Self-Supervised Learning Phase

• Self-supervised learning phase is a process where models autonomously learn robust, task-agnostic representations from unlabeled data using automatically generated supervisory signals.
• It employs diverse techniques such as contrastive, bootstrapping, and kernel methods that compare augmented views or shift embeddings to enforce invariance and prevent collapse.
• This phase underpins applications in computer vision, NLP, and autonomous perception by transferring learned features to downstream tasks with strong generalization.

Self-supervised learning (SSL) phase refers to the stage in machine learning where representations are learned from unlabeled data by leveraging automatically constructed supervisory signals. During this phase, models are trained to predict inherent structure or context within the data itself, without relying on human-annotated labels. SSL has become foundational across domains such as computer vision, natural language processing, and autonomous perception, with a diverse array of algorithms that encompass contrastive, cluster-based, generative, kernel, and multi-task paradigms. The SSL phase aims to produce task-agnostic representations that generalize well to a broad distribution of downstream tasks.

1. Formalization of the SSL Phase

In the SSL phase, a model—often a deep feature extractor—learns by solving a pretext task defined purely by unlabeled or weakly labeled data. For input data $x \in \mathcal{X}$, the model $f_\theta$ is optimized with respect to a loss $\mathcal{L}_{SSL}$ constructed from "pseudo-labels" or invariant relations:

$$\mathcal{L}_{SSL}(\theta) = \frac{1}{N} \sum_{i=1}^{N} \ell(f_\theta(T_a(x_i)),\,T_b(x_i))$$

where $T_a, T_b$ are stochastic data augmentation operators, or proxies in more general forms (e.g., analytic supervisors $A(x_i, x_n)$ as in autonomous perception (Chiaroni et al., 2019)).

The SSL pipeline typically consists of:

• Data augmentation or analytic pseudo-labeling (defining invariance/equivariance or supervision from structure/auxiliary sensors)
• A trainable backbone (e.g., ResNet, ViT) possibly equipped with projection and/or prediction heads
• A training loss that pulls together representations of related data (positives) and, when appropriate, pushes apart unrelated samples (negatives/decorrrelation)

The learned representation $g_\theta$ is subsequently transferred to downstream tasks by replacing or augmenting the SSL-task-specific head.

2. Key Algorithmic Paradigms and Objectives

2.1 Contrastive and Bootstrap Methods

Contrastive methods (e.g., SimCLR, MoCo) and non-contrastive/bootstrapping methods (e.g., BYOL, SimSiam, DINO) are distinguished by their objective functions:

• Contrastive: Use explicit positive and negative pairs, optimizing for agreement between augmentations of the same sample and disagreement between others, most commonly via the InfoNCE loss:

$$\mathcal{L}_{\text{InfoNCE}} = -\log \frac{\exp(\langle z_i, z_j^+ \rangle/\tau)}{\exp(\langle z_i, z_j^+ \rangle/\tau) + \sum_{k} \exp(\langle z_i, z_k^- \rangle/\tau)}$$

where $z_i, z_j^+$ are positive pairs, and $\tau$ is the temperature (Marks et al., 16 Jul 2024).

• Bootstrapping (Non-contrastive): Use asymmetry, predictor or EMA teacher, and architectural or optimization bias to avoid collapse. The loss reduces to minimizing distance or maximizing similarity between outputs of two networks with different views, with architectural choices (predictor, EMA, centering) enforcing stability (Jha et al., 22 Feb 2024).

2.2 Mean-Shift and Group-based Approaches

• Mean-Shift for SSL (MSF): Generalizes BYOL by "shifting" embeddings towards the mean of $k$ nearest neighbors in the embedding space, avoiding explicit negative pairs. The loss:

$$L_i = \frac{1}{k} \sum_{z_j \in N_i} \| v_i - z_j \|_2^2$$

recovers BYOL as $k=1$. Memory banks store embeddings for local neighbor search, and strong augmentations such as those in MoCo v2 are employed. MSF achieves state-of-the-art results for small $k$ with lower risk of semantic class collision (Koohpayegani et al., 2021).

• Group Masked and Multi-Concept SSL: MC-SSL0.0 extends single-concept SSL by masking groups of connected patches and learning pseudo-labels for each patch via a momentum encoder. The loss combines reconstruction (for context-aware grouping) and pseudo-concept classification (for multi-concept clustering), resulting in token-level concept discovery (Atito et al., 2021).

2.3 Kernel and Spectral Methods

• Joint Embedding in Kernel Regime: SSL objectives are formulated as spectral filters on kernels induced by data augmentation and architecture. The optimal embedding minimizes losses such as:

$$\mathcal{L}_{\rm contrastive}(W) = \left\| W\Phi(X)^\top \Phi(X) W^\top - (A + I_N) \right\|_F^2$$

with $A$ the positive pair adjacency, and the solution is given via eigendecomposition and projection in RKHS (Kiani et al., 2022).

• Spectral Bounds: Generalization is tightly characterized by eigenspectra of augmentation and architecture operators; strong augmentations contract the invariant subspace, regularization and architectural bias (e.g., convolutional kernels) encourage transferability and avoid collapse (Cabannes et al., 2023).

2.4 Multi-Task and Aggregative SSL

• Complementarity-driven Aggregation: Rather than relying on a single pretext task, features from multiple proxy tasks are fused. Selection can be greedy and based on least-correlated (measured by centered kernel alignment) representation subspaces. Auxiliary optimization penalizes over-alignment to previous SSL solutions, promoting feature diversity (Zhu et al., 2020).

2.5 Specialized and Domain-Informed SSL

• Autonomous Perception: In settings with structured sensors (stereo, LIDAR, odometry), analytic modules generate dense geometric or semantic pseudo-labels. SSL heads are trained on outputs such as depth, traversable area, dynamic segmentation, or even future occupancy grids in a fully self-supervised fashion (Chiaroni et al., 2019).
• Motion Forecasting with Multi-Task SSL: Tasks such as lane-masking, distance-to-intersection, maneuver, and success/failure prediction are jointly optimized within an agent+map encoder, using auxiliary MLP heads and cross-entropy/autoencoder/regression losses. This produces a single backbone with strong transfer to downstream trajectory forecasting (Bhattacharyya et al., 2022).

3. Architectural and Optimization Considerations

Component	Common Choices	Notable Variants/Results
Backbone	ResNet-18/50, ViT-S/16	ConvNet partial (S3L), multi-view ViT
Projection/Prediction Head	MLP: 2–3 layers, BN, ReLU	Per-pixel (LEWEL), token (ViT patch), alignment maps
Teacher-Student/EMA	BYOL, DINO, MC-SSL	EMA momentum $m=0.99\rightarrow1$.
Memory Bank	MoCo/MSF: $M\approx 1$M, FIFO	FAISS/inner product search, ablations to 128K
Augmentations	MoCo v2 (strong), SimCLR recipe	Weak/weak, weak/strong (MSF ablations and gains)
Optimization	SGD/Adam: LR decay, batch norm	S3L: scale input/backbone to data/task size

Efficient training and stability are influenced by matching the model and data resolution/capacity to the effective information content of SSL signals. S3L demonstrates that high-resolution and deep backbones often waste computation and exhibit poor generalization for contrastive SSL; reducing image size and backbone depth accelerates convergence and improves accuracy on low-resource or fine-grained datasets (Cao et al., 2021).

Stability in SSL arises from inductive biases imposing a zero-mean constraint or analogous decorrelation on the embedding space, enforced via explicit negatives, parametric prototypes, batch norm, centering, or predictor-asymmetry. Loss design in non-contrastive regimes (BYOL, SimSiam, DINO, Barlow Twins, SwAV) all functionally minimize global representational mean to avoid trivial collapse, as grounded in detailed empirical and theoretical analysis (Jha et al., 22 Feb 2024).

4. Evaluation Protocols and Progress Monitoring

SSL phase performance is typically assessed via protocol triads: linear probing (LP), $k$-nearest-neighbors (kNN) classification, and end-to-end fine-tuning (FT). For most in-domain and out-of-domain transfer scenarios, in-domain linear-kNN probe accuracy is the best available proxy for downstream task performance (Spearman $\rho=0.85$–$0.88$) (Marks et al., 16 Jul 2024). Batch normalization before linear heads and feature normalization is critical, especially for generative pretraining such as masked image modeling.

Label-free evaluation of SSL progress is an open challenge when annotated data is inaccessible. Entropy of the low-dimensional embedding (e.g., from UMAP projections) proves to be an architecture-agnostic measure for contrastive methods, with strong negative correlation to linear probe accuracy ($\rho \approx -0.8$ to $-0.9$). Clustering metrics (silhouette, mutual information agreement) are only reliable in same-architecture settings and often fail or reverse sign for non-contrastive methods like SimSiam, reflecting the unique collapse/expansion dynamics in their embedding spaces (Xu et al., 10 Sep 2024).

5. Theoretical Frameworks and Generalization

Recent work casts SSL in terms of generative latent variable models where samples are grouped by shared latent "content" and variable "style" factors:

• The SSL objective maximizes an evidence lower bound (ELBO):

$$\mathrm{ELBO}_{\rm SSL} = \sum_{j=1}^J \mathbb{E}_{q_\phi(z_j|x_j)}[\log p_\theta(x_j|z_j)] - \sum_{j=1}^J \mathbb{E}_{q(y|x_{1:J})}[\mathrm{KL}(q_\phi(z_j|x_j)\| p(z_j|y))]$$

where the second term "pulls positive views together", while the reconstruction term ensures information preservation and prevents collapse. Discriminative SSL objectives (contrastive, clustering) are special cases replacing reconstruction with entropy/variance surrogates; generative SSL (SimVAE) restores reconstruction leading to representations that preserve both style and semantic content (Bizeul et al., 2 Feb 2024).

Generalization in SSL depends on the spectral properties of the augmentation operator (enforcing invariance) and the architecture-induced kernel (regularizing for simplicity/smoothness). Proper regularization and hyperparameter tuning (regularization, early stopping, architectural bottleneck) prevent degenerate, collapsed solutions and ensure that the learned subspace is both maximally invariant and sufficiently expressive for downstream transfer (Cabannes et al., 2023).

6. Practical Guidelines and Limitations

SSL phase design must account for task, domain, and resource constraints:

• For unsupervised domains with rich structure or multi-modal sensors, analytic self-labelers should be selected to target semantically proximate pretext tasks and provide dense, reliable supervision. Multi-task and joint-aggregation strategies further promote robust, generalizable representations (Chiaroni et al., 2019, Zhu et al., 2020).
• When learning on limited data or compute budgets, scaling down input resolution and network depth (partial backbone, S3L) matches model capacity to mutual information content—yielding better performance per compute than standard "large data/large network" recipes (Cao et al., 2021).
• Progress and collapse should be monitored both via linear probes and, in unlabelled settings, via entropy of projected embeddings; however, care must be taken to account for method-specific collapse dynamics, especially in non-contrastive methods (Xu et al., 10 Sep 2024).
• In semi-supervised scenarios with distribution shift, interleaving self-supervised auxiliary adaptation steps (SSFA) decouples pseudo-labels from the main model and substantially improves performance under domain drift (Liang et al., 31 May 2024).

SSL phase design remains constrained by pseudo-label noise, optimizer-induced collapse, and potential mismatch between pretext and downstream invariance. Theoretical bounds derived in the kernel/spectral regime help in guiding augmentation and architecture choices, yet further work is required to fully characterize non-linear, finite-width, and multi-modal regimens.

7. Summary Table: SSL Phase Design Choices

Aspect	Standard SSL	Variants / Techniques	Main Insights
Objective	InfoNCE, BYOL, etc	Mean-Shift, group-masking, kernel spectral, aggregative	Mechanism balances invariance (positive-pair) and stability/collapse
Architecture	ResNet, ViT	Partial backbone, pixel/token head, multi-branch, kernel	Tune to task/augmentation strength; weight-sharing for localization
Evaluation	Linear/kNN/FT	Entropy, clustering agreement (label-free)	LP/kNN best OOD predictors; entropy robust for contrastive settings
Optimization	SGD/Adam	S3L coarse resolution, augment batch, memory bank, EMA	Reduced capacity speeds convergence, avoids overfitting/collapse
Stability	Negatives, predictor, centering, BN	Asymmetry, Sinkhorn, grouped features	All methods enforce $\|s\|\approx 0$ via implicit/explicit mechanisms
Theory	Mutual information, spectral/ridge	Full ELBO (SimVAE), kernel eigenspace	Theoretical guarantees now connect pretraining loss and transfer

SSL phase—in all its practical, algorithmic, and theoretical variants—remains the essential foundation for modern representation learning, with continued advances focused on improved invariance discovery, stability mechanisms, evaluation robustness, and adaptation to varied domains and resource constraints.