170
1.259
2.265
P
1.802
1.856
1.368
1.132
Table 3: Results of average entropy of predictions by single modality test sets of CREMA-D and UCF101 datasets. H(Mr denotes the entropy of predictions of the 'M' modality, and represents the ratio of the entropy of the weak modality to the entropy of the strong modality. H(vy/ H(A)
Opach
130ch
(c) UCFIOI Loss
(d) UCFI01 Acc
Figure 4: Train loss and test accuracy of joint learning, unimodal learning, and TCMax on CREMA-D and UCF101 datasets.
For CREMA-D and UCF101 datasets, and p /or ((BB)), respectively.
TCMax Prevents Overfitting. Here, we visualize how TCMax effectively mitigates the risk of overfitting. As depicted in Figure 4, on both the CREMA-D and UCF101 datasets, TCMax loss remains consistently higher than that for joint and unimodal learning, which prevents the model parameters from updating at all. Although TCMax exhibits inferior performance compared to unimodal learning in the early stages of training, as the training progresses into the middle stage, TCMax begins to gradually presents its strengths and ultimately converges to a stable performance level.
Average Entropy of Predictions. In Table 3, we compute the average entropy predictions by single modality and the ratio between strong and weak modalities. This reflects the model's ability to balance predictions across different modalities. Typically, lower ratio indicates more equitable contribution from both modalities. The table reveals that our method successfully achieves a balanced representation of the various modalities.
Analysis with Pretrained Encoders As shown in Table 4, we adopt CLIP Radford et al. (2021) as the frozen feature encoder for both image and text modalities the MVSA dataset. During training, only the multimodal classifier is optimized while keeping the encoder parameters fixed. Our results show that: (1) Joint learning outperforms unimodal learning because the limited parameter space pre- vents overfitting; (2) TCMax maintains competitive performance by effectively modeling cross-moda. interactions, similar to joint learning.
Table 4: Result of the average test accuracy($) (%) of 10 random seeds on MVSA with frozen CLIP pretrained encoders.
RN50
ViT-B/32 Text Multi Image Text Multi
Methods
Image
Joint
75.76 73.60 81.23 76.88 74.27 82.83 76.74 77.16 80.02 78.54 76.97 81.77
Unimodal
TCMax
75.38 74.97 81.75 78.03 76.55 84.05
5 DISCUSSION
Conclusion This study investigates the causes of modality imbalance in multimodal classification tasks from information-theoreiic perspective and proposes learning objective to maximize total correlation to fully utilize cross-modal information in multimodal datasets. We propose the Total Correlation Neural (Ttim)) which employs neural networks to estimate the lower bound of total correlation. Building on this theoretical foundation, we introduce parameter-free loss function, TCMax, for multimodal classification tasks. By maximizing total correlation, our approach enables more comprehensive utilization of prior information in multimodal datasets, thereby achieving enhanced robustness. Comparative experiments with state-of-the of-t methods demonstrate the effectiveness of our approach across multiple multimodal classification benchmarks.
Limitation The current TCMax framework is primarily designed for classification tasks and cannot be directly extended to other multimodal applications such as multimodal object detection or generative tasks. Successful adaptation to these domains would require explicit definitions of input- output probability distributions. Furthermore, while TCMax establishes foundational multimodal learning paradigm, its full potential depends on developing model architectures specifically optimized for this framework.

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ACKNOWLEDGEMENTS
This work is supported by the NSFC (62276131, 62506168), Natural Science Foundation of Jiangsu Province of China under Grant (BK20240081, BK20251431).
The authors gratefully acknowledge financial support from the China Scholarship Council (CSC) (Grant No. 202506840036).
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A PROOFS
A.1 PROOF OF COROLLARY
Corollary (Corollary 1 restated, TCNE) The total correlation between M + 1 variables z(1) 2(1, ,...,,(MM) E (M) and E Y, admits the following dual representation:
(MM)
2(M)
TC(: (M)
sup Ep z(1)..... 2(0)....2M1 [T] -log (Ep 2(1) x.x xP 201r xPy (e"])
(17)
T--+R
where the supremum taken over all functions T such that the expectations are finite and Ω = En x...X x EM x Y. As neural networks To with parameter 0 E θ composed a family of functions which a subset of + R, we have:
TC(2 (M)) v) sup Er 2()) 200
(To) log EEgas x 2(10) xPy [c")])
(18)
BE
We follow the proof in the paper of MINE Belghazi et al. (2018) prove TCNE. First, we begin with the Donsker- Varadhan representation theorem.
Theorem 2 (The Donsker- Varadhan representation Donsker & Varadhan (1983)) The KL divergence admits the following dual representation:
DKL (III
sup [ (Eqle")), T-R
(19)
where the supremum is taken over all functions' T such that the two expectations are finite.
For a given function T', consider the Gibbs distribution defined by dG = dQ, where = Eg (e") is he partition function and T servers the energy function in the Gibbs distribution. The right hand of Equation 19 can be written as:
dG aQ
Ep ET(7] - log (Bele")) = Ep (T) log = Ep log 7
E7
log
(20)
Let A the gap:
A DKL (PI Ep[[]] log (Bole"))
(21)
with Equation 20, we can write A as KL-divergence:
dP
dG
dP
Ep
log
log
Ee
log
DeL (PI
(22)
dQ
dQ
dc
The positivity of the KL-divergence gives A 0. We have thus shown that for any T.
DKL (PIIQ) > Ep[T] log (Eole")),
(23)
The inequality is preserved upon taking the supremum over the hinht-hand side. The bound is tight
when G P., namely for optimal functions T taking over the form T log aQ constant Const TR.
dB Const for some
To prove Equation 17 in Corollary 2, we replace P and Q with PP zon, and P P2o1 x ..... X
P2(M) Py in Equation 19 so we have:
DKL (P 22).....
20) x P FZ(M) Py)
(24)
T 20 2(M) [T] - log EEp 2 20) x...P
sup E
2(10)
With the KL-divergence form of total correlation:
(1)
(C.,, (M))
= DKL. (Pzz,,... IP za) x ... Pan x Py),
(25)
we can proof the Equation 17 Corollary 2. As neural networks To with parameter E θ belongs to {T|T: Ω + R}. the supremum taken over all networks To is less than or equal to the supremum taken over all functions T.
()
2 (M) sup Eg
T:O gg0.....(MM, z(M).y [T] log [Ep z(1 x..XP Benn xpy (e"])
(26)
sup Ee 828
20))....a ( [Tb] log Ep a X... sory xpy (e70)).
Thus prove Corollary 2.
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A.2 PROOF OF PROPOSITION
1
Proposition 4 (Proposition 1 restated) The TC between the input data and labels, the TC between features and labels, and our proposed TCMax loss satisfy the following inequality:
TC(x (M) v) 2 TC(=(), ,...,, (M)) ,2) 2 - -TTMaa
(27)
We first consider the TCNE form of (C(x (M)) y) and ,C.,
(M) .y):
TC(x x (M)
Ep x (M)) [Tx] log Bp x(1) x.. x(M) xPy [E2x]]
sup
Tx +B
(28)
TC(2(1) (C(=,)),..,,20))) (M0) ,9)
sup Tz:02
+2 2(0) ((M))
Ep
[Tz] - log
EE EE x11xxxxp 2(1r) [et*]),
(29)
where f2xx and f2 are the input space (including the label) and the embedding space, respectively. As mppality-specific encoders are used extract the embedding z(1, from the input x (L,,,,, .M) a fix function f2x + S2z is defined here. So we can rewrite Equation 29:
TC(2(1)
(M) v)
sup Er Tx +R
[ Tz]
log
Ep x x-
XIMyXTy
ToTx
(30)
Since ( oT2 [Tz 22 R) is subset of [Tx[Tx: : 2x RJ. the supremum in Equation 30 is not surpass than the supremum Equation 28. Thus, we prove first inequality the proposition.
We first consider form TCMax loss prove he second inequality:
201) x xP 2 x2y [e5o])
LieMa - Ep 20),....
(00, [fa] + log Ee
(31)
As the predicted head a special case in T2 fz + R, therefore:
TC(: (1)
(M)
4)
sup
E.
2()
[Tz] log Be 2 XP ((20) x7y
(e=x])
(32)
[fo] log (F x..X s(1) xry [otol)
F 20)
LreMa:
(M))
thus, we prove the second inequality in the proposition.
A.3 PROOF OF PROPOSITION 2
Proposition 5 (Proposition 2 restated) The supremum in in Equation 17 reaches its upper bound if and only if
P2()).... (00,) = G, where G is the Gibbs distribution defined as dG Eg dQ and Q = P 2(1) x ... X
P2(ar x Py.
The supremum in Equation 17 reaches its upper bound when the gap equal O,
Dxa (PI Es [4] log (Bele")) O,
(33)
where = FF 2() ((4,) y
( X ... x I (00) x Py. With the Gibbs distribution defined as
dG doQ we have:
0= Dxt.
(T)
EF [T]] log (Eg (eT])
DRL. (PI[G).
(34)
where the second equality uses Equation 22. With Gibbs" incquality, we know DRL (PIIG) equals if and only P Q. Thus, we prove Proposition 5.
A.4 PROOF OF PROPOSITION 3
Proposition (Proposition restated) The two inequalities in Equation 27 simultaneously hold as equalities
if and only if P. ((30)... = G. where & is the Gibbs distribution defined as dG Ral dQ and
Px) Px0 Py.
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Consider the TCMax loss:
LTCMax -Br 211) (MM)) [Fe] + log (rr x x-.x xrles xBy (6fu)
(35)
When two inequalities in Equation simultaneously hold, we have:
TC(x (1)
(M)
4)
sup
Ep x(1)) x(M)) [Tx] log Ex x(1) x1))x x.xx x(0rr) xEy [c
Ty -R +R
LiCMax
(36)
-Er x(M)) [Fa] log (Bext x.. xine xpy (cftO).
Hence, Fe reaches the upper bound the supremum. With Proposition we know Equation holds and only P xx.)).... = G. Thus, we prove the proposition.
A.5 DERIVATION OF EQUATION
Since batch is sampled according to overall data distribution, we can consider the samples (z/[), (x) vs).
Vi drawn from V.v. where =.(), ,x("), and yi follow the marginal distributions FA. Pv. and Fy. respectively. Since label distributions are generally assumed to be relatively uniform, we hypothesize Py to be uniform distribution over V. Thus, in calculations, Py is directly treated as uniform without relying on batch sampling results. Substituting the assumptions into Equation 11 yields:
Cremax
Σ EB
fo (Ve.
(0) (cc
V Vo (a.)))
[8
}
+ log
E
(. exp
(o))
18 x B x
(AW JE8x8xy
exp
(4)
(37)
log
log 18 1
[
E Gikoo De JBBBBy exp (/ (z) (o))))))
1EB
exp fo (2) (1()))
log
log BB)P)
B
ex (4 (1)) (c))))
Thus, Equation 14 is obtained.
B DETAILS OF EXPERIMENT
B. DETAILS BASELINES
Concatenation is straightforward approach to multimodal fusion where the features from different modalities are combined by concatenating them into single feature vector. In our experiments, we feed the combining vector into single fully connected layer get the prediction, which can be denoted as
Concatenation
f(X;) = W [hu (z,,1). .......... hur (Ir, +)]++b +.b It can be decomposed as f (X,) = -M 2-m=1 (Wm him (2i,m) ) + b/M} can be simplified during training and define the output of modality is fm W mm (Fi.m) ( following
Peng et al. (2022).
Share Prediction Head This method uses a shared prediction head to calculate the output of every modality, then sums up all outputs from all modalities as the final output. Same concatenation, we use single fully connected layer as the shared head, and output can denoted as f (X.) EM (Whm (av.m) + b/M)- Output of modality m is defined as fm W hm (xt.m) + b/M.
FiLM Perez al. (2018) FiLM modulates feature from modality using the feature from the other modality. Specifically, a FiLM layer performs a straightforward afline transformation on each feature a neural network's intermediate representations, modulated by an arbitrary input. The output by FiLM is denoted as f(X)) = g (y (h2(2),)) (x..1) 1)+ + B (h2 (x),))) where g, 7 and / are fully connected layers and here is the Hadamard product.
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Gated Kiela et al. (2018) Similar FiLM, Gated the feature from modality to modulate the other. The output of Gated is denoted as f(X)) = g (y (h1 (x.,)))) o (3 (2)(), where g. Y and | fully connected layers and is the sigmoid function. Notice the form of output by FiLM and Gated can not be decomposed into parts of modalities, so in our experiment, we deactivate modality by inputting zero tensor to get the single modality performance. In our experiment, audio modality is modality I and visual modality is modality 2 in the formula.
Unimodal Learning Naive Unimodal Learning trains each modality separately and combines them during the prediction phase. Training separately helps the encoder of each modality efficiently learn modality-specific information. However, the model is unable tell whether inputs from different modalities come from the same sample modalities inputted independently during training.
B.2 DETAILS OF THE EXPERIMENT ON MVSA (TABLE 3)
experiment, align with CLIP's prediction paradigm, we define class-specific features e and c for each class. For each label y. the model's output logit is computed as:
fo(f. fo) = s(c f.)
s(c ft
(38)
where:
(c y }} (c0 E y} the trainable class-specific features
fi and are CLIP's output features
is CLIP's temperature coefficient
s(..) denotes cosine similarity
Training configuration:
Total epochs: 100
Batch size: 32
Learning rate: 0.01 (decayed to 0.001 after epoch 70)
Due to relatively small accuracy differences observed in the experiment, we include error bounds with 95% confidence intervals in Table 5. The results show that although the performance is very close, there is no overlap between the confidence intervals of multimodal accuracy (Multi) of TCMax and the second-bes best method (Joint Learning). This statistically significant differenee (p > 0.975² 0.95) confirms that the performance gap is not caused by experimental variance.
Table 5: Result of the average test accuracy (%) of random seeds on MVSA with frozen CLIP pretrained encoders. We report the 95% confidence intervals.
RN50 Text
VIT-B/32 Text
Methods
Image
Multi
Image
Multi
Joint
75.76 + 0.20
73.60 + 0.16
81.23
0.27
76.88 0.09
74.27 + 0.27
82.83 = 0.15
Unimodal
76.74 + 0.07
77.16
0.22
80.02 0.13
78.54 + 0.09
76.97 + 0.07
81.77 0.15
TCMax
75.38 + 0.12
74.97 + 0.54
81.75 4 0.23
78.03 4 0.16
76.55 + 0.22
84.05 + 0.15
C POTENTIAL IN REGRESSION TASKS
Although this paper primarily focuses on the task of multimodal image classification, TCMax may also be applied to other tasks, such regression. Here, we simple regression task example explore the potential TCMax regression scenarios.
We employ two sentiment analysis datasets: CMU-MOSI and CMU-MOSEL We use MAG-BERT Rahman et al. (2020) as the baseline, which takes multimodal inputs from audio (AA), visual (V). and text (C) modalities and outputs continuous value ())) representing the degree of positive sentiment. To train with TCMax we first define the mapping Fe A x L R in Equation 11.
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We modified the prediction head output both the predicted value and its confidence: Upred Mpread (a, v, and Cared(a, v, 1). We define our paper's Equation 11 as:
Fa (, (a, v, v)²
ACpred(a, e, (,
(39)
d²
where a represents the standard deviation in the predicted Gaussian distribution, and À multiplicative coefficient to facilitate analysis. Let B and Bm denote the batch and sampled negative set, respectively. Substituting this into Equation 11 yields:
(Upred(a, v. - 8)² + -Apreedaa,
LieMax = E(agnAster
(40)
exp (-
(Ubreala, v, v)² depreala, v,,),,,)))) v.1)]]
+ log (io.
a²
For classification tasks where takes discrete values, conventionally labels typically occur with roughly equal frequency. However, this continuous y case, we must explicitly define y's probability distribution in B For the derivation, we assume follows uniform distribution over interval (a, bj. yielding the following loss function:
uniform distribution Fy since
LreMax
v.vvv. [(yrralaa, e, })²]
oa
+ x
Y-B(ornAuEE [epred v. log Ela,ndy)ER, [exp (Cpred v,1)]}
(41)
[" exp (- (Ubred va, v)² dy log (b.)).
+ log
By taking the limits as + -oc and b + +oo (i.c., extending to R), while observing that the - log (b a)
term becomes divergent vanishes during differentiation (heing constant), we obtain the final form:
LTeMa
E(a.vd.)e [(upred(a, v, =)
MSE
Ela.ddaees [Cpred(a, + log E 1. (exp (aprad a v, ()]]]
lim log '-" exp σ2
(Upred(a, v, 21 dy
(42)
Ea....eee [(ypred(a, v, m)²
MSE
E(a.vddn) [apreala, u. + log Ea (exp (Cprou(aa, (,)),, + log vio.
TCMax
The resulting loss function naturally decomposes into components: (1) The first term constrains regression accuracy (MSE); (2) The second term enforces TCMax's 's cross modal alignment constraint on (a, v, I) triplcts. When À = (eliminating (pred), the loss reduces to conventional MSE as the second term is eliminated.
Table 6 presents the experimental results the CMU-MOSI and CMU-MOSEI datasets. After training with TCMax, the model achieves modest improvements on both datasets. This suggests that TCMax may hold potential research value for such regression tasks, and further in in-epph studies will be conducted the future.
Table 6: Result CMU-MOSI and CMU-MOSEI datasets. For CMU-MOSI, set 0.5, while for CMU-MOSEL, 0.75. all experiments, seeds.
all results represent averages across three random
Dataset
Mehod
Binary Acct
F1f
MAEJ
Corrt
Baseline (MAG-BERT) TCMax
83.36
83.21
0.7938
0.7644
CMU-MOSI
84.27
84.13
0.7775
0.7753
Baseline (MAG-BERT)
85.14
85.10
0.5903
0.7867
CMU-MOSEI
TCMax
85.61
85.52
0.5889
0.7887
17


Reviews:
[{"review_id": "70Wn0GJli8", "reviewer": "Reviewer_TfiU", "summary": "This paper addresses the problem of modality competition in multimodal learning, where multimodal models tend to overfit dominant modalities and underutilize weaker ones, sometimes performing worse than unimodal baselines. While previous methods have attempted to rebalance or combine joint and unimodal learning empirically, this work takes an information-theoretic approach. The authors analyze modality competition through the lens of total correlation.\n\nThe authors propose a new method for multimodal classification that maximizes total correlation between multimodal features and target labels, which naturally promotes more balanced learning and integrates multimodal interactions. They build on Mutual Information Neural Estimation (MINE) and introduce Total Correlation Neural Estimation (TCNE), which estimates a lower bound on total correlation. Using this, they develop TCMax, a novel loss function that optimizes total correlation via a variational bound. Experimental results reportedly show that TCMax outperforms both joint and unimodal baselines, on several datasets.\n\nWhile the method is currently limited to fully supervised classification tasks, the proposed theoretical framework is both rigorous and well-justified, offering valuable insights that could inspire broader multimodal learning research.", "questions": "- How do the authors quantitatively define “weak” and “strong” modalities in their analysis?\n\n- The paper claims that analyzing two modalities holds “without loss of generality.” Could the authors clarify the theoretical justification for this claim? How does the proposed framework account for higher-order dependencies (e.g., synergy, redundancy) that arise when $M > 2$ Would the total correlation objective or optimization strategy require modifications?\n\n- Is the proposed total correlation objective compatible with or could be adapted for self-supervised learning setups?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Strong theoretical foundation: The paper provides a clear and rigorous information-theoretic formulation for learning from multimodal inputs.\n\n2. Novel objective function: The introduction of Total Correlation Neural Estimation (TCNE) and the TCMax loss.\n\n3. Conceptual clarity: The theoretical motivation is well-grounded and is easily applied into practice.\n\n4. Empirical validation: The experimental results consistently demonstrate performance improvements over multimodal and unimodal baselines.", "weaknesses": "1. **Vague definition of weak and strong modalities.**\nAlthough the paper discusses modality competition, the criteria used to define or quantify “weak” versus “strong” modalities are not clearly specified. Providing a more explicit operational definition or empirical measure would strengthen the theoretical analysis and clarify the interpretation of the results. Additional experiments that explicitly quantify these distinctions would further support the claims.\n\n2. **The claim that the analysis with two modalities holds “without loss of generality” is not justified (l. 141).** In multimodal settings with $M>2$ higher-order dependencies (synergy, redundancy) emerge that are irreducible to pairwise terms. Consequently, the total-correlation objective, identifiability conditions, and estimation behavior differ qualitatively from the bimodal case. Any guarantees or intuitions derived for two modalities therefore cannot be presumed to extend to \n$M>2$ without additional analysis.\n\n3. **In the same vibe as the previous point, scalability to multiple modalities is not clear.**\nThe current formulation and experiments seem primarily focused on bimodal settings. It is not obvious how the proposed total correlation maximization framework extends to scenarios involving more than two modalities, where inter-modal dependencies become more complex.\n\n4. **Restriction to supervised learning.**\nThe approach assumes access to fully labeled data, limiting its applicability to self-supervised multimodal scenarios, settings that are highly relevant in practice and that have been addressed in previous works [1, 2].\n\n\n5. **Missing discussion of relevant related work (FactorCL, CoMM).**\nThe paper could more clearly articulate how its information-theoretic perspective relates to or differs from recent approaches that explicitly model shared and modality-specific information, such as FactorCL [1] (which uses mutual information–based decomposition) and CoMM [2] (which leverages partial information decomposition). A comparative discussion, both conceptual and empirical, would clarify the novelty and positioning of the proposed framework within this emerging research direction.\n\n[1] Liang, P. P., Deng, Z., Ma, M. Q., Zou, J. Y., Morency, L. P., & Salakhutdinov, R. (2023). Factorized contrastive learning: Going beyond multi-view redundancy. Advances in Neural Information Processing Systems, 36, 32971-32998.\n\n[2] Dufumier, B., Castillo-Navarro, J., Tuia, D., & Thiran, J. P. (2025). What to align in multimodal contrastive learning?. International Conference on Learning Representations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rTSckeJw5n", "reviewer": "Reviewer_K9M3", "summary": "this paper tackles multimodal supervised learning using an information theory perspective. It shows why the modality competition occurs classically when optimizing the cross-entropy loss in a joint-learning framework and advocates for a different strategy: total correlation maximization between modalities and the target. The model is evaluated on six multimodal classification benchmarks and two regression benchmarks, and it demonstrates state-of-the-art results across all datasets.", "questions": "-\tIn equation 6, can you clarify why optimizing I(za, zv |y) is useful in your case since it quantifies the information contained in za and zv irrelevant for y. I would expect this term to actually decrease during training.\n-\tImplementation details: what is the architecture of the prediction (fusion) head? How did you choose it? Is it similar to other baselines? Does the architecture impact the results? \n-\tAre you going to release your code for reproducibility? \n-\tYou mentioned the computation cost of your method (at least during training). Did you quantify it in practice ?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "-\tThe paper is well written and clearly explains the motivation for their method from an information theory perspective.\n-\tThe mathematical analysis is easy to follow, and the proposed loss is simple, yet effective.\n-\tThe evaluation of the proposed method against baselines is fair and thorough, spanning across different domains and modalities (images, audios, videos).\n-\tThe results are strong in most cases and clearly confirms the hypothesis made by the authors regarding the modeling of cross-modal interactions.", "weaknesses": "-\tWhile I appreciate the completeness in the evaluation protocol in Table 2, I think it neglects the recent emergence of foundation models in the field of unimodal or multimodal representation learning (such as CLIP for vision and language, DINOv3 for vision, Wav2vec 2.0 for speech). I think it is also important to consider these pre-trained models as feature extractors and to apply your method on top of these, as you did afterwards in Table 4 for another dataset. It would clearly demonstrate the benefit of TCMax in a real-life scenario. \n-\tSupervised multimodal learning is a bit restrictive in terms of applications. Large-scale multimodal data come usually with very few annotations. I wonder how the proposed model would perform in the case of few-shot learning of semi-supervised learning. \n-\tBaseline models and concurrent approaches: since this work is deeply rooted in information theory, I think the works by Paul Pu Liang need to be properly cited and added to the baselines, for instance [1]. His work on self-supervised and supervised multimodal learning (using for instance the Partial Information Decomposition approach [2]) is very close to the one developed in this paper.\n-\tYou mentioned: « without loss of generality, we analyze the scenario with two modalities (audio and visual) »: from an information theory perspective, it restricts the analysis very much. As the authors mentioned, the MI between n=3 variables can be negatives (not the case when n=2), quantifying the interactions generally between n>2 variables is hard (see for instance the Partial Information Decomposition theory, O-Information, gradient of O-Information, etc…) and Total Correlation gives you only a very broad measure of independence between your input variables (without telling anything about  the interactions between paired or triplet of variables in a general system of n variables). I would expect at least a reformulation of this sentence, if not a discussion about it at the end (along with the other limitations of your work). \n-\tTypos: Figure 2 “Illusions” -> ”Illustration”\n\n[1] Learning factorized multimodal representations, Tsai et al., ICLR 2019\n[2] Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework, Liang et al., NeurIPS 2023", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FlNh20fYzy", "reviewer": "Reviewer_48tw", "summary": "This paper proposes TCMax, a multimodal classification objective that consists a lower-bound of Total Correlation. To achieve this lower bound, the authors utilize the MINE of Belghazi and the Donsker-Varadhan representation. The idea of rebasing the expectation of $E_P$ with $Q$ being the factorized $P_{Z_1} P_{Z_2}..P_Y$ is quite interesting for the multimodal training.", "questions": "Could you provide results with a separate validation/test set that doesnt include any form of data leakage, and explain this extensively somewhere in your supplementary matterial?\n\nHow does you method compare to MCR, D&R and supervised contrastive learning, both conceptually and experimentally?\n\nCould you include an intuitive explanation of your method?\n\nIt has been shown that MINE suffers from high variance as an estimator of MI, do you face a similar issue?", "limitations": "", "rating": 2, "confidence": 5, "soundness": 1, "presentation": 3, "contribution": 3, "strengths": "The paper has a sound proof to derive the lower bound to TC and an interesting idea to compare the expectation of the joint multimodal distribution with the unimodal ones. The problem and the solution as well motivated.", "weaknesses": "There is one quite major issue. Following the code in the anonymized repo, it seems that the method is using the test set to select the best model during training. This falls under the data leakage between the validation/test set, which are the same in this case. With this major issue, we drive the paper for rejection. Despite that, I will provide some more input on the rest of the paper since the idea is well put.   \n\nThe $I(Z_1;Y) + I(Z_2;Y) + I(Z_1, Z_2 | Y) = TC$ ignores that $Z_1, Z_2$ could correlate to predict $Y$, which essentially would be the synergy described by other papers. When you suggest that unimodal training and alignment beyond the task could achieve TC, you ignore this part. I consider this minor since you don't include it somehow in your method, if I understand it well. If you do, please elaborate.\n\nThe paper has not included a very important work that is quite close to the method proposed, MCR [1]. There are four parts that are worth discussing. First, they propose a different factorization of the joint mutual information (similarly to TC). Second, they showcase that supervised contrastive learning is lower-bound to some specific MI terms. I will come back to this. Third, they suggest that maximizing the CMI solely is not always the best option since you can still be stuck in a local minimum that you have optimized only one part of this. Finally, what you suggest is also a permutation of modalities and a penalization of their predictive probability which is quite close to permutation importance. Overall, I think comparing with this work and elaborating on improvements/differences will be highly necessary to illustrate the power and novelty of your paper.\n\nAbout the supervised contrastive learning, what you suggest resembles an InfoNCE that has one positive and many negatives, even the ones with the same label. Including comparison with supervised contrastive or other ways to choose the positive/negative sets shall improve the understanding of the method. Additionally, commenting in terms of MI terms would be extra useful here. \n\nAn intuitive explanation of what the final loss tries to push for will help readers convey the final message. \n\nAlso, please include D\\&R [2] for comparison since it has shown to be a strong baseline.\n\nLastly, I would like to incentivize scaling beyond the typical datasets and models. That should contribute further to our understanding of multimodal competition. \n\n[1] Kontras, Konstantinos, et al. \"Multimodal Fusion Balancing Through Game-Theoretic Regularization.\" arXiv preprint arXiv:2411.07335 (2024).\n\n[2] Yake Wei, Siwei Li, Ruoxuan Feng, and Di Hu. Diagnosing and re-learning for balanced multimodal learning. In European Conference on Computer Vision, pages 71–86. Springer, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9cIznCgf5l", "reviewer": "Reviewer_PGpr", "summary": "- Addresses an important problem: competition between modalities in training by maximizing total correlation (across modalities + labels) instead of tweaking per-modality losses.\n- Derives a lower bound (TCNE) and turns it into a practical, hyperparameter-free loss (TCMax)\n- Drop-in training objective; no inference changes or extra heads/schedulers.\n- Consistently boosts multimodal accuracy on audio-visual and image–text benchmarks; shows better cross-modal agreement (lower JS-divergence) and more balanced per-modality predictions.", "questions": "- How does this transfer across domains? because you're maximizing joint correlation with the labels on this dataset, it makes sense that you might fit the proper modality contributions here, but how do you know that you're not leading to modality competition in the transfer learning setting (which is common b/c this is probably going to be used for large scale pretraining)?\n- What do you lose by sampling instead of doing all the forward passes theoretically required by the method? \n- Do you have some explanation for why TCMax does not outperform baselines on unimodal? How would this fare in cases with high modality imbalance, where joint learning approaches unimodal learning?\n- How would this the change in training loss function lead to changes in the realistic downstream uses of the model? e.g., using argmax predictions over logit distributions using distributions as a measure of confidence calibration?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- Clean, well motivated information-theoretic formulation, and nice conversion into a usable loss function with strong results\n- Generally strong results across several datasets vs. recent balancing baselines.\n- Compute-aware: sampling reduces forward passes\n- Analysis beyond accuracy: JS-divergence and negative pair analysis are insightful", "weaknesses": "- Nit: Figure 2: an \"illusion\" -> illustration?\n- See questions", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)