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Abstract: Low-Rank Adaptation (LoRA) is often highly sensitive to learning-rate (LR) choices. Recent empirical studies suggest that, once LRs are carefully tuned, vanilla LoRA can remain competitive with many proposed LoRA variants. This shifts the central practical question from designing ever more variants to reducing the cost and brittleness of LR selection. LoRA+ addresses this issue with asymmetric LRs, using a larger LR for the up-projection matrix $B$ than for the down-projection matrix $A$. However, the ratio $η_B / η_A$ itself becomes an additional hyperparameter: large ratios can improve adaptation, but under the standard LoRA initialization they can also cause unstable training and ratio-dependent performance collapse. We identify the source of this brittleness through a signal--noise decomposition of LoRA dynamics. Under standard \initA, the update contains an initialization-induced noise term whose magnitude can be affected by the LR for $B$, $η_B$, the initialization scale $β$, and the adapter rank $r$. In practical LLM fine-tuning, this non-vanishing noise can limit the performance gains expected from LoRA+ style asymmetric LRs. To suppress this effect, we propose \initAA, a simple initialization that scales the variance of $A$ as $σ_A^2 \propto n^{-2}$ while keeping $B_0=0$. Under matched rank and training time for both initializations, this reduces the initialization-noise energy by an additional factor of $1/n$, stabilizing asymmetric LoRA training while preserving zero initial adapter output. Empirically, \initAA substantially widens the stable LR region across initialization scales, adapter ranks, and LoRA update multipliers. Across tasks and models, \initAA reduces best-ratio drift, prevents the high-ratio collapse observed with standard \initA, and makes the width-based guideline $η_B \approx n η_A$ a useful starting point for finite pretrained models.

Abstract: Muon's gains in data efficiency motivate evaluating its performance under explicit data, time, and tuning budgets. On a single A100 GPU, we compare a reference single-device Muon implementation with AdamW across 17.7M- and 33.6M-parameter causal language models and 2.70M-parameter vision transformers. A common 23-candidate development budget selects configurations evaluated with five matched seeds, full validation trajectories, optimizer-step timing, and a frozen one-shot test. Muon reduces validation-loss area under the curve by 3.25--22.44\% at equal data and lowers test loss in all 20 primary pairs. In this configuration, Muon improves time-normalized loss area} by 19.68--22.31\% on vision, while AdamW is better by 3.38--6.96\% on language. The full Muon optimizer call, including auxiliary AdamW updates, consumes 56.1--69.6\% of training time, compared with 6.1--9.1\% for the AdamW baseline. Muon also has higher expected regret under restricted access to these candidate pools. These results characterize small models with reference kernels; their wall-clock ordering does not establish a ranking for larger models or optimized implementations.

Abstract: Simplicity bias, which can arise from sequential feature learning during training, has been proposed as a general explanation for the success of deep learning. An important driver of this phenomenon is saddle-to-saddle behavior, in which the gradient flow trajectory remains close to a sequence of saddle manifolds while learning one feature at a time. However, Muon, a state-of-the-art optimizer based on spectral descent, does not exhibit such dynamics in the full-batch setting and instead learns features in parallel. How is it then that Muon is so successful in deep learning settings? We show that stochastic gradient noise fundamentally changes this behavior: small-batch noise restores sequential feature learning, providing a mechanism for simplicity bias that is absent from full-batch Muon. We explain this transition through stochastic smoothing of the spectral descent operator underlying Muon. When gradients are small relative to the noise scale, the expected spectral update becomes approximately proportional to the actual gradient, which restores gradient-flow-like dynamics. We formalize this mechanism for deep linear models by deriving the effective continuous dynamics of noisy spectral descent. Experiments on low-rank matrix reconstruction, vision transformers, and large language models (LLMs) support these findings.

Abstract: Reliable predictive uncertainty in Laplace approximations depends critically on the prior precision, yet selecting it requires a posterior sweep that is prohibitively expensive for neural networks with billions of parameters. Under the Maximal Update Parametrization ($μ\mathrm{P}$), we derive a rescaling of the prior covariance that makes the selected precision stable as model width grows. This leads to $σ\mathrm{Transfer}$: we select the precision on a smaller model and zero-shot transfer it to the much larger model, i.e., without searching for the precision on the larger model at all. We show convergence of the prior kernel, posterior covariance, selected precision, and posterior-derived decisions under explicit conditions, and verify $σ\mathrm{Transfer}$ across regression, image classification, and Transformer readouts. For example, measured precision-sweep speedups reach $\sim 5000\times$ when transferring from width 128 to 4096 on MNIST, at a target-NLL degradation of $0.002$; transferring from a public 1B to 7B model gives a median search speedup of $\sim 2.3\times$ (up to $\sim 330\times$), with a mean measured target-NLL increase below $10^{-4}$ across ten tasks. The same posterior stability also enables transfer of acquisition, OOD-detection, and abstention decisions without constructing a target posterior.

Abstract: Continual pre-training and fine-tuning in Large Language Models (LLMs) inevitably induce catastrophic forgetting, typically mitigated by replay using often-inaccessible original data. In this data-free regime, we analyze where forgetting occurs and why. Systematic parameter freezing across five settings up to 1.4B reveals that forgetting concentrates selectively in the output embeddings of tokens rarely seen in the new corpus, whereas the same sqrt(v-hat) band of the body is inert and new learning resides elsewhere. This localization is governed by the vocabulary deficiency of the corpus rather than the training mode, allowing pre-retraining risk ranking from token counts alone within a fixed base model. Mechanistically, absent tokens receive persistent one-sided softmax gradients that Adam's second-moment (sqrt(v-hat)) normalization amplifies into full-sized updates. We therefore propose an intervention: raising Adam's epsilon exclusively for the output projection during training. Across eight settings spanning 160M to 12B parameters and four model families, this removes 39.4% to 67.9% of forgetting across all seven stable configurations without degrading target learning or requiring per-model tuning. The defense combines additively or better with replay (79.8% on Qwen/Korean) and rescues released-head LoRA from a 23-fold forgetting surge. Because post-hoc editing of the drifted rows recovers under 5% of forgetting, the intervention must operate during training. Our findings indicate that a single-line optimizer adjustment may serve as the primary defense against catastrophic forgetting where the corpus starves the vocabulary.

Abstract: Parameter-efficient fine-tuning (PEFT) offers many parameterizations, yet their methodological and functional differences remain unclear. We compare six methods in language and diffusion models to examine how their parameterizations relate to task performance, forgetting, and changes in pretrained weight geometry. Motivated by the spectrum-preserving design of orthogonal fine-tuning (OFT), we first ask whether spectral preservation is itself important for adaptation and retention. We find that the selected LoRA-family methods also approximately preserve pretrained geometry, and that restoring their slightly drifted singular-value spectra largely preserves task performance, questioning the necessity of explicit geometric preservation. Beyond this, we observe that some methods exhibit distinct adaptation--retention trade-offs that vary across settings: LoRA most consistently limits forgetting at competitive performance, DoRA achieves higher mean task scores than LoRA in most comparisons, while PiSSA often incurs greater retention costs. Further intervention experiments suggest that while performance gains from different PEFT methods can be attributed to modifications in different groups of spectral components, we consistently find that restoring dominant rather than intermediate or trailing components produces the largest mean reduction in general-text NLL or base-image drift. Together, these results motivate evaluating geometric constraints through their functional consequences rather than preservation alone. Code is available at https://github.com/Kuaaannn/PEFT_methods.

Abstract: Removing copyrighted, unsafe, or user-specified concepts from a deployed text-to-image diffusion model is now a practical requirement. Weight-editing methods can suppress fixed targets, but they require per-target retraining and modify the model checkpoint. Training-free methods, on the other hand, are deployment-friendly, but they suffer from text-side routing failures on compositional prompts. In such prompts, the erase target may be invoked through a related class rather than its lexical name, and its modifiers may migrate onto preserved objects. This paper proposes Hierarchically Grounded Semantic Surgery (HGSS), a training-free framework for compositional concept erasure. The framework lifts both the routing signal and the edit operator used by text-side erasure. First, hierarchical span grounding resolves erase-target spans through lexical, taxonomic, and semantic evidence, while guarding against broad-hypernym and compound-head false positives. Second, dynamic attribute binding refines the text conditioning during early denoising via a counterfactual reference and a preserve-aware cross-attention objective, keeping surviving attribute-noun bindings intact. HGSS selectively removes the erase target without updating model weights or adding learned parameters. On SEE, HGSS cuts hierarchical evasion from 29.54 to 10.02 and roughly halves pairwise attribute leakage, achieving the best Neighbor E and AttrP scores among the reported erasure methods. On UnlearnCanvas, HGSS slightly improves the six-metric average over the matched Semantic Surgery baseline, reaching state-of-the-art.

Abstract: Reinforcement learning with verifiable rewards (RLVR) trains a language model on problems that may themselves be confidential, and the trained model can reveal which problems it saw. We study RLVR under prompt-level differential privacy: the released weights must be (ε,δ)-differentially private with respect to the presence of any one training problem. Taking the group of responses to one prompt as the privacy record, our method aggregates their gradients, clips the prompt's contribution once, adds Gaussian noise, and composes the privacy loss across updates, so the budget depends on neither the number of responses per prompt nor the clipping norm; to our knowledge this is the first differential privacy guarantee for RLVR training. We train Qwen2.5-1.5B-Instruct with LoRA at a per-run budget of ε=8 and compare, on the same prompts and at the same budget, a control that removes only the reward signal and two private supervised fine-tuning recipes. The reward signal improves accuracy over the control by 2.65 points on MATH and 3.24 on GSM8K, in every seed; the improvement survives a format-robust scorer, at 1.3 points on MATH, and is not explained by response length. At the same budget the private model outperforms both supervised recipes on MATH and GSM8K by 2.3 to 3.8 points, retains 85--90% of the gain of non-private GRPO on these tasks, and on MATH the noise of an eightfold tighter budget costs at most 1.2 points. The reward effect also carries to CommonsenseQA, an exploratory non-mathematical task. Verifier feedback thus remains a usable learning signal under prompt-level privacy.

Abstract: Typed decision models return choices or distributions over answer options supplied at request time. Accuracy with complete options does not establish whether a model recognizes that a reference answer is missing or avoids rejecting valid candidates. We present a paired candidate-coverage benchmark protocol and an initial evaluation of Laya and Jev across AG News, DBpedia, Emotion, and TREC. The models receive identical frozen texts and requests: 300 calibration and 589 test texts yield 23,932 predictions per model. Present/absent pairs match ordinary candidate count, and name variants preserve descriptions, members, and order. Native rejection behavior differs sharply: at five TREC candidates with natural names, Laya detects 97.2% of missing-answer cases but falsely rejects 69.7% of present controls; Jev's rates are 24.8% and 0.0%. Calibration-only none-score thresholds change these rates to 33.9%/3.7% and 45.0%/1.8%, respectively. On DBpedia, Jev's high coverage-score AUROC supports a stronger operating point, whereas both models have weak complete-set accuracy on Emotion. Competence-conditioned analysis, probability-precision sensitivity, and interface audits show why classification, score ranking, and rejection policies need separate measurement. This initial benchmark is descriptive and limited to reference-label omission; it does not establish natural out-of-scope generalization, causal mechanisms, or a new rejection method.

Abstract: Class-Incremental Learning (CIL) aims to continuously learn new classes without forgetting previously acquired knowledge. Parameter-efficient fine-tuning with pre-trained models reduces parameter overhead but can suffer from cumulative interference and suboptimal alignment between inference samples and specialized modules. We propose Dynamic LoRA-Experts and Prototype-Ensemble Matching (DLEPEM), a two-stage rehearsal-free framework. DLEPEM allocates a task-specific LoRA-Expert for each incremental task to reduce cross-task interference, then combines frozen pre-trained-model prototypes with task-adaptive LoRA-Expert prototypes for reliable task-level discrimination. Experiments on standard CIL and Few-Shot CIL benchmarks demonstrate strong performance under the evaluated protocols.

Abstract: Learner simulation aims to reproduce how a particular learner behaves on new tasks. Although Large Language Models (LLMs) can generate increasingly fine-grained learning behaviors, existing approaches often need to repeatedly process a growing interaction history to reconstruct the learner. This introduces additional context and inference costs and makes the acquired learner-specific simulation capability difficult to reuse across different LLMs. We therefore propose Learner2Skill, which externalizes the simulation capability acquired from historical interactions into a persistent and reusable Simulation Skill. The Skill captures the learner's current learning state and recurring response patterns, evolves as new real interactions arrive, and can be adapted to a new LLM through lightweight executor calibration without reconstructing the learner from scratch. Experiments show that Learner2Skill more faithfully reproduces fine-grained learner behavior while reducing overall token cost, and that the same constructed Skills can be effectively reused across different LLM executors.

Abstract: Deploying a language model under different computing and latency budgets calls for compact models with different quality-cost trade-offs. Towards this end, elastic spectral state space models provide ordered and temporally decomposed channels that can be truncated, but they are associated with linear time-invariant filters that cannot selectively preserve relevant past information or forget irrelevant information as the context evolves. To address this, we introduce the Elastic Selective Spectral Hybrid (ESSH), which realizes each Hankel spectral channel as an independent recurrent unit using fitted damped rotation modes. It also features an input-dependent decay and write/read gates that make temporal retention and state update input-dependent while preserving channel-wise truncation and a structured recurrence for efficient execution. ESSH combines these selective spectral mixers with sliding-window attention and jointly trains multiple capacities by reducing spectral-channel count and feed-forward width at different rates through a two-rate capacity map with full-model distillation. The resulting models support chunked parallel training and fused recurrent decoding while avoiding computation for discarded channels. At full capacity, ESSH achieves language-modeling quality comparable to similarly sized independently trained models, while smaller exports exhibit a smooth quality-cost trade-off. We validate the effectiveness of the proposed framework using language understanding, retrieval, cross-domain text, and DNA experiments, by assessing quality retention and the trade-off against independently trained and elastic baselines. At the 1.53B model configuration, fused batch-one decoding takes 1.37 ms per token on a B300, providing a 2.14-2.80x speedup over the tested Mamba-2 and Mamba-3 implementations and 3.03x over Transformer++ at matched parameter counts.

Abstract: RandOpt samples weight-perturbed language models and ensembles top-ranked candidates through plurality voting, but its global perturbation scale ignores heterogeneous module geometry. We propose \mbox{\textbf{\emph{Modular Norm RandOpt}}}, an architecture-aware sampling method using module-wise natural norms and calibrated scales while preserving selection and voting. It outperforms RandOpt using $3\times$ fewer candidates on Countdown and at least $12\times$ fewer on GSM8K, with corresponding wall-clock savings. Evaluations across seven tasks and three Qwen scales ($0.5$B--$3$B) show higher mean accuracy than RandOpt on Countdown, GSM8K, and MATH-500 at every scale. The gains extend to Llama 3.2 $3$B and Gemma 3 $4$B on Countdown and GSM8K. On Qwen2.5-1.5B, our ensembles also achieve higher mean accuracy than iterative baselines on both tasks at comparable main-run evaluation budgets. On GSM8K, a tail-density diagnostic implies only a $1.2$--$1.8\times$ candidate reduction, while most ensemble improvement is associated with more favorable correct-expert support. These results highlight perturbation geometry as a key design choice for population-efficient, gradient-free search around pretrained models.

Abstract: Benchmark scores describe what a checkpoint can do now, but they do not determine how it will respond to the next training episode. We measure this missing state by branching four short, standardized, target-independent micro-interventions from the same checkpoint and recording their effects in a common capability space. Together with current capability, these responses form L-State; its pulse block supports a flexible direct readout and a structure-preserving operator readout. Under smooth local dynamics, the operator construction admits an end-to-end cross-family bound with explicit source- and target-family coordinate heterogeneity. In three-family leave-one-family-out development, both pulse readouts reduce source-standardized MSE by 39.4% relative to capability alone, while separating the best response and direction estimates. On sealed GLM-4-9B, the direct and operator readouts reduce MSE by 71.8% and 78.3%, respectively, and the operator readout raises sign balanced accuracy from 0.366 to 0.754. On sealed Granite-3.1-8B, the direct readout reaches RMSE 0.544 and a development-fitted action-wise selector reaches 0.554, compared with 1.172 for capability alone. A five-family audit finds that the operator coordinate varies by action and family, and that modeling these deviations improves retrospective held-trajectory prediction. Target-independent interventions therefore expose training-response information that current capability misses, with direct and structured readouts covering complementary transfer regimes.