Common prototype-based medical image few-shot segmentation (FSS) methods model foreground and background classes using class-specific prototypes. However, given the high variability of the background, a more promising direction is to focus solely on foreground modeling, treating the background as an anomaly -- an approach introduced by ADNet. Yet, ADNet faces three key limitations: dependence on a single prototype per class, a focus on binary classification, and fixed thresholds that fail to adapt to patient and organ variability. To address these shortcomings, we propose the Tied Prototype Model (TPM), a principled reformulation of ADNet with tied prototype locations for foreground and background distributions. Building on its probabilistic foundation, TPM naturally extends to multiple prototypes and multi-class segmentation while effectively separating non-typical background features. Notably, both extensions lead to improved segmentation accuracy. Finally, we leverage naturally occurring class priors to define an ideal target for adaptive thresholds, boosting segmentation performance. Taken together, TPM provides a fresh perspective on prototype-based FSS for medical image segmentation. The code can be found at https://github.com/hjk92g/TPM-FSS.

We study the problem of predictive runtime monitoring of black-box dynamical systems with quantitative safety properties. The black-box setting stipulates that the exact semantics of the dynamical system and the controller are unknown, and that we are only able to observe the state of the controlled (aka, closed-loop) system at finitely many time points. We present a novel framework for predicting future states of the system based on the states observed in the past. The numbers of past states and of predicted future states are parameters provided by the user. Our method is based on a combination of Taylor's expansion and the backward difference operator for numerical differentiation. We also derive an upper bound on the prediction error under the assumption that the system dynamics and the controller are smooth. The predicted states are then used to predict safety violations ahead in time. Our experiments demonstrate practical applicability of our method for complex black-box systems, showing that it is computationally lightweight and yet significantly more accurate than the state-of-the-art predictive safety monitoring techniques.

Diffusion and flow models have achieved remarkable successes in various applications such as text-to-image generation. However, these models typically rely on the same predetermined denoising schedules during inference for each prompt, which potentially limits the inference efficiency as well as the flexibility when handling different prompts. In this paper, we argue that the optimal noise schedule should adapt to each inference instance, and introduce the Time Prediction Diffusion Model (TPDM) to accomplish this. TPDM employs a plug-and-play Time Prediction Module (TPM) that predicts the next noise level based on current latent features at each denoising step. We train the TPM using reinforcement learning, aiming to maximize a reward that discounts the final image quality by the number of denoising steps. With such an adaptive scheduler, TPDM not only generates high-quality images that are aligned closely with human preferences but also adjusts the number of denoising steps and time on the fly, enhancing both performance and efficiency. We train TPDMs on multiple diffusion model benchmarks. With Stable Diffusion 3 Medium architecture, TPDM achieves an aesthetic score of 5.44 and a human preference score (HPS) of 29.59, while using around 50% fewer denoising steps to achieve better performance. We will release our best model alongside this paper.

Existing 3D mask learning methods encounter performance bottlenecks under limited data, and our objective is to overcome this limitation. In this paper, we introduce a triple point masking scheme, named TPM, which serves as a scalable framework for pre-training of masked autoencoders to achieve multi-mask learning for 3D point clouds. Specifically, we augment the baselines with two additional mask choices (i.e., medium mask and low mask) as our core insight is that the recovery process of an object can manifest in diverse ways. Previous high-masking schemes focus on capturing the global representation but lack the fine-grained recovery capability, so that the generated pre-trained weights tend to play a limited role in the fine-tuning process. With the support of the proposed TPM, available methods can exhibit more flexible and accurate completion capabilities, enabling the potential autoencoder in the pre-training stage to consider multiple representations of a single 3D object. In addition, an SVM-guided weight selection module is proposed to fill the encoder parameters for downstream networks with the optimal weight during the fine-tuning stage, maximizing linear accuracy and facilitating the acquisition of intricate representations for new objects. Extensive experiments show that the four baselines equipped with the proposed TPM achieve comprehensive performance improvements on various downstream tasks. Our code and models are available at https://github.com/liujia99/TPM.

Boolean Network (BN) and its extension Probabilistic Boolean Network (PBN) are popular mathematical models for studying genetic regulatory networks. BNs and PBNs are also applied to model manufacturing systems, financial risk and healthcare service systems. In this paper, we propose a novel Greedy Entry Removal (GER) algorithm for constructing sparse PBNs. We derive theoretical upper bounds for both existing algorithms and the GER algorithm. Furthermore, we are the first to study the lower bound problem of the construction of sparse PBNs, and to derive a series of related theoretical results. In our numerical experiments based on both synthetic and practical data, GER gives the best performance among state-of-the-art sparse PBN construction algorithms and outputs sparsest possible decompositions on most of the transition probability matrices being tested.

Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships between porosity and persistence entropy with the shape factor of TPMS. We propose conjectures suggesting that these relationships are polynomial in nature, derived through the application of machine learning techniques. This study exemplifies the integration of machine learning methodologies in pure mathematical research. Besides the conjectures, we provide the mathematical models that might have the potential implications for the design and modeling of TPMS structures in various practical applications.

In this paper, a unified transformation method in learned image compression(LIC) is proposed from the perspective of modulation. Firstly, the quantization in LIC is considered as a generalized channel with additive uniform noise. Moreover, the LIC is interpreted as a particular communication system according to the consistency in structures and optimization objectives. Thus, the technology of communication systems can be applied to guide the design of modules in LIC. Furthermore, a unified transform method based on signal modulation (TSM) is defined. In the view of TSM, the existing transformation methods are mathematically reduced to a linear modulation. A series of transformation methods, e.g. TPM and TJM, are obtained by extending to nonlinear modulation. The experimental results on various datasets and backbone architectures verify that the effectiveness and robustness of the proposed method. More importantly, it further confirms the feasibility of guiding LIC design from a communication perspective. For example, when backbone architecture is hyperprior combining context model, our method achieves 3.52$\%$ BD-rate reduction over GDN on Kodak dataset without increasing complexity.

Deep learning methods are transforming research, enabling new techniques, and ultimately leading to new discoveries. As the demand for more capable AI models continues to grow, we are now entering an era of Trillion Parameter Models (TPM), or models with more than a trillion parameters -- such as Huawei's PanGu-$\Sigma$. We describe a vision for the ecosystem of TPM users and providers that caters to the specific needs of the scientific community. We then outline the significant technical challenges and open problems in system design for serving TPMs to enable scientific research and discovery. Specifically, we describe the requirements of a comprehensive software stack and interfaces to support the diverse and flexible requirements of researchers.