VICReg-Based Semi-Supervised Strategy

• VICReg-Based Semi-Supervised Strategy is a framework that employs a two-stage pipeline combining self-supervised pretraining with VICReg loss and supervised fine-tuning for label-scarce scenarios.
• It harnesses a composite loss that enforces invariance, variance, and decorrelation to prevent representation collapse and enhance feature learning across modalities.
• Empirical results demonstrate significant performance gains in handwriting verification, vegetation estimation, and soundscape classification compared to traditional methods.

A VICReg-based semi-supervised strategy leverages the Variance-Invariance-Covariance Regularization (VICReg) objective as the core mechanism for extracting robust representations from large collections of unlabeled data, followed by supervised adaptation on a limited labeled subset. VICReg explicitly avoids representation collapse by regularizing invariance to augmentations, per-dimension variance, and feature decorrelation, and can be integrated into a wide range of semi-supervised pipelines across computer vision, remote sensing, and acoustic domains (Bardes et al., 2021, Chauhan et al., 28 May 2024, Zhang et al., 20 Dec 2025, Dias et al., 2023).

1. Fundamentals of VICReg Loss

The defining feature of VICReg is its composite loss function applied during self-supervised pretraining. For each input, two independent augmented views $(x^a, x^b)$ are generated, embedded via encoder and projection head into $y^a, y^b \in \mathbb{R}^d$, and the following losses are symmetrized over the batch:

• Invariance Term ($\mathcal{L}_\mathrm{inv}$): Penalizes mean-squared Euclidean distance between paired embeddings:

$$\mathcal{L}_\mathrm{inv} = \frac{1}{N} \sum_{i=1}^N \| y^a_i - y^b_i \|_2^2$$

This enforces that augmentations of the same image are mapped to similar representations.

• Variance Regularization ($\mathcal{L}_\mathrm{var}$): Ensures per-dimension sample standard deviation is at least $\gamma$:

$$\mathcal{L}_\mathrm{var} = \frac{1}{2d} \sum_{Z \in \{y^a, y^b\}}\sum_{j=1}^d \max\bigl( 0, \gamma - s_j(Z) \bigr)^2$$

where $$s_j(Z) = \sqrt{\mathrm{Var}(Z_{:,j}) + \varepsilon}$$, $\gamma = 1.0$, $\varepsilon = 10^{-4}$.

• Covariance Decorrelation ($\mathcal{L}_\mathrm{cov}$): Penalizes off-diagonal entries in the batch covariance:

$$\mathcal{L}_\mathrm{cov} = \frac{1}{d} \sum_{Z \in \{y^a, y^b\}} \sum_{j\neq k} [C_{jk}(Z)]^2$$

with $C(Z)$ the empirical covariance of $Z$.

• Overall VICReg Loss:

$$\mathcal{L}_{\text{VICReg}} = \lambda\cdot\mathcal{L}_\mathrm{inv} + \mu\cdot\mathcal{L}_\mathrm{var} + \nu\cdot\mathcal{L}_\mathrm{cov}$$

Standard hyperparameters: $\lambda = 25$, $\mu = 25$, $\nu = 1$ (Bardes et al., 2021).

2. General VICReg-Based Semi-Supervised Training Pipeline

VICReg-based semi-supervised frameworks share a two-stage protocol:

1. Self-Supervised VICReg Pretraining:
   • Unlabeled samples are augmented to form positive pairs.
   • The encoder plus projection head (MLP expander) are trained with the VICReg loss until representation collapse is abated and feature decorrelation is achieved.
2. Supervised Fine-Tuning:
   • The encoder is either frozen or unfrozen.
   • A task-specific supervised head is attached (classification or regression).
   • Labeled data is used to optimize only the supervised loss (e.g., cross-entropy or mean squared error).
   • No contrastive or VICReg terms are typically added at this stage.

This protocol is realized in handwriting verification (Chauhan et al., 28 May 2024), LAI/SPAD estimation for vegetation (Zhang et al., 20 Dec 2025), and soundscape classification (Dias et al., 2023).

3. Architectural and Implementation Details

The architectural choices are adapted to modality and task but exhibit consistent patterns:

Modality	Encoder	Projector/Head	VICReg Dim $d$	Batch Size	Pretraining Optimization
Handwriting	ResNet-18	3-layer MLP, 2048 hidden	2048	256	SGD, cosine annealing, 100 ep
Multispectral VI	Custom CNN + VI-SA	2-layer MLP, 256 hidden	256	100	AdamW, fixed LR, 500 ep
Soundscapes	ResNet-50, others	3-layer MLP, 512 hidden	512	30–50	Adam/SGD, 100 ep

Encoder adaptation during fine-tuning varies: MCVI-SANet freezes the backbone (Zhang et al., 20 Dec 2025), while others fine-tune the whole network (Chauhan et al., 28 May 2024, Dias et al., 2023). Projector heads used for VICReg loss are typically discarded for downstream tasks.

Data augmentations are modality-specific and strongly influence representation quality. For image and audio, augmentations include random crops, flips, color jitter, rotation, and spectrogram-level modifications. For multispectral data, only spatial augmentations preserving channel semantics are employed.

4. Domain-Specific Adaptations and Attention Mechanisms

Task-specific modifications to standard VICReg practice have tangible impact:

• MCVI-SANet integrates a Vegetation-Index Saturation-Aware Block (VI-SA Block) before VICReg pretraining. This block computes channel statistics (GAP, STD), channel recalibration (FRE), and depthwise spatial attention (DSAM) to generate more variance-rich, decorrelated feature maps resilient to VI saturation (Zhang et al., 20 Dec 2025).
• In soundscape and handwriting, no explicit attention module is used, but the various data augmentations and indented architectural choices play a similar regularizing role (Chauhan et al., 28 May 2024, Dias et al., 2023).

No paper reports direct ablation of the VICReg loss weights, but the strong boost over SimCLR, MoCo, and Barlow Twins under standard VICReg settings (λ=25, μ=25, ν=1) demonstrates the importance of balanced regularization (Chauhan et al., 28 May 2024, Dias et al., 2023).

5. Performance and Empirical Results

VICReg-based semi-supervised strategies consistently yield leading or near-leading performance across domains and label-scarce scenarios:

• Handwriting Verification: VICReg pretrain + fine-tune achieves 78% accuracy (+9% relative) with only 10% labeled writers (ResNet-18 baseline: 72%) (Chauhan et al., 28 May 2024).
• Vegetation LAI/SPAD Estimation: MCVI-SANet (VI-SA Block + VICReg SSL) gives LAI $R^2 = 0.8123$ (vs. $0.7456$) and SPAD $R^2 = 0.6846$ (vs. $0.6329$), exceeding fully-supervised baselines by 8.95% and 8.17% respectively (Zhang et al., 20 Dec 2025).
• Bioacoustic Classification: VICReg pretraining on ResNet-50 recovers balanced accuracy within 5pp of ImageNet pretraining (0.72 vs 0.77) and outperforms Barlow Twins and SimCLR (Dias et al., 2023).

Ablation studies confirm the necessity of all VICReg terms to avoid collapse and maximize transfer. Increased unlabeled data beyond 2× gives diminishing returns, and projector width above standard settings offers minimal improvement (Bardes et al., 2021, Dias et al., 2023).

6. Best Practices, Implementation, and Extensions

Adherence to the following practices is validated empirically (Bardes et al., 2021, Dias et al., 2023):

• Fine-tune the entire network (not just the head) for best semi-supervised accuracy; freezing is sometimes effective in regression (Zhang et al., 20 Dec 2025).
• Batch normalization in projectors stabilizes variance/covariance computation.
• Early stopping on validation metrics prevents overfitting in the low-label regime.
• For mixed mini-batch training (labeled and unlabeled), combine supervised and VICReg losses as:

$$\mathcal{L}_{\rm total} = \alpha\,\mathcal{L}_{\rm sup} + \beta\,\mathcal{L}_{\text{VICReg}}$$

with $\alpha=1$, $\beta \simeq 1$ as defaults, but further tuning is recommended when proportions are imbalanced (Bardes et al., 2021).

• Label-stratified validation (e.g., k-means on phenological variables (Zhang et al., 20 Dec 2025)) improves cross-stage generalization.

Optionally, pseudo-labeling can be introduced: model-generated soft labels on high-confidence unlabeled samples are incorporated into the supervised loss with reduced weight (Bardes et al., 2021).

7. Comparative Analysis and Domain Impact

VICReg-based semi-supervised strategies demonstrate robust, label-efficient feature learning across visually (handwriting, remote sensing) and acoustically (bioacoustics) diverse domains. In all cases, the balance between invariance, variance, and covariance regularization is critical for effective non-collapsed representation learning and downstream transfer. Methods relying on weaker regularization (e.g., SimCLR, MoCo) do not match VICReg's performance in low-label scenarios. Domain-specific augmentations and attention mechanisms, such as the VI-SA Block and stratified sampling, further amplify benefits in complex real-world settings (Chauhan et al., 28 May 2024, Zhang et al., 20 Dec 2025, Dias et al., 2023, Bardes et al., 2021).