Xinrui Wang, Zhihao Chen, Jia Tang, Alexandra Gomez-Villa, Bartlomiej Twardowski, Joost van de Weijer, Songcan Chen
Unified multimodal models (UMMs), which can process and generate diverse modalities within a single framework, have recently emerged as a powerful paradigm. However, when these models undergo continual learning on multiple tasks across different modalities, their learning and forgetting dynamics remain poorly understood. In this paper, we systematically investigate how architectural design and adaptation method shape intra-modal learning and cross-modal interference between the generation and understanding sides. Specifically, we report three findings. First, the severity of cross-modal interference decreases with the degree of modality-specific parameter isolation. Second, a within-model asymmetry: the generation side of a UMM is markedly more fragile than its understanding side. Third, what post-training adds is the first to be forgotten: purely post-training capabilities such as personalized generation collapse by 84\% to 90\%, while pretraining capabilities remain stable. Together, these results clarify how parameter isolation and post-training fragility shape UMMs' learning and forgetting dynamics, offering a starting point for developing continually evolving UMMs.
Animals exhibit diverse shape-changing behaviors, from the undulatory swimming of eels to the arching movements of inchworms. Reproducing these biological shapes with modular soft robots offers a promising approach to developing versatile bioinspired robotic systems. However, translating a desired shape into a feasible robotic configuration remains challenging. Existing cable-driven modular soft robots rely on computationally expensive physics-based modeling and combinatorial search for inverse design, making it difficult to efficiently reproduce diverse target shapes. To address this challenge, we present a learning-based real-to-sim-to-real framework that translates biological curves into robotic configurations through surrogate-assisted inverse design and uncertainty-guided refinement. The proposed method combines learned inverse prediction with targeted candidate exploration, using a fast forward surrogate to evaluate and select suitable designs. The learned forward surrogate reduces deformation prediction time from $1.53 \times 10^5$ ms to 0.0008 ms, achieving approximately a $1.9 \times 10^8$-fold speedup. At the same time, the proposed inverse design method reduces design time from $1.99 \times 10^6$ ms to 4.18 ms. On 5,000 test samples generated from previously unseen threading patterns, the method achieves a 93% shape reconstruction success rate under surrogate-based evaluation. Physical demonstrations with four bioinspired robots further illustrate the translation of biological curves into realizable robotic shapes.
Many problems in computational statistics and machine learning can be formulated as approximating a target distribution by minimizing a discrepancy over a restricted class of candidate distributions. This minimum-discrepancy viewpoint appears, for example, in numerical integration, sampling, generative modelling, and statistical inference, but these instances are often studied separately in the literature. This thesis develops the first unified treatment of these many problems through the minimization of the maximum mean discrepancy (MMD), a kernel-based discrepancy between probability measures. The central theme is that MMD is not only a statistically meaningful distance between probability distributions, but also a tractable optimization objective to design practical and efficient algorithms. This thesis summarizes the recent theoretical and empirical advancements of such minimum-MMD based algorithms.
Hyperbolic graph representation learning has emerged as a powerful paradigm for modeling hierarchical data. Unlike Euclidean space, which exhibits polynomial volume growth, hyperbolic space grows exponentially with radius, naturally accommodating tree-like structures without the geometric distortion known as Euclidean crowding. Despite strong empirical performance, the theoretical mechanisms underlying hyperbolic embeddings remain poorly understood. In this work, we provide a geometric quantifcation research for Euclidean crowding, a generalization-theoretic explanation for the superiority of hyperbolic space on hierarchical data, and further develop an adaptive Euclidean-hyperbolic fusion learning framework toward bridging this gap. Specifically, we \textbf{first} establish a geometric quantification of Euclidean crowding by analyzing layer-wise minimum separation in node embeddings, proving that fixed-dimensional Euclidean embeddings of tree-like graphs inevitably exhibit layer-wise crowding that leads to weaker margin-based generalization bounds. \textbf{Second}, we provide a generalization-bound for the superiority of hyperbolic geometry on hierarchical data. \textbf{Third}, we propose EH-Fusion, a geometry-adaptive framework that lifts Euclidean GNN representations into hyperbolic space via exponential mapping and adaptively fuses both geometries based on node-level neighborhood expansion patterns. Extensive experiments validate our theoretical insights and demonstrate the effectiveness of EH-Fusion on benchmark datasets.
Generating drug-induced transcriptional responses requires a model to account for cellular background together with molecular identity and dose. We present scTREAT, the first diffusion framework to factorize state and drug guidance for single-cell drug-response prediction. A shared latent expression space connects baseline and response, while Guided Decomposable Attention (GD-Attn) injects a baseline representation and a dose-conditioned molecular embedding. Independent channel dropout exposes four conditioning states during training; inference combines three conditional predictions with separately specified state and drug coefficients, and dose modulates drug-guidance strength. On condition-level pseudobulk profiles derived from the Tahoe-100M single-cell atlas, scTREAT achieves the best value on 10 of 12 metrics for unseen cell line-drug combinations (UC) and 11 of 12 for unseen drugs (UD). Ablations examine condition injection, molecular representation, and guidance design. On UD, the relative gains over the second-best model reach 36.11% and 34.21% for DEG logFC-Spearman and logFC-Pearson. These results demonstrate the effectiveness of combining shared latent expression modeling with explicit state and drug conditioning for response prediction.
Zonghao Chen, Aratrika Mustafi, Pierre Glaser, Anna Korba, Arthur Gretton, Bharath K. Sriperumbudur
We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either lack tractable numerical implementation ($f$-divergence flows) or require strong assumptions, and modifications such as noise injection, to ensure convergence (Maximum Mean Discrepancy flows). In contrast, DrMMD flow can simultaneously (i) guarantee near-global convergence for a broad class of targets in both continuous and discrete time, and (ii) be implemented in closed form using only samples. The former is achieved by leveraging the connection between the DrMMD and the $χ^2$-divergence, while the latter comes by treating DrMMD as MMD with a de-regularized kernel. Our numerical scheme uses an adaptive de-regularization schedule throughout the flow to optimally trade off between discretization errors and deviations from the $χ^2$ regime. The potential application of the DrMMD flow is demonstrated across several numerical experiments, including a large-scale setting of training student/teacher networks.