A theoretical analysis positioning CoCo with respect to related objectives shows that the new proposed loss benefits from closer initialization to the optimal configuration, more informative gradients, and stronger incentives for class-wise representation collapse.
Abstract
In this work, we introduce CoCo, a loss function aimed at learning normalized and well-structured representations. The proposed loss encourages intra-class collapse and inter-class contrast while preserving sufficient flexibility for neural networks to approximate geometrically optimal embeddings with large angular separation between classes. We provide a theoretical analysis positioning CoCo with respect to related objectives such as dot regression and cross-entropy, showing that the new proposed loss benefits from closer initialization to the optimal configuration, more informative gradients, and stronger incentives for class-wise representation collapse. Extensive experiments on diverse tabular datasets from the OpenML-CC18 benchmark show that CoCo achieves competitive performance with state-of-the-art methods, including kernel SVM, Random Forest, dot regression, and cross-entropy-based neural networks. In addition, both theoretical arguments and empirical analyses demonstrate that the proposal promotes tighter class clustering and faster convergence. These results highlight CoCo loss as an effective objective for learning discriminative representations while maintaining competitive predictive performance.
A progressive multi-objective optimization framework is proposed that enhances t-SNE by integrating complementary loss functions, including a ranking-aware divergence (KLmax) and a Wasserstein-based term for global alignment.
S. Belhaouari, Skander Bensegueni, Lyes Fennour et al.· International Conference on...· 0 citations
Despite recent advances, self-supervised learning (SSL) models and Joint-Embedding Predictive Architectures (JEPAs) remain susceptible to learning spurious biases in the dataset. These techniques rely on regularization, which prevents representation collapse by enforcing a global target distribution such as a multivariate Gaussian or a uniform distribution on the sphere. However, these global constraints are insufficient to prevent bias entanglement, as task-irrelevant features can still segregate the latent space into distinct sub-regions. While recent approaches like Entangling and Disentangling (EnD) and Fair Supervised Contrastive Learning (FSCL) empirically debias the latent space, we show that they act as partial approximations of conditional distribution matching. To enforce this matching explicitly, we propose Unbiased Open World Regularization (UOWReg), an encoder-only framework. We show that this shift from a global to a conditional objective guarantees statistical independence between the learned representations and the targeted attributes, regardless of the chosen target distribution. We empirically validate this framework across both Gaussian and spherical latent spaces, using statistical measures to enforce these target distributions. While conditional matching successfully mitigates bias with both distributions, we demonstrate that enforcing conditional uniformity on the sphere yields a lower linearprobing classification error. Empirically, UOWReg reduces Equalized Odds violations on the CelebA benchmark while maintaining competitive classification accuracy compared to existing encoder-only baselines. Furthermore, we introduce the Synthetic Engraving Task-a novel setting in which a dominant macro-structure masks a fine-grained micro-signature. We show that UOWReg effectively prevents the subpopulation collapse observed in standard SSL, successfully isolating micro-signatures even when heavily entangled with the global structure.
Léo Nicollier, M. Pic, Pablo Musé et al.· arXiv.org· 0 citations
This work proposes Normalizing Autoencoder (NAE), which employs a novel conditional loss that aligns the surrogate loss gradient with that of reconstruction loss, directly improving upon the current standard.
H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and Möbius matrix multiplication, is proposed, demonstrating that faithful preservation of fine-grained structural details requires faithful preservation of fine-grained structural details in graph learning.
Heng Zhang, Jin Huang· Proceedings of the 32nd ACM...· 0 citations
It is found that SAE activation sets do not recover human category boundaries or within-category typicality more faithfully than dense embeddings or residual-stream states, but instead track model-internal similarity structure.
Nikolai Bolik, Lennart Stöpler, Artur Andrzejak· 0 citations
Deep neural networks generalize well despite their highly nonconvex, overparameterized loss landscapes, a phenomenon often associated with the geometry of the minima found by stochastic optimization. We study how incremental grow-and-optimize strategies bias training toward flatter regions by viewing growth as progressive constraint relaxation. Starting from a low-dimensional submodel, we iteratively expand the trainable parameters by unlocking nested random subspaces while freezing the orthogonal complement at the network initialization, re-optimizing after each expansion until the full architecture is reached. Under standard local regularity conditions around non-degenerate minima, we prove that local sublevel sets are well approximated by ellipsoids and that basin accessibility under frozen constraints can be characterized by an explicit effective curvature in the frozen directions. This leads to an explanation of the bias: progressive growth increases the relative weight of wide basins and suppresses sharp ones through a volume effect induced by the frozen constraints. We empirically validate these predictions in controlled toy landscapes and in a realistic ResNet/CIFAR-100 setting and confirm that although progressive subspace growth reliably produces flatter solutions, curvature reductions do not universally translate into improved test performance, highlighting subtleties in the flatness-generalization connection. The code is available at https://github.com/p0lcAi/Across-the-Loss-Landscape.
Paul Caillon, Christophe Cerisara, Alexandre Allauzen· 0 citations
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