Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive language models. While discrete DLMs achieve strong performance across language generation tasks, continuous DLMs remain relatively underexplored despite their smooth latent-space dynamics. In this work, we present a unified embedding-space interpretation of continuous and discrete DLMs. Within this framework, we analyze continuous diffusion dynamics as a retention channel that preserves intermediate denoising information during sampling. Motivated by this perspective, we propose 𝜆-DLM, which smoothly interpolates between continuous and discrete diffusion dynamics through a controllable parameter 𝜆. By training with randomly sampled 𝜆, a single model generalizes across continuous, discrete, and intermediate diffusion dynamics, unifying diverse retention behaviors within one framework. Unlike prior methods that rely on fixed or self-confidence-guided diffusion dynamics, 𝜆-DLM enables controllable exploitation–exploration trade-offs without retraining. Experiments on LM1B and OWT unconditional generation benchmarks show that 𝜆-DLM consistently outperforms strong baselines. Moreover, varying 𝜆 enables semantically diverse generation without additional training. Compared with temperature sweeps, varying 𝜆 shows a more structured relationship between lexical diversity and sentence-embedding-based mode coverage.

Transformers have achieved great success in effectively processing sequential data such as text. Their architecture consisting of several attention and feedforward blocks can model relations between elements of a sequence in parallel manner, which makes them very efficient to train and effective in sequence modeling. Even though they have shown strong performance in processing sequential data, the size of their parameters is considerably larger when compared to other architectures such as RNN and CNN based models. Therefore, several approaches have explored parameter sharing and recurrence in Transformer models to address their computational demands. However, such methods struggle to maintain high performance compared to the original transformer model. To address this challenge, we propose our novel approach, RingFormer, which employs one Transformer layer that processes input repeatedly in a circular, ring-like manner, while utilizing low-rank matrices to generate input-dependent level signals. This allows us to reduce the model parameters substantially while maintaining high performance in a variety of tasks such as translation and image classification, as validated in the experiments.

Automatically assessing handwritten mathematical solutions is an important problem in educational technology with practical applications, but remains a significant challenge due to the diverse formats, unstructured layouts, and symbolic complexity of student work. To address this challenge, we introduce VEHME-a Vision-Language Model for Evaluating Handwritten Mathematics Expressions—designed to assess open-form handwritten math responses with high accuracy and interpretable reasoning traces. VEHME integrates a two-phase training pipeline: (i) supervised fine-tuning using structured reasoning data, and (ii) reinforcement learning that aligns model outputs with multi-dimensional grading objectives, including correctness, reasoning depth, and error localization. To enhance spatial understanding, we propose an Expression-Aware Visual Prompting Module, trained on our synthesized multi-line math expressions dataset to robustly guide attention in visually heterogeneous inputs. Evaluated on AIHub and FERMAT datasets, VEHME achieves state-of-the-art performance among open-source models and approaches the accuracy of proprietary systems, demonstrating its potential as a scalable and accessible tool for automated math assessment. Our training and experiment code is publicly available at our GitHub repository.