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Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…

Machine Learning · Statistics 2015-07-01 Ravi Ganti , Nikhil Rao , Rebecca M. Willett , Robert Nowak

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…

Machine Learning · Statistics 2020-08-17 Steven Kleinegesse , Michael U. Gutmann

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational…

Machine Learning · Computer Science 2023-03-06 Avik Pal , Alan Edelman , Christopher Rackauckas

Today's most powerful machine learning approaches are typically designed to train stateless architectures with predefined layers and differentiable activation functions. While these approaches have led to unprecedented successes in areas…

Machine Learning · Computer Science 2023-12-25 Alexander Grushin

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

Semi-implicit distributions have shown great promise in variational inference and generative modeling. Hierarchical semi-implicit models, which stack multiple semi-implicit layers, enhance the expressiveness of semi-implicit distributions…

Machine Learning · Statistics 2025-06-10 Longlin Yu , Jiajun Zha , Tong Yang , Tianyu Xie , Xiangyu Zhang , S. -H. Gary Chan , Cheng Zhang

A key capability of intelligent agents is operating under partial observability: reasoning and acting effectively despite missing or incomplete state observations. While recurrent (memory-based) policies learned via reinforcement learning…

Machine Learning · Computer Science 2026-05-12 David Leeftink , Max Hinne , Marcel van Gerven

State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs…

Machine Learning · Computer Science 2026-02-26 Makram Chahine , Philipp Nazari , Daniela Rus , T. Konstantin Rusch

A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…

Machine Learning · Computer Science 2021-02-19 Kenji Kawaguchi

Image super-resolution (SR) has attracted increasing attention due to its wide applications. However, current SR methods generally suffer from over-smoothing and artifacts, and most work only with fixed magnifications. This paper introduces…

Computer Vision and Pattern Recognition · Computer Science 2023-09-06 Sicheng Gao , Xuhui Liu , Bohan Zeng , Sheng Xu , Yanjing Li , Xiaoyan Luo , Jianzhuang Liu , Xiantong Zhen , Baochang Zhang

The nonliteral interpretation of a text is hard to be understood by machine models due to its high context-sensitivity and heavy usage of figurative language. In this study, inspired by human reading comprehension, we propose a novel,…

Computation and Language · Computer Science 2020-01-17 Guoxiu He , Zhe Gao , Zhuoren Jiang , Yangyang Kang , Changlong Sun , Xiaozhong Liu , Wei Lu

We propose INFAMOUS-NeRF, an implicit morphable face model that introduces hypernetworks to NeRF to improve the representation power in the presence of many training subjects. At the same time, INFAMOUS-NeRF resolves the classic…

Computer Vision and Pattern Recognition · Computer Science 2023-12-29 Andrew Hou , Feng Liu , Zhiyuan Ren , Michel Sarkis , Ning Bi , Yiying Tong , Xiaoming Liu

Representing visual signals by implicit representation (e.g., a coordinate based deep network) has prevailed among many vision tasks. This work explores a new intriguing direction: training a stylized implicit representation, using a…

Computer Vision and Pattern Recognition · Computer Science 2022-08-23 Zhiwen Fan , Yifan Jiang , Peihao Wang , Xinyu Gong , Dejia Xu , Zhangyang Wang

Reconstructing high-quality 3D objects from sparse, partial observations from a single view is of crucial importance for various applications in computer vision, robotics, and graphics. While recent neural implicit modeling methods show…

Computer Vision and Pattern Recognition · Computer Science 2021-11-29 Shivam Duggal , Zihao Wang , Wei-Chiu Ma , Sivabalan Manivasagam , Justin Liang , Shenlong Wang , Raquel Urtasun

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there…

Machine Learning · Computer Science 2024-01-23 Xihaier Luo , Wei Xu , Yihui Ren , Shinjae Yoo , Balu Nadiga

Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is…

Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…

Machine Learning · Computer Science 2026-04-01 Jialin Liu , Lisang Ding , Stanley Osher , Wotao Yin

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of…

Machine Learning · Statistics 2017-11-07 Dustin Tran , Rajesh Ranganath , David M. Blei

This paper focuses on training implicit models of infinite layers. Specifically, previous works employ implicit differentiation and solve the exact gradient for the backward propagation. However, is it necessary to compute such an exact but…

Machine Learning · Computer Science 2022-01-13 Zhengyang Geng , Xin-Yu Zhang , Shaojie Bai , Yisen Wang , Zhouchen Lin

Deep neural networks often suffer from poor generalization caused by complex and non-convex loss landscapes. One of the popular solutions is Sharpness-Aware Minimization (SAM), which smooths the loss landscape via minimizing the maximized…

Machine Learning · Computer Science 2022-10-25 Peng Mi , Li Shen , Tianhe Ren , Yiyi Zhou , Xiaoshuai Sun , Rongrong Ji , Dacheng Tao