Exact Dual Geometry of SOC-ICNN Value Functions

Input Convex Neural Networks (ICNNs) are commonly used in a two-stage manner: one first trains a convex network and then minimizes it over its input in a downstream inference problem. Recent second-order-cone ICNNs (SOC-ICNNs) enrich ReLU-based ICNNs with quadratic and conic modules and admit an exact representation as value functions of second-order cone programs (SOCPs). This value-function structure enables an explicit convex-analytic treatment of SOC-ICNN inference. In this paper, we study the exact first-order and local second-order geometry of SOC-ICNNs from the dual viewpoint. We show that supporting slopes, subdifferentials, directional derivatives, and local Hessians can be recovered directly from optimal dual variables. These results provide the geometric primitives for white-box SOC-ICNN inference, going beyond black-box automatic differentiation. Numerical experiments validate the exact multiplier readout, the local Hessian formula, and the set-valued behavior at structurally degenerate inputs. We also provide a step-by-step tutorial showing how the readout mechanism instantiates a complete white-box inference loop. The code is available at https://anonymous.4open.science/r/SOC-ICNN-Theory-BEFC/.

Budget-aware Auto Optimizer Configurator

Optimizer states occupy massive GPU memory in large-scale model training. However, gradients in different network blocks exhibit distinct behaviors, such as varying directional stability and scale anisotropy, implying that expensive optimizer states are not universally necessary and using a global optimizer is often memory-inefficient. We propose the Budget-Aware Optimizer Configurator (BAOC) to reduce memory cost by assigning suitable optimizer configurations to individual blocks under given budgets. Specifically, BAOC samples gradient streams to derive statistical metrics that quantify the potential performance risk of applying cheaper configurations (e.g., low precision or removing momentum). It then solves a constrained allocation problem to minimize total risk under memory and time budgets, selecting a budget-feasible configuration for each block. Experiments across vision, language, and diffusion workloads demonstrate that BAOC maintains training quality while significantly reducing the memory usage of optimizer states. The code is available at https://anonymous.4open.science/r/BAOC-45C6.

SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions

Classical ReLU-based Input Convex Neural Networks (ICNNs) are equivalent to the optimal value functions of Linear Programming (LP). This intrinsic structural equivalence restricts their representational capacity to piecewise-linear polyhedral functions. To overcome this representational bottleneck, we propose the SOC-ICNN, an architecture that generalizes the underlying optimization class from LP to Second-Order Cone Programming (SOCP). By explicitly injecting positive semi-definite curvature and Euclidean norm-based conic primitives, our formulation introduces native smooth curvature into the representation while preserving a rigorous optimization-theoretic interpretation. We formally prove that SOC-ICNNs strictly expand the representational space of ReLU-ICNNs without increasing the asymptotic order of forward-pass complexity. Extensive experiments demonstrate that SOC-ICNN substantially improves function approximation, while delivering competitive downstream decision quality. The code is available at https://github.com/Kanyooo/SOC-ICNN.

OPBO: Order-Preserving Bayesian Optimization

Bayesian optimization is an effective method for solving expensive black-box optimization problems. Most existing methods use Gaussian processes (GP) as the surrogate model for approximating the black-box objective function, it is well-known that it can fail in high-dimensional space (e.g., dimension over 500). We argue that the reliance of GP on precise numerical fitting is fundamentally ill-suited in high-dimensional space, where it leads to prohibitive computational complexity. In order to address this, we propose a simple order-preserving Bayesian optimization (OPBO) method, where the surrogate model preserves the order, instead of the value, of the black-box objective function. Then we can use a simple but effective OP neural network (NN) to replace GP as the surrogate model. Moreover, instead of searching for the best solution from the acquisition model, we select good-enough solutions in the ordinal set to reduce computational cost. The experimental results show that for high-dimensional (over 500) black-box optimization problems, the proposed OPBO significantly outperforms traditional BO methods based on regression NN and GP. The source code is available at https://github.com/pengwei222/OPBO.

Biomed-DPT: Dual Modality Prompt Tuning for Biomedical Vision-Language Models

Prompt learning is one of the most effective paradigms for adapting pre-trained vision-language models (VLMs) to the biomedical image classification tasks in few shot scenarios. However, most of the current prompt learning methods only used the text prompts and ignored the particular structures (such as the complex anatomical structures and subtle pathological features) in the biomedical images. In this work, we propose Biomed-DPT, a knowledge-enhanced dual modality prompt tuning technique. In designing the text prompt, Biomed-DPT constructs a dual prompt including the template-driven clinical prompts and the large language model (LLM)-driven domain-adapted prompts, then extracts the clinical knowledge from the domain-adapted prompts through the knowledge distillation technique. In designing the vision prompt, Biomed-DPT introduces the zero vector as a soft prompt to leverage attention re-weighting so that the focus on non-diagnostic regions and the recognition of non-critical pathological features are avoided. Biomed-DPT achieves an average classification accuracy of 66.14\% across 11 biomedical image datasets covering 9 modalities and 10 organs, with performance reaching 78.06\% in base classes and 75.97\% in novel classes, surpassing the Context Optimization (CoOp) method by 6.20\%, 3.78\%, and 8.04\%, respectively. Our code are available at \underline{https://github.com/Kanyooo/Biomed-DPT}.

Learning based convex approximation for constrained parametric optimization

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.

Reconstructing Visual Stimulus Images from EEG Signals Based on Deep Visual Representation Model

Reconstructing visual stimulus images is a significant task in neural decoding, and up to now, most studies consider the functional magnetic resonance imaging (fMRI) as the signal source. However, the fMRI-based image reconstruction methods are difficult to widely applied because of the complexity and high cost of the acquisition equipments. Considering the advantages of low cost and easy portability of the electroencephalogram (EEG) acquisition equipments, we propose a novel image reconstruction method based on EEG signals in this paper. Firstly, to satisfy the high recognizability of visual stimulus images in fast switching manner, we build a visual stimuli image dataset, and obtain the EEG dataset by a corresponding EEG signals collection experiment. Secondly, the deep visual representation model(DVRM) consisting of a primary encoder and a subordinate decoder is proposed to reconstruct visual stimuli. The encoder is designed based on the residual-in-residual dense blocks to learn the distribution characteristics between EEG signals and visual stimulus images, while the decoder is designed based on the deep neural network to reconstruct the visual stimulus image from the learned deep visual representation. The DVRM can fit the deep and multiview visual features of human natural state and make the reconstructed images more precise. Finally, we evaluate the DVRM in the quality of the generated images on our EEG dataset. The results show that the DVRM have good performance in the task of learning deep visual representation from EEG signals and generating reconstructed images that are realistic and highly resemble the original images.