Dynamic Large Concept Models: Latent Reasoning in an Adaptive Semantic Space

Large Language Models (LLMs) apply uniform computation to all tokens, despite language exhibiting highly non-uniform information density. This token-uniform regime wastes capacity on locally predictable spans while under-allocating computation to semantically critical transitions. We propose $\textbf{Dynamic Large Concept Models (DLCM)}$, a hierarchical language modeling framework that learns semantic boundaries from latent representations and shifts computation from tokens to a compressed concept space where reasoning is more efficient. DLCM discovers variable-length concepts end-to-end without relying on predefined linguistic units. Hierarchical compression fundamentally changes scaling behavior. We introduce the first $\textbf{compression-aware scaling law}$, which disentangles token-level capacity, concept-level reasoning capacity, and compression ratio, enabling principled compute allocation under fixed FLOPs. To stably train this heterogeneous architecture, we further develop a $\textbf{decoupled $μ$P parametrization}$ that supports zero-shot hyperparameter transfer across widths and compression regimes. At a practical setting ($R=4$, corresponding to an average of four tokens per concept), DLCM reallocates roughly one-third of inference compute into a higher-capacity reasoning backbone, achieving a $\textbf{+2.69$\%$ average improvement}$ across 12 zero-shot benchmarks under matched inference FLOPs.

When a driver challenges the kernel's assumptions

Conformal Prediction in Dynamic Biological Systems

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial because it addresses the challenges posed by nonlinearity and parameter sensitivity, allowing us to properly understand and extrapolate the behavior of complex biological systems. Here, we focus on dynamic models represented by deterministic nonlinear ordinary differential equations. Many current UQ approaches in this field rely on Bayesian statistical methods. While powerful, these methods often require strong prior specifications and make parametric assumptions that may not always hold in biological systems. Additionally, these methods face challenges in domains where sample sizes are limited, and statistical inference becomes constrained, with computational speed being a bottleneck in large models of biological systems. As an alternative, we propose the use of conformal inference methods, introducing two novel algorithms that, in some instances, offer non-asymptotic guarantees, enhancing robustness and scalability across various applications. We demonstrate the efficacy of our proposed algorithms through several scenarios, highlighting their advantages over traditional Bayesian approaches. The proposed methods show promising results for diverse biological data structures and scenarios, offering a general framework to quantify uncertainty for dynamic models of biological systems.The software for the methodology and the reproduction of the results is available at https://zenodo.org/doi/10.5281/zenodo.13644870.

Differential Logic and Dynamic Systems • Overview