arXiv subjects

Timur Carstensen

Publications and source records attributed to Timur Carstensen.

8 recordsLinked to original sources

arXiv2026

Complex KDA: Understanding and Enhancing the Expressivity of Kimi Delta Attention

Linear RNNs based on the delta-rule enable efficient sequence modeling, but their linear updates with a low-rank correction constrain their expressivity. Prior work has shown that composing two delta-rule transitions in a single recurrent update can model a 2D rotation, but this increases the rank and the cost of the updates compared to a single transition. We show that Kimi Delta Attention (KDA) can realize 2D rotations by combining a single delta-rule transformation with a second reflection supplied by its channel-wise gate. This requires extending the parameter ranges of KDA by combining two existing range extensions: allowing gates in $[-1,1]$ and the delta-rule coefficient $β$ in $[0,2]$. We call the resulting model Complex KDA (CKDA). It preserves KDA's stability and efficiency, with transitions that remain diagonal-plus-rank-one and non-expansive, while reaching the state-tracking expressivity of DeltaProduct$_2$. We characterize the expressivity of CKDA and prove that every orthogonal diagonal-plus-rank-one matrix is exactly a CKDA transition matrix. A single CKDA layer can track every finite group isomorphic to a subgroup of $\mathrm{SO}(3)$, and many state-tracking results use one fewer layer for CKDA compared to other diagonal-plus-rank-one Linear RNNs. Empirically, combining both extensions yields the strongest length extrapolation among tested KDA range settings on $S_3$, $S_4$, and periodic audio continuation. In language modeling, CKDA outperforms Transformers and other linear RNNs, obtains similar results to a KDA baseline, and shows promising scaling behavior. Our code is open source at https://github.com/OpenEuroLLM/ComplexKDA and our models are available at https://huggingface.co/collections/openeurollm/complexkda.

cs.LG↗

arXiv2026

Selective Rotary Position Embedding

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

cs.CL↗

arXiv2026

TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting

Foundation models for zero-shot time series forecasting face challenges in efficient long-horizon prediction and reproducibility, with existing synthetic-only approaches underperforming on challenging benchmarks. This paper presents TempoPFN, a univariate time series foundation model based on linear Recurrent Neural Networks (RNNs) pre-trained exclusively on synthetic data. The model uses a GatedDeltaProduct architecture with state-weaving for fully parallelizable training across sequence lengths, eliminating the need for windowing or summarization techniques while maintaining robust temporal state-tracking. Our comprehensive synthetic data pipeline unifies diverse generators, including stochastic differential equations, Gaussian processes, and audio synthesis, with novel augmentations. In zero-shot evaluations on the Gift-Eval, fev-bench and Chronos-ZS benchmarks, TempoPFN achieves top-tier competitive performance, outperforming all existing synthetic-only approaches and surpassing the majority of models trained on real-world data, while being more efficient than existing baselines by leveraging fully parallelizable training and inference. We open-source our complete data generation pipeline and training code, providing a reproducible foundation for future research.

cs.LG↗

arXiv2026

Where to Begin: Efficient Pretraining via Subnetwork Selection and Distillation

Small Language models (SLMs) offer an efficient and accessible alternative to Large Language Models (LLMs), delivering strong performance while using far fewer resources. We introduce a simple and effective framework for pretraining SLMs that brings together three complementary ideas. First, we identify structurally sparse sub-network initializations that consistently outperform randomly initialized models of similar size under the same compute budget. Second, we use evolutionary search to automatically discover high-quality sub-network initializations, providing better starting points for pretraining. Third, we apply knowledge distillation from larger teacher models to speed up training and improve generalization. Together, these components make SLM pretraining substantially more efficient: our best model, discovered using evolutionary search and initialized with LLM weights, matches the validation perplexity of a comparable Pythia SLM while requiring 5.16x and 1.26x fewer floating point operations for token budgets of 10B and 100B, respectively. We release all code publicly, offering a practical and reproducible path toward cost-efficient small language model development at scale.

cs.CL↗

arXiv2025

Open-sci-ref-0.01: open and reproducible reference baselines for language model and dataset comparison

We introduce open-sci-ref, a family of dense transformer models trained as research baselines across multiple model (0.13B to 1.7B parameters) and token scales (up to 1T) on 8 recent open reference datasets. Evaluating the models on various standardized benchmarks, our training runs set establishes reference points that enable researchers to assess the sanity and quality of alternative training approaches across scales and datasets. Intermediate checkpoints allow comparison and studying of the training dynamics. The established reference baselines allow training procedures to be compared through their scaling trends, aligning them on a common compute axis. Comparison of open reference datasets reveals that training on NemoTron-CC HQ consistently outperforms other reference datasets, followed by DCLM-baseline and FineWeb-Edu. In addition to intermediate training checkpoints, the release includes logs, code, and downstream evaluations to simplify reproduction, standardize comparison, and facilitate future research.

cs.LG↗

arXiv2025

DeltaProduct: Improving State-Tracking in Linear RNNs via Householder Products

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank--1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing state-transition matrices to have negative eigenvalues. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple ($n_h$) steps per token. This naturally leads to diagonal plus rank--$n_h$ state-transition matrices, formed as products of $n_h$ generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision, showing how it improves by increasing $n_h$. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

cs.LG↗

arXiv2025

Quickly Tuning Foundation Models for Image Segmentation

Foundation models like SAM (Segment Anything Model) exhibit strong zero-shot image segmentation performance, but often fall short on domain-specific tasks. Fine-tuning these models typically requires significant manual effort and domain expertise. In this work, we introduce QTT-SEG, a meta-learning-driven approach for automating and accelerating the fine-tuning of SAM for image segmentation. Built on the Quick-Tune hyperparameter optimization framework, QTT-SEG predicts high-performing configurations using meta-learned cost and performance models, efficiently navigating a search space of over 200 million possibilities. We evaluate QTT-SEG on eight binary and five multiclass segmentation datasets under tight time constraints. Our results show that QTT-SEG consistently improves upon SAM's zero-shot performance and surpasses AutoGluon Multimodal, a strong AutoML baseline, on most binary tasks within three minutes. On multiclass datasets, QTT-SEG delivers consistent gains as well. These findings highlight the promise of meta-learning in automating model adaptation for specialized segmentation tasks. Code available at: https://github.com/ds-brx/QTT-SEG/

cs.CV↗

arXiv2025

Frozen Layers: Memory-efficient Many-fidelity Hyperparameter Optimization

As model sizes grow, finding efficient and cost-effective hyperparameter optimization (HPO) methods becomes increasingly crucial for deep learning pipelines. While multi-fidelity HPO (MF-HPO) trades off computational resources required for DL training with lower fidelity estimations, existing fidelity sources often fail under lower compute and memory constraints. We propose a novel fidelity source: the number of layers that are trained or frozen during training. For deep networks, this approach offers significant compute and memory savings while preserving rank correlations between hyperparameters at low fidelities compared to full model training. We demonstrate this in our empirical evaluation across ResNets and Transformers and additionally analyze the utility of frozen layers as a fidelity in using GPU resources as a fidelity in HPO, and for a combined MF-HPO with other fidelity sources. This contribution opens new applications for MF-HPO with hardware resources as a fidelity and creates opportunities for improved algorithms navigating joint fidelity spaces.

cs.LG↗