TailLoR: Spectral-domain continual learning via protected principal components
TailLoR is a new parameter-efficient finetuning method for continual learning that uses the singular value decomposition of pre-trained weights as a fixed reference frame, applying low-rank updates only to the singular value matrix. A soft spectral penalty discourages updates aligned with dominant singular directions, reducing catastrophic interference while routing adaptation into long-tail spectral coordinates. The approach targets the forgetting problem in continual learning through a principled spectral lens.
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SETA: Sparse Subspace-to-Expert Sharing for Continual Learning in LLMs
Researchers introduce SETA (Mixture of Sparse Experts for Task Agnostic Continual Learning), a framework addressing catastrophic forgetting in LLMs via adaptive sparse subspace decomposition into task-specific and shared expert modules. The approach uses adaptive elastic anchoring and routing-aware regularization to protect shared knowledge at both weight and routing levels. Experiments on LLaMA-2 7B and Qwen3-4B show competitive or superior performance versus continual learning baselines, with strong retention of early-task knowledge.
SMoA: Spectrum Modulation Adapter for Parameter-Efficient Fine-Tuning
SMoA is a new parameter-efficient fine-tuning method that addresses LoRA's trade-off between rank size and parameter budget. It partitions model layers into spectral blocks and applies Hadamard-modulated low-rank branches to each diagonal block, enabling broader coverage of pretrained spectral directions without proportionally increasing trainable parameters. Theoretical analysis and empirical results on multiple tasks show SMoA outperforms LoRA and competitive LoRA-style baselines in lower-budget settings.
Using LoRA for Efficient Stable Diffusion Fine-Tuning
This Hugging Face blog post explains how Low-Rank Adaptation (LoRA) can be applied to fine-tune Stable Diffusion models efficiently. LoRA reduces the number of trainable parameters by decomposing weight updates into low-rank matrices, enabling fine-tuning on consumer hardware with significantly less memory. The post covers practical implementation details using the diffusers library.
Parametric Memory Law for LoRA Finetuning: Quantifying LLM Memory Capacity
This paper introduces the Parametric Memory Law, a power-law relationship linking loss reduction to effective parameters and sequence length during LoRA-based LLM finetuning. The authors identify a phase transition at the token level where prediction probability p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Building on these findings, they propose MemFT, a threshold-guided optimization strategy that dynamically reallocates training budget toward sub-threshold tokens, improving memory fidelity and efficiency.
CoRP: Gradient-Free Consolidation of Rewarded Perturbations for LLM Post-Training
CoRP (Consolidating Rewarded Perturbations) is a gradient-free post-training operator that folds an ensemble of reward-weighted weight-space perturbations into a single deployable model, eliminating the inference-time cost of ensemble methods like RandOpt. A split-half analysis across 25 model-task pairs reveals reproducible low-rank structure in the rewarded perturbation population, which CoRP exploits via reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate. Evaluated on five models (0.5B–8B) across math, code, and creative writing, CoRP improves the base model by 8.1 points on average, exceeds single-inference RandOpt by 6.5 points using one-tenth the perturbation budget, and recovers more than half the gain of a 50-pass majority-vote ensemble at one forward pass per test example.
PC Layer: Polynomial weight preconditioning for stable LLM pre-training
Researchers propose a PC (preconditioning) layer that applies polynomial preconditioning to reshape the singular-value spectrum of weight matrices during LLM training, improving conditioning stability. The preconditioned weights merge back into the original architecture at inference time with no overhead. Experiments on Llama-1B pre-training show advantages over standard transformers for both AdamW and Muon optimizers, with theoretical convergence guarantees for deep linear networks.
GaLore: Advancing Large Model Training on Consumer-grade Hardware
GaLore (Gradient Low-Rank Projection) is a memory-efficient training technique that reduces optimizer state memory by projecting gradients into a low-rank subspace during training, enabling large model training on consumer-grade hardware. The Hugging Face blog post covers integration of GaLore into the transformers and peft ecosystems. Unlike LoRA, GaLore applies low-rank projection to the full training process rather than constraining weight updates, allowing full-parameter learning with reduced memory footprint. This makes training models like LLaMA-7B feasible on single consumer GPUs.
RL without TD Learning: Divide-and-Conquer Value Learning for Long-Horizon Off-Policy RL
A BAIR blog post introduces a divide-and-conquer paradigm for off-policy reinforcement learning that avoids temporal difference (TD) learning's error accumulation problem by reducing Bellman recursions logarithmically rather than linearly. The approach leverages the triangle inequality structure of goal-conditioned RL to define a transitive Bellman update rule, enabling value learning that scales to long-horizon tasks. The authors claim this is the first practical realization of divide-and-conquer value learning at scale in goal-conditioned RL settings, building on an idea traceable to Kaelbling (1993). The post frames this as a third paradigm alongside TD and Monte Carlo methods, addressing a key gap in scalable off-policy RL.