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Self-Supervised Splitting Losses

Updated 5 October 2025

Self-supervised splitting losses are loss functions that partition training objectives into distinct supervised and auxiliary components.
They enable robust, transferable feature learning by balancing multiple constraints, leading to improved generalization across diverse applications.
Implementation strategies include multi-head networks and component-wise splits, enhancing performance in settings like few-shot classification and federated learning.

Self-supervised splitting losses refer to a class of loss function designs wherein learning objectives are partitioned, combined, or “split” into multiple complementary components—often mixing supervised and self-supervised signals, or partitioning self-supervised constraints by data transformation, architecture, or representation level. This approach enables neural networks to learn more robust, generalizable, and transferable feature representations without explicit external supervision, leveraging the structure and transformations of available data. Self-supervised splitting losses are applied widely in domains such as few-shot classification, representation learning for vision and audio, anomaly detection, inverse problems, federated learning, and high-content imaging.

1. Principles and Formulation of Self-Supervised Splitting Losses

Self-supervised splitting losses decompose the overall training objective into distinct components, each targeting different aspects of data or representation. Typical splits include:

Supervised loss ( $\mathcal{L}_s$ ): Standard classification or regression loss measured between predictions on unmodified input and ground-truth labels ( $\mathcal{L}_s = \sum_i \ell(g \circ f(x_i), y_i) + \mathcal{R}(f, g)$ as in (Su et al., 2019)).
Self-supervised auxiliary loss ( $\mathcal{L}_{ss}$ ): Computed by applying known transformations to input data (e.g., jigsaw puzzles, rotations) and requiring the network to predict an auxiliary label derived from the transformation; typically constructed as $\mathcal{L}_{ss} = \sum_i \ell(h \circ f(\hat{x}_i), \hat{y}_i)$ .
Contrastive losses: Often split into “positive” (alignment) and “entropy” (diversity, uniformity, negative) terms, with separate weighting or aggregation strategies; e.g., in (Sors et al., 2021), $\mathcal{L}(z) = \lambda_p \overline{\ell}_p(z) + \lambda_e \overline{\ell}_e(z)$ .
Measurement splitting and equivariant splitting: Inverse problem settings employ measurement splitting losses to train a network to reconstruct unobserved data, with further splitting achieved by equivariant transformations (Sechaud et al., 1 Oct 2025).

Splitting losses encourage networks to optimize not just for main tasks but also for auxiliary or structural constraints, often acting as regularizers and supporting generalization.

2. Architectural and Methodological Patterns

Splitting losses can be implemented via architectural choices and optimization strategies:

Multi-head networks: Partitioned loss components are typically handled by separate output heads (e.g., one for supervised task, one for self-supervised auxiliary classification; see $g$ and $h$ in (Su et al., 2019)).
Temporal or transformation split: In federated or distributed settings, layers are split between client and server (or agents), and losses are computed over the linearly separated representations, e.g., InfoNCE contrastive loss applied on split activations in federated setups (Przewięźlikowski et al., 12 Jun 2024).
Component-wise splitting: SpliCER (Farndale et al., 10 Mar 2025) divides inputs into sections and aligns chunks of embedding vectors to privilege information from each image region or spectral band, formulating the loss as a sum over conditional mutual information objectives for each component.
Equivariant and measurement splitting: In inverse problems, the loss can be split over virtual observations and transformation groups, enabling training from incomplete data while matching the optimal supervised solution in expectation (Sechaud et al., 1 Oct 2025).

These methodological designs support the parallel optimization of multiple representation constraints, enforce competition or complementarity at the architectural level, and improve the efficiency or privacy of distributed model training.

3. Empirical Impact and Benchmark Results

Self-supervised splitting losses yield measurable improvements in generalization, robustness, and transferability:

Setting	Method (Paper)	Metric/Improvement
Few-shot classification	Jigsaw split (Su et al., 2019)	5–27.8% relative error rate reduction
Scene flow estimation	NN + cycle (Mittal et al., 2019)	EPE $\sim$ 0.105m, matches supervised
Computational pathology	S5CL splits (Tran et al., 2022)	$+$ 9% accuracy, $+$ 6% F1 in label-scarce settings
Medical imaging	SpliCER (Farndale et al., 10 Mar 2025)	$+$ 4pp complex feature gain; $+$ 25pp cell subtype accuracy
MRI reconstruction	LPDSNet splitting (Janjusevic et al., 21 Apr 2025)	$+$ 2dB PSNR (supervised); robust SSDU, joint denoising

Experimental results demonstrate that splitting losses are particularly effective when the main task is challenging, labels are scarce, or high-level supervision is weak. The benefits of self-supervised splits often grow with the complexity and difficulty of the downstream problem.

4. Design Considerations: Balancing, Aggregation, and Hyperparameters

Proper balancing and aggregation of split losses are critical for optimal performance:

Balance hyperparameters ( $\lambda_p, \lambda_e$ ): Relative weighting of “alignment” and “entropy” sub-losses in contrastive objectives can be optimized via coordinate descent in reparameterized spaces, outperforming standard fixed aggregation strategies (Sors et al., 2021).
Batch size: Aggregation strategy (e.g., global vs. separate averaging over pairs) directly affects the effective loss balance as batch size changes; separate averaging maintains robustness across batch sizes.
Switching schedules: In hybrid approaches (e.g., (Ge et al., 2023)), training may begin with instance-level similarity loss before introducing clustering-level cross-entropy or modified cross-entropy components, leveraging adaptive schedules for representation quality.
Normalization and bias: Over-normalization or poorly tuned bias terms can induce unwanted dimensional collapse in feature space (Ziyin et al., 2022); careful parameterization can prevent collapse in essential feature directions while supporting regularization.

Balancing the partitioned loss terms, tuning aggregation strategies, and optimizing hyperparameters are necessary steps for the success of self-supervised splitting approaches.

5. Robustness to Data Imbalance, Privacy, and Distribution Shift

Splitting losses improve robustness in several structural settings:

Data imbalance: Losses whose effective Hessian depends primarily on augmented data covariance ( $C$ ), as in Spectral Contrastive Loss, exhibit insensitivity to imbalanced data features compared to InfoNCE (Ziyin et al., 2022).
Privacy and communication efficiency: In federated self-supervised learning, splitting network depth optimizes for privacy and communication overhead; aligning both online and momentum branches (MonAcoSFL) avoids accuracy drops due to split drift (Przewięźlikowski et al., 12 Jun 2024).
Complex feature detection: Component-wise splitting architectures (SpliCER) circumvent simplicity bias, ensuring non-dominant, high-value information is learned (Farndale et al., 10 Mar 2025).
Noise and model generalization: Explicit decoupling of observation and signal prior (LPDSNet) yields noise-level generalization and stability under self-supervision (Janjusevic et al., 21 Apr 2025).

Thus, self-supervised splitting losses can be tailored for resilience to practical challenges in supervised data acquisition, privacy, class imbalance, subtle features, and physical constraints of measurement processes.

6. Applications Across Domains

Self-supervised splitting losses are utilized in a range of domains:

Vision: Few-shot image classification (Su et al., 2019), high-content medical and satellite imaging (Farndale et al., 10 Mar 2025), 3D scene flow (Mittal et al., 2019), implicit surface extraction (Sundararaman et al., 28 May 2024), object-centric representation learning (Baldassarre et al., 2022).
Language and anomaly detection: One-class textual anomaly detection using masked LLMs, causal models, and contrastive losses (Mai et al., 2022).
Speech: Efficient, overfitting-resistant multilingual/multitask ASR via connection-level binary mask splitting (Fu et al., 2022).
Inverse problems: MRI reconstruction via primal-dual splitting (Janjusevic et al., 21 Apr 2025); unsupervised image inpainting and compressive sensing with equivariant splitting (Sechaud et al., 1 Oct 2025).
Federated and distributed learning: Privacy and communication-optimized federated representation learning via split contrastive losses (Przewięźlikowski et al., 12 Jun 2024).
Sample-efficient transfer: Adaptive contrastive distillation with memory-informed negative selection (Lengerich et al., 2022).

These applications demonstrate that splitting losses can be flexibly integrated into various self-supervised and hybrid frameworks, addressing both domain-specific and meta-learning challenges.

7. Theoretical Guarantees and Mathematical Foundations

Self-supervised splitting losses are underpinned by rigorous theoretical analysis:

Minimizers of equivariant splitting losses recover the MMSE estimator under mild assumptions, matching the supervised learner in expectation (Sechaud et al., 1 Oct 2025).
Analytical theory of loss landscapes identifies stationary points, collapse conditions, and informs normalization and bias strategies (Ziyin et al., 2022).
Gradient and convergence analyses of instance-level similarity versus clustering-level cross-entropy losses elucidate how representation quality is affected by the loss split (Ge et al., 2023).
Upper bounds on gradient norms and separability metrics drive practical regularization and diagnostic strategies.

These theoretical results inform the design, optimization, and interpretability of splitting loss frameworks, offering principled approaches for building resilient self-supervised learning systems.

Self-supervised splitting losses provide a versatile foundation for learning robust, transferable, and privacy-preserving representations in settings with limited supervision or incomplete observations. By partitioning the training objective, balancing loss components, and careful architectural integration, these methods enable high-performance learning across a spectrum of domains and problem types. For further methodological and experimental details, refer to works such as (Su et al., 2019, Mittal et al., 2019, Sors et al., 2021, Ziyin et al., 2022, Tran et al., 2022, Farndale et al., 10 Mar 2025, Sechaud et al., 1 Oct 2025), and others.