Samuel Horváth

Cuong Anh Pham, Praneeth Vepakomma, Samuel Horváth

Alleviating catastrophic forgetting while enabling further learning is a primary challenge in continual learning (CL). Orthogonal-based training methods have gained attention for their efficiency and strong theoretical properties, and many existing approaches enforce orthogonality through gradient projection. In this paper, we revisit orthogonality and exploit the fact that small singular values correspond to directions that are nearly orthogonal to the input space of previous tasks. Building on this principle, we introduce NESS (Null-space Estimated from Small Singular values), a CL method that applies orthogonality directly in the weight space rather than through gradient manipulation. Specifically, NESS constructs an approximate null space using the smallest singular values of each layer's input representation and parameterizes task-specific updates via a compact low-rank adaptation (LoRA-style) formulation constrained to this subspace. The subspace basis is fixed to preserve the null-space constraint, and only a single trainable matrix is learned for each task. This design ensures that the resulting updates remain approximately in the null space of previous inputs while enabling adaptation to new tasks. Our theoretical analysis and experiments on three benchmark datasets demonstrate competitive performance, low forgetting, and stable accuracy across tasks, highlighting the role of small singular values in continual learning. The code is available at https://github.com/pacman-ctm/NESS.

Abdulla Jasem Almansoori, Maria Ivanova, Andrey Veprikov et al.

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. In this work, we address the gap between training with full steps with low-rank projections (SVDLoRA) and LoRA fine-tuning. We propose LoRSum, a memory-efficient subroutine that closes this gap for gradient descent by casting LoRA optimization as a proximal sub-problem and solving it efficiently with alternating least squares updates, which we prove to be an implicit block power method. We recover several recently proposed preconditioning methods for LoRA as special cases, and show that LoRSum can also be used for updating a low-rank momentum. In order to address full steps with preconditioned gradient descent, we propose a scaled variant of LoRSum that uses structured metrics such as K-FAC and Shampoo, and we show that storing the diagonal of these metrics still allows them to perform well while remaining memory-efficient. Experiments on a synthetic task, CIFAR-100, and language-model fine-tuning on GLUE, SQuAD v2, and WikiText-103, show that our method can match or improve LoRA baselines given modest compute overhead, while avoiding full-matrix SVD projections and retaining LoRA-style parameter efficiency.

Nurbek Tastan, Stefanos Laskaridis, Karthik Nandakumar et al.

Mixture-of-Experts (MoE) models scale large language models efficiently by sparsely activating experts, but once an expert is selected, it is executed fully. Hence, the trade-off between accuracy and computation in an MoE model typically exhibits large discontinuities. We propose Mixture of Slimmable Experts (MoSE), an MoE architecture in which each expert has a nested, slimmable structure that can be executed at variable widths. This enables conditional computation not only over which experts are activated, but also over how much of each expert is utilized. Consequently, a single pretrained MoSE model can support a more continuous spectrum of accuracy-compute trade-offs at inference time. We present a simple and stable training recipe for slimmable experts under sparse routing, combining multi-width training with standard MoE objectives. During inference, we explore strategies for runtime width determination, including a lightweight test-time training mechanism that learns how to map router confidence/probabilities to expert widths under a fixed budget. Experiments on GPT models trained on OpenWebText demonstrate that MoSE matches or improves upon standard MoE at full width and consistently shifts the Pareto frontier for accuracy vs. cost, achieving comparable performance with significantly fewer FLOPs.

Riccardo Zaccone, Stefanos Laskaridis, Marco Ciccone et al.

The growing scale of deep neural networks, encompassing large language models (LLMs) and vision transformers (ViTs), has made training from scratch prohibitively expensive and deployment increasingly costly. These models are often used as computational monoliths with fixed cost, a rigidity that does not leverage overparametrized architectures and largely hinders adaptive deployment across different cost budgets. We argue that importance-ordered nested components can be extracted from pretrained models, and selectively activated on the available computational budget. To this end, our proposed FlexRank method leverages low-rank weight decomposition with nested, importance-based consolidation to extract submodels of increasing capabilities. Our approach enables a "train-once, deploy-everywhere" paradigm that offers a graceful trade-off between cost and performance without training from scratch for each budget - advancing practical deployment of large models.