AILoRA: Function-Aware Asymmetric Initialization for Low-Rank Adaptation of Large Language Models

Parameter-efficient finetuning (PEFT) aims to mitigate the substantial computational and memory overhead involved in adapting large-scale pretrained models to diverse downstream tasks. Among numerous PEFT strategies, Low-Rank Adaptation (LoRA) has emerged as one of the most widely adopted approaches due to its robust empirical performance and low implementation complexity. In practical deployment, LoRA is typically applied to the $W^Q$ and $W^V$ projection matrices of self-attention modules, enabling an effective trade-off between model performance and parameter efficiency. While LoRA has achieved considerable empirical success, it still encounters challenges such as suboptimal performance and slow convergence. To address these limitations, we introduce \textbf{AILoRA}, a novel parameter-efficient method that incorporates function-aware asymmetric low-rank priors. Our empirical analysis reveals that the projection matrices $W^Q$ and $W^V$ in the self-attention mechanism exhibit distinct parameter characteristics, stemming from their functional differences. Specifically, $W^Q$ captures task-specific semantic space knowledge essential for attention distributions computation, making its parameters highly sensitive to downstream task variations. In contrast, $W^V$ encodes token-level feature representations that tend to remain stable across tasks and layers. Leveraging these insights, AILoRA performs a function-aware initialization by injecting the principal components of $W^Q$ to retain task-adaptive capacity, and the minor components of $W^V$ to preserve generalizable feature representations. This asymmetric initialization strategy enables LoRA modules to better capture the specialized roles of attention parameters, thereby enhancing both finetuning performance and convergence efficiency.

Vision-Enabled LLMs in Historical Lexicography: Digitising and Enriching Estonian-German Dictionaries from the 17th and 18th Centuries

This article presents research conducted at the Institute of the Estonian Language between 2022 and 2025 on the application of large language models (LLMs) to the study of 17th and 18th century Estonian dictionaries. The authors address three main areas: enriching historical dictionaries with modern word forms and meanings; using vision-enabled LLMs to perform text recognition on sources printed in Gothic script (Fraktur); and preparing for the creation of a unified, cross-source dataset. Initial experiments with J. Gutslaff's 1648 dictionary indicate that LLMs have significant potential for semi-automatic enrichment of dictionary information. When provided with sufficient context, Claude 3.7 Sonnet accurately provided meanings and modern equivalents for 81% of headword entries. In a text recognition experiment with A. T. Helle's 1732 dictionary, a zero-shot method successfully identified and structured 41% of headword entries into error-free JSON-formatted output. For digitising the Estonian-German dictionary section of A. W. Hupel's 1780 grammar, overlapping tiling of scanned image files is employed, with one LLM being used for text recognition and a second for merging the structured output. These findings demonstrate that even for minor languages LLMs have a significant potential for saving time and financial resources.

An in-depth look at approximation via deep and narrow neural networks

In 2017, Hanin and Sellke showed that the class of arbitrarily deep, real-valued, feed-forward and ReLU-activated networks of width w forms a dense subset of the space of continuous functions on R^n, with respect to the topology of uniform convergence on compact sets, if and only if w>n holds. To show the necessity, a concrete counterexample function f:R^n->R was used. In this note we actually approximate this very f by neural networks in the two cases w=n and w=n+1 around the aforementioned threshold. We study how the approximation quality behaves if we vary the depth and what effect (spoiler alert: dying neurons) cause that behavior.

Watch and Learn: Learning to Use Computers from Online Videos

Computer use agents (CUAs) need to plan task workflows grounded in diverse, ever-changing applications and environments, but learning is hindered by the scarcity of large-scale, high-quality training data in the target application. Existing datasets are domain-specific, static, and costly to annotate, while current synthetic data generation methods often yield simplistic or misaligned task demonstrations. To address these limitations, we introduce Watch & Learn (W&L), a framework that converts human demonstration videos readily available on the Internet into executable UI trajectories at scale. Instead of directly generating trajectories or relying on ad hoc reasoning heuristics, we cast the problem as an inverse dynamics objective: predicting the user's action from consecutive screen states. This formulation reduces manual engineering, is easier to learn, and generalizes more robustly across applications. Concretely, we develop an inverse dynamics labeling pipeline with task-aware video retrieval, generate over 53k high-quality trajectories from raw web videos, and demonstrate that these trajectories improve CUAs both as in-context demonstrations and as supervised training data. On the challenging OSWorld benchmark, UI trajectories extracted with W&L consistently enhance both general-purpose and state-of-the-art frameworks in-context, and deliver stronger gains for open-source models under supervised training. These results highlight web-scale human demonstration videos as a practical and scalable foundation for advancing CUAs towards real-world deployment.

Arithmetic-Mean $μ$P for Modern Architectures: A Unified Learning-Rate Scale for CNNs and ResNets

Choosing an appropriate learning rate remains a key challenge in scaling depth of modern deep networks. The classical maximal update parameterization ($\mu$P) enforces a fixed per-layer update magnitude, which is well suited to homogeneous multilayer perceptrons (MLPs) but becomes ill-posed in heterogeneous architectures where residual accumulation and convolutions introduce imbalance across layers. We introduce Arithmetic-Mean $\mu$P (AM-$\mu$P), which constrains not each individual layer but the network-wide average one-step pre-activation second moment to a constant scale. Combined with a residual-aware He fan-in initialization - scaling residual-branch weights by the number of blocks ($\mathrm{Var}[W]=c/(K\cdot \mathrm{fan\text{-}in})$) - AM-$\mu$P yields width-robust depth laws that transfer consistently across depths. We prove that, for one- and two-dimensional convolutional networks, the maximal-update learning rate satisfies $\eta^\star(L)\propto L^{-3/2}$; with zero padding, boundary effects are constant-level as $N\gg k$. For standard residual networks with general conv+MLP blocks, we establish $\eta^\star(L)=\Theta(L^{-3/2})$, with $L$ the minimal depth. Empirical results across a range of depths confirm the $-3/2$ scaling law and enable zero-shot learning-rate transfer, providing a unified and practical LR principle for convolutional and deep residual networks without additional tuning overhead.

DragGANSpace: Latent Space Exploration and Control for GANs

This work integrates StyleGAN, DragGAN and Principal Component Analysis (PCA) to enhance the latent space efficiency and controllability of GAN-generated images. Style-GAN provides a structured latent space, DragGAN enables intuitive image manipulation, and PCA reduces dimensionality and facilitates cross-model alignment for more streamlined and interpretable exploration of latent spaces. We apply our techniques to the Animal Faces High Quality (AFHQ) dataset, and find that our approach of integrating PCA-based dimensionality reduction with the Drag-GAN framework for image manipulation retains performance while improving optimization efficiency. Notably, introducing PCA into the latent W+ layers of DragGAN can consistently reduce the total optimization time while maintaining good visual quality and even boosting the Structural Similarity Index Measure (SSIM) of the optimized image, particularly in shallower latent spaces (W+ layers = 3). We also demonstrate capability for aligning images generated by two StyleGAN models trained on similar but distinct data domains (AFHQ-Dog and AFHQ-Cat), and show that we can control the latent space of these aligned images to manipulate the images in an intuitive and interpretable manner. Our findings highlight the possibility for efficient and interpretable latent space control for a wide range of image synthesis and editing applications.

StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

Robust Barycenters of Persistence Diagrams

This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the barycenter and the persistence diagrams. However, this procedure only works for the transportation cost related to the $q$-Wasserstein distance $W_q$ when $q=2$. We adapt an alternative fixed-point method to compute a barycenter diagram for generic transportation costs ($q > 1$), in particular those robust to outliers, $q \in (1,2)$. We show the utility of our work in two applications: \emph{(i)} the clustering of persistence diagrams on their metric space and \emph{(ii)} the dictionary encoding of persistence diagrams. In both scenarios, we demonstrate the added robustness to outliers provided by our generalized framework. Our Python implementation is available at this address: https://github.com/Keanu-Sisouk/RobustBarycenter .

Q-ROAR: Outlier-Aware Rescaling for RoPE Position Interpolation in Quantized Long-Context LLMs

Extending LLM context windows is crucial for long range tasks. RoPE-based position interpolation (PI) methods like linear and frequency-aware scaling extend input lengths without retraining, while post-training quantization (PTQ) enables practical deployment. We show that combining PI with PTQ degrades accuracy due to coupled effects long context aliasing, dynamic range dilation, axis grid anisotropy, and outlier shifting that induce position-dependent logit noise. We provide the first systematic analysis of PI plus PTQ and introduce two diagnostics: Interpolation Pressure (per-band phase scaling sensitivity) and Tail Inflation Ratios (outlier shift from short to long contexts). To address this, we propose Q-ROAR, a RoPE-aware, weight-only stabilization that groups RoPE dimensions into a few frequency bands and performs a small search over per-band scales for W_Q,W_K, with an optional symmetric variant to preserve logit scale. The diagnostics guided search uses a tiny long-context dev set and requires no fine-tuning, kernel, or architecture changes. Empirically, Q-ROAR recovers up to 0.7% accuracy on standard tasks and reduces GovReport perplexity by more than 10%, while preserving short-context performance and compatibility with existing inference stacks.

Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation

A key challenge in scientific machine learning is solving partial differential equations (PDEs) on complex domains, where the curved geometry complicates the approximation of functions and their derivatives required by differential operators. This paper establishes the first simultaneous approximation theory for deep neural networks on manifolds. We prove that a constant-depth $\mathrm{ReLU}^{k-1}$ network with bounded weights--a property that plays a crucial role in controlling generalization error--can approximate any function in the Sobolev space $\mathcal{W}_p^{k}(\mathcal{M}^d)$ to an error of $\varepsilon$ in the $\mathcal{W}_p^{s}(\mathcal{M}^d)$ norm, for $k\geq 3$ and $s<k$, using $\mathcal{O}(\varepsilon^{-d/(k-s)})$ nonzero parameters, a rate that overcomes the curse of dimensionality by depending only on the intrinsic dimension $d$. These results readily extend to functions in H\"older-Zygmund spaces. We complement this result with a matching lower bound, proving our construction is nearly optimal by showing the required number of parameters matches up to a logarithmic factor. Our proof of the lower bound introduces novel estimates for the Vapnik-Chervonenkis dimension and pseudo-dimension of the network's high-order derivative classes. These complexity bounds provide a theoretical cornerstone for learning PDEs on manifolds involving derivatives. Our analysis reveals that the network architecture leverages a sparse structure to efficiently exploit the manifold's low-dimensional geometry.