Shared LoRA Subspaces for almost Strict Continual Learning

Adapting large pretrained models to new tasks efficiently and continually is crucial for real-world deployment but remains challenging due to catastrophic forgetting and the high cost of retraining. While parameter-efficient tuning methods like low rank adaptation (LoRA) reduce computational demands, they lack mechanisms for strict continual learning and knowledge integration, without relying on data replay, or multiple adapters. We propose Share, a novel approach to parameter efficient continual finetuning that learns and dynamically updates a single, shared low-rank subspace, enabling seamless adaptation across multiple tasks and modalities. Share constructs a foundational subspace that extracts core knowledge from past tasks and incrementally integrates new information by identifying essential subspace directions. Knowledge from each new task is incorporated into this evolving subspace, facilitating forward knowledge transfer, while minimizing catastrophic interference. This approach achieves up to 100x parameter reduction and 281x memory savings over traditional LoRA methods, maintaining performance comparable to jointly trained models. A single Share model can replace hundreds of task-specific LoRA adapters, supporting scalable, asynchronous continual learning. Experiments across image classification, natural language understanding, 3D pose estimation, and text-to-image generation validate its effectiveness, making Share a practical and scalable solution for lifelong learning in large-scale AI systems.

Optimism Stabilizes Thompson Sampling for Adaptive Inference

Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are random and coupled with the rewards through the action-selection rule. We study this phenomenon in the $K$-armed Gaussian bandit and identify \emph{optimism} as a key mechanism for restoring \emph{stability}, a sufficient condition for valid asymptotic inference requiring each arm's pull count to concentrate around a deterministic scale. First, we prove that variance-inflated TS \citep{halder2025stable} is stable for any $K \ge 2$, including the challenging regime where multiple arms are optimal. This resolves the open question raised by \citet{halder2025stable} through extending their results from the two-armed setting to the general $K$-armed setting. Second, we analyze an alternative optimistic modification that keeps the posterior variance unchanged but adds an explicit mean bonus to posterior mean, and establish the same stability conclusion. In summary, suitably implemented optimism stabilizes Thompson sampling and enables asymptotically valid inference in multi-armed bandits, while incurring only a mild additional regret cost.

Layer-wise LoRA fine-tuning: a similarity metric approach

Pre-training Large Language Models (LLMs) on web-scale datasets becomes fundamental for advancing general-purpose AI. In contrast, enhancing their predictive performance on downstream tasks typically involves adapting their knowledge through fine-tuning. Parameter-efficient fine-tuning techniques, such as Low-Rank Adaptation (LoRA), aim to reduce the computational cost of this process by freezing the pre-trained model and updating a smaller number of parameters. In comparison to full fine-tuning, these methods achieve over 99\% reduction in trainable parameter count, depending on the configuration. Unfortunately, such a reduction may prove insufficient as LLMs continue to grow in scale. In this work, we address the previous problem by systematically selecting only a few layers to fine-tune using LoRA or its variants. We argue that not all layers contribute equally to the model adaptation. Leveraging this, we identify the most relevant layers to fine-tune by measuring their contribution to changes in internal representations. Our method is orthogonal to and readily compatible with existing low-rank adaptation techniques. We reduce the trainable parameters in LoRA-based techniques by up to 50\%, while maintaining the predictive performance across different models and tasks. Specifically, on encoder-only architectures, this reduction in trainable parameters leads to a negligible predictive performance drop on the GLUE benchmark. On decoder-only architectures, we achieve a small drop or even improvements in the predictive performance on mathematical problem-solving capabilities and coding tasks. Finally, this effectiveness extends to multimodal models, for which we also observe competitive results relative to fine-tuning with LoRA modules in all layers. Code is available at: https://github.com/c2d-usp/Layer-wise-LoRA-with-CKA

Characterizing Human Semantic Navigation in Concept Production as Trajectories in Embedding Space

Semantic representations can be framed as a structured, dynamic knowledge space through which humans navigate to retrieve and manipulate meaning. To investigate how humans traverse this geometry, we introduce a framework that represents concept production as navigation through embedding space. Using different transformer text embedding models, we construct participant-specific semantic trajectories based on cumulative embeddings and extract geometric and dynamical metrics, including distance to next, distance to centroid, entropy, velocity, and acceleration. These measures capture both scalar and directional aspects of semantic navigation, providing a computationally grounded view of semantic representation search as movement in a geometric space. We evaluate the framework on four datasets across different languages, spanning different property generation tasks: Neurodegenerative, Swear verbal fluency, Property listing task in Italian, and in German. Across these contexts, our approach distinguishes between clinical groups and concept types, offering a mathematical framework that requires minimal human intervention compared to typical labor-intensive linguistic pre-processing methods. Comparison with a non-cumulative approach reveals that cumulative embeddings work best for longer trajectories, whereas shorter ones may provide too little context, favoring the non-cumulative alternative. Critically, different embedding models yielded similar results, highlighting similarities between different learned representations despite different training pipelines. By framing semantic navigation as a structured trajectory through embedding space, bridging cognitive modeling with learned representation, thereby establishing a pipeline for quantifying semantic representation dynamics with applications in clinical research, cross-linguistic analysis, and the assessment of artificial cognition.

LSA: Localized Semantic Alignment for Enhancing Temporal Consistency in Traffic Video Generation

Controllable video generation has emerged as a versatile tool for autonomous driving, enabling realistic synthesis of traffic scenarios. However, existing methods depend on control signals at inference time to guide the generative model towards temporally consistent generation of dynamic objects, limiting their utility as scalable and generalizable data engines. In this work, we propose Localized Semantic Alignment (LSA), a simple yet effective framework for fine-tuning pre-trained video generation models. LSA enhances temporal consistency by aligning semantic features between ground-truth and generated video clips. Specifically, we compare the output of an off-the-shelf feature extraction model between the ground-truth and generated video clips localized around dynamic objects inducing a semantic feature consistency loss. We fine-tune the base model by combining this loss with the standard diffusion loss. The model fine-tuned for a single epoch with our novel loss outperforms the baselines in common video generation evaluation metrics. To further test the temporal consistency in generated videos we adapt two additional metrics from object detection task, namely mAP and mIoU. Extensive experiments on nuScenes and KITTI datasets show the effectiveness of our approach in enhancing temporal consistency in video generation without the need for external control signals during inference and any computational overheads.

Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely on a standard Gaussian distribution, a choice inherited from diffusion models, and rarely consider the source distribution itself as an optimization target in such settings. In this work, we show that principled design of the source distribution is not only feasible but also beneficial at the scale of modern text-to-image systems. Specifically, we propose learning a condition-dependent source distribution under flow matching objective that better exploit rich conditioning signals. We identify key failure modes that arise when directly incorporating conditioning into the source, including distributional collapse and instability, and show that appropriate variance regularization and directional alignment between source and target are critical for stable and effective learning. We further analyze how the choice of target representation space impacts flow matching with structured sources, revealing regimes in which such designs are most effective. Extensive experiments across multiple text-to-image benchmarks demonstrate consistent and robust improvements, including up to a 3x faster convergence in FID, highlighting the practical benefits of a principled source distribution design for conditional flow matching.

Orthogonal Model Merging

Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.

Multi-Scale Global-Instance Prompt Tuning for Continual Test-time Adaptation in Medical Image Segmentation

Distribution shift is a common challenge in medical images obtained from different clinical centers, significantly hindering the deployment of pre-trained semantic segmentation models in real-world applications across multiple domains. Continual Test-Time Adaptation(CTTA) has emerged as a promising approach to address cross-domain shifts during continually evolving target domains. Most existing CTTA methods rely on incrementally updating model parameters, which inevitably suffer from error accumulation and catastrophic forgetting, especially in long-term adaptation. Recent prompt-tuning-based works have shown potential to mitigate the two issues above by updating only visual prompts. While these approaches have demonstrated promising performance, several limitations remain:1)lacking multi-scale prompt diversity, 2)inadequate incorporation of instance-specific knowledge, and 3)risk of privacy leakage. To overcome these limitations, we propose Multi-scale Global-Instance Prompt Tuning(MGIPT), to enhance scale diversity of prompts and capture both global- and instance-level knowledge for robust CTTA. Specifically, MGIPT consists of an Adaptive-scale Instance Prompt(AIP) and a Multi-scale Global-level Prompt(MGP). AIP dynamically learns lightweight and instance-specific prompts to mitigate error accumulation with adaptive optimal-scale selection mechanism. MGP captures domain-level knowledge across different scales to ensure robust adaptation with anti-forgetting capabilities. These complementary components are combined through a weighted ensemble approach, enabling effective dual-level adaptation that integrates both global and local information. Extensive experiments on medical image segmentation benchmarks demonstrate that our MGIPT outperforms state-of-the-art methods, achieving robust adaptation across continually changing target domains.

Approximation of Log-Partition Function in Policy Mirror Descent Induces Implicit Regularization for LLM Post-Training

Policy mirror descent (PMD) provides a principled framework for reinforcement learning (RL) by iteratively solving KL-regularized policy improvement subproblems. While this approach has been adopted in training advanced LLMs such as Kimi K1.5/K2, the ideal closed-form PMD updates require reliable partition function estimation, a significant challenge when working with limited rollouts in the vast action spaces of LLMs. We investigate a practical algorithm, termed PMD-mean, that approximates the log-partition term with the mean reward under the sampling policy and performs regression in log-policy space. Specifically, we characterize the population solution of PMD-mean and demonstrate that it implicitly optimizes mirror descent subproblems with an adaptive mixed KL--$χ^2$ regularizer. This additional $χ^2$ regularization constrains large probability changes, producing more conservative updates when expected rewards are low and enhancing robustness against finite-sample estimation errors. Experiments on math reasoning tasks show that PMD-mean achieves superior performance with improved stability and time efficiency. These findings deepen our understanding of PMD-mean and illuminate pathways toward principled improvements in RL algorithms for LLMs. Code is available at https://github.com/horizon-rl/OpenKimi.

Polyglots or Multitudes? Multilingual LLM Answers to Value-laden Multiple-Choice Questions

Multiple-Choice Questions (MCQs) are often used to assess knowledge, reasoning abilities, and even values encoded in large language models (LLMs). While the effect of multilingualism has been studied on LLM factual recall, this paper seeks to investigate the less explored question of language-induced variation in value-laden MCQ responses. Are multilingual LLMs consistent in their responses across languages, i.e. behave like theoretical polyglots, or do they answer value-laden MCQs depending on the language of the question, like a multitude of monolingual models expressing different values through a single model? We release a new corpus, the Multilingual European Value Survey (MEVS), which, unlike prior work relying on machine translation or ad hoc prompts, solely comprises human-translated survey questions aligned in 8 European languages. We administer a subset of those questions to over thirty multilingual LLMs of various sizes, manufacturers and alignment-fine-tuning status under comprehensive, controlled prompt variations including answer order, symbol type, and tail character. Our results show that while larger, instruction-tuned models display higher overall consistency, the robustness of their responses varies greatly across questions, with certain MCQs eliciting total agreement within and across models while others leave LLM answers split. Language-specific behavior seems to arise in all consistent, instruction-fine-tuned models, but only on certain questions, warranting a further study of the selective effect of preference fine-tuning.