Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit neural representations (INRs) for modeling such deformations, due to their meshlessness and differentiability; however, extracting coherent and accurate morphings from standard MLPs typically relies on costly regularizations, which often lead to unstable training and prevent effective feature alignment. To overcome these limitations, we propose FLOWING (FLOW morphING), a framework that recasts warping as the construction of a differential vector flow, naturally ensuring continuity, invertibility, and temporal coherence by encoding structural flow properties directly into the network architectures.

Gene regulatory network (GRN) inference serves as a cornerstone for deciphering cellular decision-making processes. Early approaches rely exclusively on gene expression data, thus their predictive power remain fundamentally constrained by the vast combinatorial space of potential gene-gene interactions. Subsequent methods integrate prior knowledge to mitigate this challenge by restricting the solution space to biologically plausible interactions. However, we argue that the effectiveness of these approaches is contingent upon the precision of prior information and the reduction in the search space will circumscribe the models' potential for novel biological discoveries. To address these limitations, we introduce KINDLE, a three-stage framework that decouples GRN inference from prior knowledge dependencies.

Testing hypotheses on how representational changes occur in biological systems is challenging, but large language models (LLMs) offer a scalable alternative. Building on LLMs' in-context learning, we adapt a cognitive neuroscience associative learning paradigm and investigate how representations evolve across six models. Our initial findings reveal a non-monotonic pattern consistent with the Non-Monotonic Plasticity Hypothesis, with moderately similar items differentiating after learning. Leveraging the controllability of LLMs, we further show that this differentiation is modulated by the overlap of associated items with the broader vocabulary-a factor we term vocabulary interference, capturing how new associations compete with prior knowledge. We find that higher vocabulary interference amplifies differentiation, suggesting that representational change is influenced by both item similarity and global competition.

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices.

A common approach for accelerating optimization algorithms is to minimize the loss achieved in a fixed time, which enables a differentiable framework with respect to the algorithm's hyperparameters. In contrast, the complementary objective of minimizing the time to reach a target loss is traditionally considered non-differentiable. To address this limitation, we propose a differentiable discrete stopping time and theoretically justify it based on its connection to continuous differential equations. We design an efficient algorithm to compute its sensitivities, thereby enabling a new differentiable formulation for directly accelerating algorithms. We demonstrate its effectiveness in applications such as online hyperparameter tuning and learning to optimize. Our proposed methods show superior performance in comprehensive experiments across various problems, which confirms their effectiveness.

Associative learning--forming links between co-occurring items--is fundamental to human cognition, reshaping internal representations in complex ways. Testing hypotheses on how representational changes occur in biological systems is challenging, but large language models (LLMs) offer a scalable alternative. Building on LLMs' in-context learning, we adapt a cognitive neuroscience associative learning paradigm and investigate how representations evolve across six models. Our initial findings reveal a non-monotonic pattern consistent with the Non-Monotonic Plasticity Hypothesis, with moderately similar items differentiating after learning. Leveraging the controllability of LLMs, we further show that this differentiation is modulated by the overlap of associated items with the broader vocabulary--a factor we term vocabulary interference, capturing how new associations compete with prior knowledge. We find that higher vocabulary interference amplifies differentiation, suggesting that representational change is influenced by both item similarity and global competition.

Although this might initially seem more intuitive, we will show with a small counterexample why we should consider any stochastic nodes ordered topologically before i instead of just those that directly influence i.