Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems

The paper introduces Conformal Online Learning of Koopman embeddings (COLoKe), a framework designed for adaptively updating representations of nonlinear dynamical systems using streaming data. This approach integrates deep feature learning with multistep prediction consistency in a linear evolution space. To mitigate overfitting, COLoKe focuses on the consistency of the current model's predictions, triggering updates only when errors exceed a calibrated threshold. Empirical results show COLoKe's effectiveness in maintaining predictive accuracy while minimizing unnecessary updates.

Vision-Language Models (VLMs) are emerging models that integrate visual content with natural language. Current methods typically fuse data either early in the encoding process or late through pooled embeddings. This paper introduces a lightweight fusion module utilizing cross-only, bidirectional attention layers to align hidden states from both modalities, enhancing understanding while keeping encoders non-causal. The proposed method aims to improve the performance of VLMs by leveraging the inherent structure of visual and textual data.

The paper titled 'Bias-Restrained Prefix Representation Finetuning for Mathematical Reasoning' introduces a new method called Bias-REstrained Prefix Representation FineTuning (BREP ReFT). This approach aims to enhance the mathematical reasoning capabilities of models by addressing the limitations of existing Representation finetuning (ReFT) methods, which struggle with mathematical tasks. The study demonstrates that BREP ReFT outperforms both standard ReFT and weight-based Parameter-Efficient finetuning (PEFT) methods through extensive experiments.

The study investigates the ability of transformer models to predict long steps in the Collatz sequence, a complex arithmetic function that maps odd integers to their successors. The accuracy of the models varies significantly depending on the base used for encoding, achieving up to 99.7% accuracy for bases 24 and 32, while dropping to 37% and 25% for bases 11 and 3. Despite these variations, all models exhibit a common learning pattern, accurately predicting inputs with similar residuals modulo 2^p.

Higher-order Neural Additive Models (HONAMs) have been introduced as an advancement over Neural Additive Models (NAMs), which are known for their predictive performance and interpretability. HONAMs address the limitation of NAMs by effectively capturing feature interactions of arbitrary orders, enhancing predictive accuracy while maintaining interpretability, crucial for high-stakes applications. The source code for HONAM is publicly available on GitHub.