Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently been proposed to solve complex differential equations and have demonstrated superior performance in many applications. While the L2 loss function is usually a default choice in PINNs, it has been shown that the corresponding numerical solution is incorrect and unstable for some complex equations. In this work, we propose a new PINNs framework named Kernel Packet accelerated PINNs (KP-PINNs), which gives a new expression of the loss function using the reproducing kernel Hilbert space (RKHS) norm and uses the Kernel Packet (KP) method to accelerate the computation. Theoretical results show that KP-PINNs can be stable across various differential equations. Numerical experiments illustrate that KP-PINNs can solve differential equations effectively and efficiently. This framework provides a promising direction for improving the stability and accuracy of PINNs-based solvers in scientific computing.

This paper proposes AS-ASR, a lightweight aphasia-specific speech recognition framework based on Whisper-tiny, tailored for low-resource deployment on edge devices. Our approach introduces a hybrid training strategy that systematically combines standard and aphasic speech at varying ratios, enabling robust generalization, and a GPT-4-based reference enhancement method that refines noisy aphasic transcripts, improving supervision quality. We conduct extensive experiments across multiple data mixing configurations and evaluation settings. Results show that our fine-tuned model significantly outperforms the zero-shot baseline, reducing WER on aphasic speech by over 30% while preserving performance on standard speech. The proposed framework offers a scalable, efficient solution for real-world disordered speech recognition.

Visual-spatial understanding, the ability to infer object relationships and layouts from visual input, is fundamental to downstream tasks such as robotic navigation and embodied interaction. However, existing methods face spatial uncertainty and data scarcity, limiting the 3D spatial reasoning capability of pre-trained vision-language models (VLMs). To address these challenges, we present a unified framework for enhancing 3D spatial reasoning in pre-trained VLMs without modifying their architecture. This framework combines SpatialMind, a structured prompting strategy that decomposes complex scenes and questions into interpretable reasoning steps, with ScanForgeQA, a scalable question-answering dataset built from diverse 3D simulation scenes through an automated construction process designed for fine-tuning. Extensive experiments across multiple benchmarks demonstrate the individual and combined effectiveness of our prompting and fine-tuning strategies, and yield insights that may inspire future research on visual-spatial understanding.

W e explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology . W e show that torsion can be lost during encoding, altered in the latent space, and in many cases, not reconstructed by standard decoders. Using both synthetic and high-dimensional data, we evaluate torsion sensitivity to perturbations and assess its recoverability across several autoencoder architectures. Our findings reveal key limitations of field-based approaches and underline the need for architectures or loss terms that preserve torsional information for robust data representation.

Tool use in stateful environments presents unique challenges for large language models (LLMs), where existing test-time compute strategies relying on repeated trials in the environment are impractical. We propose dynamics modelling (DyMo), a method that augments LLMs with a state prediction capability alongside function calling during post-training. This enables LLMs to predict the future states of their actions through an internal environment model. On the Berkeley Function Calling Leaderboard V2, DyMo improves success rates and significantly reduces hallucinations. We further integrate the internal environment model into self-verification sampling (SVS), and show that this substantially improves pass^k over number of trials k, and allows the model to refuse unreliable outputs. Together, DyMo and SVS greatly enhance the effectiveness and reliability of LLMs for tool use. We believe this work charts a path towards scalable planning RL methods for LLM inference without repeatedly querying the oracle environment.

The automatic classification of medical time series signals, such as electroencephalogram (EEG) and electrocardiogram (ECG), plays a pivotal role in clinical decision support and early detection of diseases. Although Transformer based models have achieved notable performance by implicitly modeling temporal dependencies through self-attention mechanisms, their inherently complex architectures and opaque reasoning processes undermine their trustworthiness in high stakes clinical settings. In response to these limitations, this study shifts focus toward a modeling paradigm that emphasizes structural transparency, aligning more closely with the intrinsic characteristics of medical data. We propose a novel method, Channel Imposed Fusion (CIF), which enhances the signal-to-noise ratio through cross-channel information fusion, effectively reduces redundancy, and improves classification performance. Furthermore, we integrate CIF with the Temporal Convolutional Network (TCN), known for its structural simplicity and controllable receptive field, to construct an efficient and explicit classification framework. Experimental results on multiple publicly available EEG and ECG datasets demonstrate that the proposed method not only outperforms existing state-of-the-art (SOTA) approaches in terms of various classification metrics, but also significantly enhances the transparency of the classification process, offering a novel perspective for medical time series classification.

Controlling multiple behavioral attributes in large language models (LLMs) at inference time is a challenging problem due to interference between attributes and the limitations of linear steering methods, which assume additive behavior in activation space and require per-attribute tuning. We introduce K-Steering, a unified and flexible approach that trains a single non-linear multi-label classifier on hidden activations and computes intervention directions via gradients at inference time. This avoids linearity assumptions, removes the need for storing and tuning separate attribute vectors, and allows dynamic composition of behaviors without retraining. To evaluate our method, we propose two new benchmarks, ToneBank and DebateMix, targeting compositional behavioral control. Empirical results across 3 model families, validated by both activation-based classifiers and LLM-based judges, demonstrate that K-Steering outperforms strong baselines in accurately steering multiple behaviors.

Transformer-based models have shown strong performance across diverse time-series tasks, but their deployment on resource-constrained devices remains challenging due to high memory and computational demand. While prior work targeting Microcontroller Units (MCUs) has explored hardware-specific optimizations, such approaches are often task-specific and limited to 8-bit fixed-point precision. Field-Programmable Gate Arrays (FPGAs) offer greater flexibility, enabling fine-grained control over data precision and architecture. However, existing FPGA-based deployments of Transformers for time-series analysis typically focus on high-density platforms with manual configuration. This paper presents a unified and fully automated deployment framework for Tiny Transformers on embedded FPGAs. Our framework supports a compact encoder-only Transformer architecture across three representative time-series tasks (forecasting, classification, and anomaly detection). It combines quantization-aware training (down to 4 bits), hardware-aware hyperparameter search using Optuna, and automatic VHDL generation for seamless deployment. We evaluate our framework on six public datasets across two embedded FPGA platforms. Results show that our framework produces integer-only, task-specific Transformer accelerators achieving as low as 0.033 mJ per inference with millisecond latency on AMD Spartan-7, while also providing insights into deployment feasibility on Lattice iCE40. All source code will be released in the GitHub repository (https://github.com/Edwina1030/TinyTransformer4TS).

Fine-grained personas have recently been used for generating 'diverse' synthetic data for pre-training and supervised fine-tuning of Large Language Models (LLMs). In this work, we measure the diversity of persona-driven synthetically generated prompts and responses with a suite of lexical diversity and redundancy metrics. First, we find that synthetic prompts/instructions are significantly less diverse than human-written ones. Next, we sample responses from LLMs of different sizes with fine-grained and coarse persona descriptions to investigate how much fine-grained detail in persona descriptions contribute to generated text diversity. Our results indicate that persona prompting produces higher lexical diversity than prompting without personas, particularly in larger models. In contrast, adding fine-grained persona details yields minimal gains in diversity compared to simply specifying a length cutoff in the prompt.

Existing reasoning datasets saturate and fail to test abstract, multi-step problems, especially pathfinding and complex rule constraint satisfaction. We introduce SPaRC (Spatial Pathfinding Reasoning Challenge), a dataset of 1,000 2D grid pathfinding puzzles to evaluate spatial and symbolic reasoning, requiring step-by-step planning with arithmetic and geometric rules. Humans achieve near-perfect accuracy (98.0%; 94.5% on hard puzzles), while the best reasoning models, such as o4-mini, struggle (15.8%; 1.1% on hard puzzles). Models often generate invalid paths (>50% of puzzles for o4-mini), and reasoning tokens reveal they make errors in navigation and spatial logic. Unlike humans, who take longer on hard puzzles, models fail to scale test-time compute with difficulty. Allowing models to make multiple solution attempts improves accuracy, suggesting potential for better spatial reasoning with improved training and efficient test-time scaling methods. SPaRC can be used as a window into models' spatial reasoning limitations and drive research toward new methods that excel in abstract, multi-step problem-solving.