Aussie AI

Probabilistic Optimizations

Last Updated 27 August, 2025

by David Spuler, Ph.D.

I'm going to say it straight up: all neural networks are probabilistic algorithms. The entire concept of a neural network is a probabilistic approximation of reality based on what it's seen during training. In that sense, an AI engine is one big probabilistic algorithm, and optimizing it with another low-level probabilistic algorithm is really creating a doubly-probabilistic algorithm. After all, conceptually speaking, the result of an AI engine's output, called "logits", are probabilities of the likelihood of outputting a particular word. The core functionality of an AI model is to train it so it knows what words are "likely", and then it becomes good enough to "guestimate" what words should be output based on the probabilities that it calculates.

Similar to probabilistic algorithms are "stochastic algorithms", where an amount of randomness is injected to give results. For example, in the core theory of Computer Science, the "Monte Carlo method" is a well-known algorithm for measuring the area under a curve using randomly generated points. Some of these concepts can also be applied to AI models. These stochastic algorithms are technically a subset of probabilistic algorithms, since there are probabilistic methods that do not require random numbers, but still rely on probabilities for correct execution (e.g. neural networks). An example of a stochastic algorithm for neural networks is "stochastic quantization", where intentional randomness attempts to improve a quantized model.

The main use of probabilistic algorithms in AI inference is the randomness injected into decoding algorithms with the top-k, top-p, and temperature hyper-parameters. The randomness in these methods ensure that the AI engine doesn't output the exact same response when it receives the same input, so it can show creativity and originality in its responses to prompts. Note that the goal of randomness in decoding algorithms is variety of responses, and does not improve the speed of inference. However, the final stage of decoding is rarely a bottleneck, so the randomness doesn't degrade latency either.

Randomness of stochastic algorithms is not always beneficial. It can be useful to turn off the randomness in these decoding algorithms when regression testing an AI engine, which is a situation where having the exact same responses can be useful.

Probabilistic Optimizations

Probabilistic optimizations are methods of speeding up inference based on the relative probabilities of events. There are both high-level and lower-level ways that neural networks can use probabilistic algorithms. There are two main types of probabilistic algorithms:

Common case first. These are optimizations where a likely case is handled first, using fast code, but the unlikely case is also handled as a backup, with slower code. In such cases, the probabilistic algorithm does not affect the result of the neural network, only its speed.
Lossy or error-accepting algorithms. These are probabilistic algorithms where the unlikely case is simply ignored, and an error in such cases is accepted as part of the logic. Such algorithms may be appropriate for neural networks because they have an inherent resilience to errors.

Arguably, many of the inference optimization techniques and almost all model compression optimizations are lossy probabilistic optimizations, where a known level of error is tolerated. They take the probabilistic AI engine, add some known extra error sources to it (but making it faster), and the result is a faster, but slightly less accurate model. Examples of such "probabilistic optimizations" that offer trade-offs at a high-level are techniques such as:

Quantization (accepts errors resulting from the loss of precision).
Early exits (assumes that later layers won't change results, tolerating cases where this is erroneous).
Magnitude pruning (assumes that low-value weights have little impact, accepting the resulting errors).
Big-little models (common case first method; see ensemble algorithms)
Approximate algorithms (various types)

Some examples of the lower-level specific uses of probabilistic algorithms in neural networks include:

Probabilistic Algorithm Research Papers

General research papers on specific probabilistic algorithms (including stochastic algorithms) in neural networks:

Ao Ren, Ji Li, Zhe Li, Caiwen Ding, Xuehai Qian, Qinru Qiu, Bo Yuan, Yanzhi Wang, 2017, "SC-DCNN: Highly-scalable deep convolutional neural network using stochastic computing", ACM SIGPLAN Notices, vol. 52, no. 4, pp. 405-418, 2017. https://arxiv.org/abs/1611.05939 (Stochastic method with multiplication and addition approximations via AND gates and multiplexers.)
R. Hojabr et al., "SkippyNN: An embedded stochastic-computing accelerator for convolutional neural networks", Proc. 56th ACM/IEEE Design Automat. Conf. (DAC), pp. 1-6, Jun. 2019. https://ieeexplore.ieee.org/document/8806970
Nikola Popovic, Danda Pani Paudel, Thomas Probst, Luc Van Gool, July 2022, Improving the Behaviour of Vision Transformers with Token-consistent Stochastic Layers, https://arxiv.org/abs/2112.15111
N Popovic, DP Paudel, T Probst, L Van Gool, 2023, Token-Consistent Dropout For Calibrated Vision Transformers, 2023 IEEE International Conference on Image Processing (ICIP), https://ieeexplore.ieee.org/abstract/document/10222084
Carlos Florensa, Yan Duan, Pieter Abbeel, April 2017, Stochastic Neural Networks for Hierarchical Reinforcement Learning, arXiv preprint arXiv:1704.03012, 2017, https://arxiv.org/abs/1704.03012
E Wong, 1991, Stochastic neural networks, Algorithmica, Springer https://link.springer.com/article/10.1007/BF01759054, https://arxiv.org/pdf/1704.03012.pdf
Roohi Menon, Hangyu Zhou, Gerald Ogbonna, Vikram Raghavan, 2021, Stochastic programming, SYSEN 6800 Fall 2021, Cornell University Computational Optimization Open Textbook, https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming
John R. Birge , François Louveaux, 2011, Introduction to Stochastic Programming, Springer Series in Operations Research and Financial Engineering (ORFE), https://link.springer.com/book/10.1007/978-1-4614-0237-4
Sairam Sri Vatsavai, Venkata Sai Praneeth Karempudi, Ishan Thakkar, Ahmad Salehi, Todd Hastings, Feb 2023, SCONNA: A Stochastic Computing Based Optical Accelerator for Ultra-Fast, Energy-Efficient Inference of Integer-Quantized CNNs, https://arxiv.org/abs/2302.07036, Code: https://github.com/uky-UCAT/SC_ONN_SIM.git
Zhenda Xie, Zheng Zhang, Xizhou Zhu, Gao Huang, and Stephen Lin. 2020. Spatially adaptive inference with stochastic feature sampling and interpolation. arXiv preprint arXiv:2003.08866, https://arxiv.org/abs/2003.08866
Bengio, Yoshua, Leonard, Nicholas, and Courville, Aaron, 2013, Estimating or propagating gradients ´ through stochastic neurons for conditional computation. arXiv preprint arXiv:1308.3432, https://arxiv.org/abs/1308.3432
Hanting Chen, Zhicheng Liu, Xutao Wang, Yuchuan Tian, Yunhe Wang, 1 Apr 2024 (v2), DiJiang: Efficient Large Language Models through Compact Kernelization, https://arxiv.org/abs/2403.19928 (Using the Monte Carlo method to achieve a linear attention approximation.)
Salar Shakibhamedan, Amin Aminifar, Nima TaheriNejad, Axel Jantsch, 2024, EASE: Energy Optimization through Adaptation — A Review of Runtime Energy-Aware Approximate Deep Learning Algorithms, https://eclectx.org/Publications/2024_M13.pdf (Survey paper on techniques for adaptive inference with a focus on approximations of inference, including loop performance, stochastic algorithms, approximate arithmetic, quantization, pruning and low-rank.)
Jing Yang Lee, Kong Aik Lee, Woon-Seng Gan, Nov 2023, Partially Randomizing Transformer Weights for Dialogue Response Diversity, https://arxiv.org/abs/2311.10943
Zhengmian Hu, Heng Huang, 2024, Accelerated Speculative Sampling Based on Tree Monte Carlo, Proceedings of the 41st International Conference on Machine Learning, PMLR 235:19216-19251, 2024. https://proceedings.mlr.press/v235/hu24f.html https://openreview.net/forum?id=stMhi1Sn2G PDF: https://raw.githubusercontent.com/mlresearch/v235/main/assets/hu24f/hu24f.pdf
Lingyun Yao, Martin Trapp, Jelin Leslin, Gaurav Singh, Peng Zhang, Karthekeyan Periasamy, Martin Andraud, 22 May 2024, On Hardware-efficient Inference in Probabilistic Circuits, https://arxiv.org/abs/2405.13639
Wenlun Zhang, Shimpei Ando, Yung-Chin Chen, Satomi Miyagi, Shinya Takamaeda-Yamazaki, Kentaro Yoshioka, 29 Aug 2024, PACiM: A Sparsity-Centric Hybrid Compute-in-Memory Architecture via Probabilistic Approximation, https://arxiv.org/abs/2408.16246
Haiyue Ma, Jian Liu, Ronny Krashinsky, 10 Oct 2024, Reducing the Cost of Dropout in Flash-Attention by Hiding RNG with GEMM, https://arxiv.org/abs/2410.07531
Felix Jimenez, Matthias Katzfuss, 8 Jan 2025, Probabilistic Skip Connections for Deterministic Uncertainty Quantification in Deep Neural Networks, https://arxiv.org/abs/2501.04816
Andreas Krause, Jonas Hübotter, 7 Feb 2025, Probabilistic Artificial Intelligence, https://arxiv.org/abs/2502.05244
S Xu, L Jiayao, Z He, C Peng, W Xu, Mar 2025, The Surprising Effectiveness of Randomness in LLM Pruning, https://openreview.net/pdf?id=YncWrbIxnN https://anonymous.4open.science/r/random-prune-8F1C
Jacob Trauger, Ambuj Tewari, 16 May 2025, On Next-Token Prediction in LLMs: How End Goals Determine the Consistency of Decoding Algorithms, https://arxiv.org/abs/2505.11183
Yuchen Zhu, Wei Guo, Jaemoo Choi, Guan-Horng Liu, Yongxin Chen, Molei Tao, 14 Aug 2025, MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control, https://arxiv.org/abs/2508.10684
Jung-hun Kim and Milan Vojnovic, 14 Aug 2025, Learning to Schedule in Parallel-Server Queues with Stochastic Bilinear Rewards, https://arxiv.org/abs/2112.06362
Tianyi Wang, Bingqian Dai, Kin Wong, Yaochen Li, Yang Cheng, Qingyuan Shu, Haoran He, Puyang Huang, Hanshen Huang, and Kang L. Wang, 23 Jul 2025, Spintronic Bayesian Hardware Driven by Stochastic Magnetic Domain Wall Dynamics, https://arxiv.org/abs/2507.17193
El Mahdi Chayti and Nikita Doikov and Martin Jaggi, 23 Jul 2025, Unified Convergence Theory of Stochastic and Variance-Reduced Cubic Newton Methods, https://arxiv.org/abs/2302.11962
Yushi Feng, Junye Du, Yingying Hong, Qifan Wang, Lequan Yu, 14 Aug 2025, PASS: Probabilistic Agentic Supernet Sampling for Interpretable and Adaptive Chest X-Ray Reasoning, https://arxiv.org/abs/2508.10501
Weijian Mai, Jiamin Wu, Yu Zhu, Zhouheng Yao, Dongzhan Zhou, Andrew F. Luo, Qihao Zheng, Wanli Ouyang, Chunfeng Song, 14 Aug 2025, SynBrain: Enhancing Visual-to-fMRI Synthesis via Probabilistic Representation Learning, https://arxiv.org/abs/2508.10298
Isha Puri, Shivchander Sudalairaj, Guangxuan Xu, Kai Xu and Akash Srivastava, 14 Aug 2025, Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods, https://arxiv.org/abs/2502.01618
Daniel Zhengyu Huang, Jiaoyang Huang, Zhengjiang Lin, 14 Aug 2025, Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models, https://arxiv.org/abs/2506.13061
Pengjiu Xia, Yidian Huang, Wenchao Wei, Yuwen Tan, 22 Jul 2025, Confidence Optimization for Probabilistic Encoding, https://arxiv.org/abs/2507.16881
Jacqueline Maasch, Willie Neiswanger, Stefano Ermon, Volodymyr Kuleshov, 23 Jul 2025, Probabilistic Graphical Models: A Concise Tutorial, https://arxiv.org/abs/2507.17116
Songxuan Shi, 23 Jul 2025, Rethinking VAE: From Continuous to Discrete Representations Without Probabilistic Assumptions, https://arxiv.org/abs/2507.17255
Aritz P\'erez, Carlos Echegoyen and Guzm\'an Santaf\'e, 23 Jul 2025, Decentralized Federated Learning of Probabilistic Generative Classifiers, https://arxiv.org/abs/2507.17285
Damiano Azzolini, Fabrizio Riguzzi, Theresa Swift, 23 Jul 2025, Integrating Belief Domains into Probabilistic Logic Programs, https://arxiv.org/abs/2507.17291
Leandro Von Krannichfeldt, Kristina Orehounig and Olga Fink, 23 Jul 2025, Integrating Physics-Based and Data-Driven Approaches for Probabilistic Building Energy Modeling, https://arxiv.org/abs/2507.17526
Mohammad Taha Askari, Lutz Lampe, and Amirhossein Ghazisaeidi, 21 Jul 2025, Neural Probabilistic Shaping: Joint Distribution Learning for Optical Fiber Communications, https://arxiv.org/abs/2507.16012
Lars Hillebrand, David Biesner, Christian Bauckhage, Rafet Sifa, 22 Jul 2025, Interpretable Topic Extraction and Word Embedding Learning using row-stochastic DEDICOM, https://arxiv.org/abs/2507.16695
Minglei Yang, Yanfang Liu, Diego del-Castillo-Negrete, Yanzhao Cao, Guannan Zhang, 17 Jul 2025, Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains, https://arxiv.org/abs/2507.15990
Arseniy Andreyev and Pierfrancesco Beneventano, 22 Jul 2025, Edge of Stochastic Stability: Revisiting the Edge of Stability for SGD, https://arxiv.org/abs/2412.20553
Linxuan He, Qing-Shan Jia, Ang Li, Hongyan Sang, Ling Wang, Jiwen Lu, Tao Zhang, Jie Zhou, Yi Zhang, Yisen Wang, Peng Wei, Zhongyuan Wang, Henry X. Liu, and Shuo Feng, 22 Jul 2025, Towards provable probabilistic safety for scalable embodied AI systems, https://arxiv.org/abs/2506.05171
Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li, 22 Jul 2025, A computational transition for detecting correlated stochastic block models by low-degree polynomials, https://arxiv.org/abs/2409.00966
Kuangyu Ding and Kim-Chuan Toh, 22 Jul 2025, On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem, https://arxiv.org/abs/2507.15264
Wonjun Jeong, Dongseok Kim, Taegkeun Whangbo, 24 Jul 2025, SCOPE: Stochastic and Counterbiased Option Placement for Evaluating Large Language Models, https://arxiv.org/abs/2507.18182
Masaki Adachi, Masahiro Fujisawa, Michael A Osborne, 24 Jul 2025, Fixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature, https://arxiv.org/abs/2503.06079
Jon Vadillo, Roberto Santana, Jose A. Lozano, Marta Kwiatkowska, 18 Jul 2025, Uncertainty-Aware Explanations Through Probabilistic Self-Explainable Neural Networks, https://arxiv.org/abs/2403.13740
Thom Badings, Wietze Koops, Sebastian Junges, Nils Jansen, 18 Jul 2025, Policy Verification in Stochastic Dynamical Systems Using Logarithmic Neural Certificates, https://arxiv.org/abs/2406.00826
Dirk Tasche, 18 Jul 2025, Recalibrating binary probabilistic classifiers, https://arxiv.org/abs/2505.19068
Boris Bonev, Thorsten Kurth, Ankur Mahesh, Mauro Bisson, Jean Kossaifi, Karthik Kashinath, Anima Anandkumar, William D. Collins, Michael S. Pritchard, Alexander Keller, 18 Jul 2025, FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale, https://arxiv.org/abs/2507.12144
Lionel Wong, Katherine M. Collins, Lance Ying, Cedegao E. Zhang, Adrian Weller, Tobias Gerstenberg, Timothy O'Donnell, Alexander K. Lew, Jacob D. Andreas, Joshua B. Tenenbaum, Tyler Brooke-Wilson, 18 Jul 2025, Modeling Open-World Cognition as On-Demand Synthesis of Probabilistic Models, https://arxiv.org/abs/2507.12547
Mykhailo Buleshnyi, Anna Polova, Zsolt Zombori, Michael Benedikt, 20 Jul 2025, Constraint-aware Learning of Probabilistic Sequential Models for Multi-Label Classification, https://arxiv.org/abs/2507.15156
Owen Douglas and Aku Kammonen and Anamika Pandey and Ra\'ul Tempone, 21 Jul 2025, An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations, https://arxiv.org/abs/2507.15442
Chen Chen, Lijin Wang, Yanzhao Cao, Xupeng Cheng, 19 Jul 2025, Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network, https://arxiv.org/abs/2507.14467
Roberto Miele, Niklas Linde, 21 Jul 2025, Diffusion models for multivariate subsurface generation and efficient probabilistic inversion, https://arxiv.org/abs/2507.15809
Anthony M. Polloreno, 20 Jul 2025, Restrictions on Physical Stochastic Reservoir Computers, https://arxiv.org/abs/2307.14474
Kenny Falk{\ae}r Olsen, Mads {\O}stergaard, Karl Ulb{\ae}k, S{\o}ren F{\o}ns Nielsen, Rasmus Malik H{\o}egh Lindrup, Bj{\o}rn Sand Jensen, Morten M{\o}rup, 20 Jul 2025, Knowing When to Quit: Probabilistic Early Exits for Speech Separation, https://arxiv.org/abs/2507.09768
Jaikrishna Manojkumar Patil, Nathaniel Lee, Al Mehdi Saadat Chowdhury, YooJung Choi, Paulo Shakarian, 8 Aug 2025, Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets, https://arxiv.org/abs/2508.06706
Yuhao Liu, Rui Hu, Yu Chen, Longbo Huang, 10 Aug 2025, Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolants, https://arxiv.org/abs/2508.07333
Martin Rektoris, Milan Pape\v{z}, V\'aclav \v{S}m\'idl, Tom\'a\v{s} Pevn\'y, 11 Aug 2025, Sparse Probabilistic Graph Circuits, https://arxiv.org/abs/2508.07763
Christos Tsirigotis, Vaibhav Adlakha, Joao Monteiro, Aaron Courville, Perouz Taslakian, 9 Aug 2025, BiXSE: Improving Dense Retrieval via Probabilistic Graded Relevance Distillation, https://arxiv.org/abs/2508.06781
Toan Huynh, Ruth Lopez Fajardo, Guannan Zhang, Lili Ju, Feng Bao, 9 Aug 2025, A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions, https://arxiv.org/abs/2508.06834
Juan-Pablo Ortega and Florian Rossmannek, 11 Aug 2025, Stochastic dynamics learning with state-space systems, https://arxiv.org/abs/2508.07876
Bogdan Butyrin, Artemy Rubtsov, Alexey Naumov, Vladimir Ulyanov, Sergey Samsonov, 11 Aug 2025, Gaussian Approximation for Two-Timescale Linear Stochastic Approximation, https://arxiv.org/abs/2508.07928
Martin Rouault, R\'emi Bardenet, Myl\`ene Ma\"ida, 9 Aug 2025, Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herding, https://arxiv.org/abs/2402.11736
\'Isak P\'etursson and Mar\'ia \'Oskarsd\'ottir, 11 Aug 2025, Chaos into Order: Neural Framework for Expected Value Estimation of Stochastic Partial Differential Equations, https://arxiv.org/abs/2502.03670
Adrien Cort\'es, R\'emi Rehm, Victor Letzelter, 11 Aug 2025, Winner-takes-all for Multivariate Probabilistic Time Series Forecasting, https://arxiv.org/abs/2506.05515
Youkang Wang, Jian Wang, Rubing Chen, Xiao-Yong Wei, 10 Aug 2025, Probabilistic Optimality for Inference-time Scaling, https://arxiv.org/abs/2506.22376
Aliakbar Nafar, Kristen Brent Venable, Zijun Cui, Parisa Kordjamshidi, 10 Aug 2025, Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization, https://arxiv.org/abs/2505.15918
Liu junkang and Yuanyuan Liu and Fanhua Shang and Hongying Liu and Jin Liu and Wei Feng, 26 Jul 2025, FedSWA: Improving Generalization in Federated Learning with Highly Heterogeneous Data via Momentum-Based Stochastic Controlled Weight Averaging, https://arxiv.org/abs/2507.20016
Rezaur Rashid, Gabriel Terejanu, 27 Jul 2025, From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery, https://arxiv.org/abs/2507.20349
Aditya Ravuri, Neil D. Lawrence, 28 Jul 2025, Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements, https://arxiv.org/abs/2507.21040
Xintao Xia, Linjun Zhang, Zhanrui Cai, 28 Jul 2025, Statistical Inference for Differentially Private Stochastic Gradient Descent, https://arxiv.org/abs/2507.20560
Yuhao Liu, Yu Chen, Rui Hu and Longbo Huang, 28 Jul 2025, Finite-Time Analysis of Discrete-Time Stochastic Interpolants, https://arxiv.org/abs/2502.09130
Shenglong Zhou, Ouya Wang, Ziyan Luo, Yongxu Zhu, Geoffrey Ye Li, 26 Jul 2025, Preconditioned Inexact Stochastic ADMM for Deep Model, https://arxiv.org/abs/2502.10784
Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, Chenjuan Guo, 26 Jul 2025, $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting, https://arxiv.org/abs/2505.23017
Swagatam Das, 27 Jul 2025, A Free Probabilistic Framework for Analyzing the Transformer-based Language Models, https://arxiv.org/abs/2506.16550
Steven Braun, Sahil Sidheekh, Antonio Vergari, Martin Mundt, Sriraam Natarajan, Kristian Kersting, 26 Jul 2025, Tractable Representation Learning with Probabilistic Circuits, https://arxiv.org/abs/2507.04385
Radu Marinescu, Debarun Bhattacharjya, Junkyu Lee, Tigran Tchrakian, Javier Carnerero Cano, Yufang Hou, Elizabeth Daly, Alessandra Pascale, 26 Jul 2025, FactReasoner: A Probabilistic Approach to Long-Form Factuality Assessment for Large Language Models, https://arxiv.org/abs/2502.18573
Sara Pohland and Claire Tomlin, 26 Jul 2025, PaRCE: Probabilistic and Reconstruction-based Competency Estimation for CNN-based Image Classification, https://arxiv.org/abs/2411.16715
Chenyuan Zhang, Cristian Rojas Cardenas, Hamid Rezatofighi, Mor Vered, Buser Say, 29 Jul 2025, Probabilistic Active Goal Recognition, https://arxiv.org/abs/2507.21846
Raffaele Pojer, Andrea Passerini, Kim G. Larsen, Manfred Jaeger, 29 Jul 2025, A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data, https://arxiv.org/abs/2507.21873
Pedram Rajaei, Maryam Ostadsharif Memar, Navid Ziaei, Behzad Nazari, Ali Yousefi, 29 Jul 2025, Hierarchical Stochastic Differential Equation Models for Latent Manifold Learning in Neural Time Series, https://arxiv.org/abs/2507.21531
Paul Patrone and Anthony Kearsley, 29 Jul 2025, Probabilistic Consistency in Machine Learning and Its Connection to Uncertainty Quantification, https://arxiv.org/abs/2507.21670
Daniele Lanzoni and Olivier Pierre-Louis and Roberto Bergamaschini and Francesco Montalenti, 29 Jul 2025, Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks, https://arxiv.org/abs/2507.21763
Satoshi Kumabe, Tianyu Song, Ton Viet Ta, 29 Jul 2025, Stochastic forest transition model dynamics and parameter estimation via deep learning, https://arxiv.org/abs/2507.21486
Vasileios Manginas, Nikolaos Manginas, Edward Stevinson, Sherwin Varghese, Nikos Katzouris, Georgios Paliouras, Alessio Lomuscio, 29 Jul 2025, A Scalable Approach to Probabilistic Neuro-Symbolic Robustness Verification, https://arxiv.org/abs/2502.03274
Antonio Lorenzin, Fabio Zanasi, 28 Jul 2025, An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models, https://arxiv.org/abs/2503.11820
Yueyang Yao, Jiajun Li, Xingyuan Dai, MengMeng Zhang, Xiaoyan Gong, Fei-Yue Wang, Yisheng Lv, 29 Jul 2025, Context-Aware Probabilistic Modeling with LLM for Multimodal Time Series Forecasting, https://arxiv.org/abs/2505.10774
Tristan Aumentado-Armstrong, Stavros Tsogkas, Sven Dickinson, Allan Jepson, 29 Jul 2025, Probabilistic Directed Distance Fields for Ray-Based Shape Representations, https://arxiv.org/abs/2404.09081
Tom Liu, Anna Wu, Chao Li, 29 Jul 2025, Graph-Based Uncertainty-Aware Self-Training with Stochastic Node Labeling, https://arxiv.org/abs/2503.22745
Haoyu Wang and Chris M. Poskitt and Jun Sun and Jiali Wei, 1 Aug 2025, Pro2Guard: Proactive Runtime Enforcement of LLM Agent Safety via Probabilistic Model Checking, https://arxiv.org/abs/2508.00500
Leonidas Akritidis, Panayiotis Bozanis, 1 Aug 2025, A Conditional GAN for Tabular Data Generation with Probabilistic Sampling of Latent Subspaces, https://arxiv.org/abs/2508.00472
Liuyun Xu, Seymour M.J. Spence, 1 Aug 2025, Adaptive Machine Learning-Driven Multi-Fidelity Stratified Sampling for Failure Analysis of Nonlinear Stochastic Systems, https://arxiv.org/abs/2508.00734
Molly Noel, Gabriel Mancino-Ball, Yangyang Xu, 1 Aug 2025, Neighbor-Sampling Based Momentum Stochastic Methods for Training Graph Neural Networks, https://arxiv.org/abs/2508.00267
Matteo Bergamaschi, Andrea Cristofari, Vyacheslav Kungurtsev, and Francesco Rinaldi, 1 Aug 2025, Probabilistic Iterative Hard Thresholding for Sparse Learning, https://arxiv.org/abs/2409.01413
Etienne Buehrle and Christoph Stiller, 26 Jul 2025, Stochastic Optimal Control via Measure Relaxations, https://arxiv.org/abs/2508.00886
Siddharth Rout, Eldad Haber, Stephane Gaudreault, 1 Aug 2025, Flow Matching for Probabilistic Learning of Dynamical Systems from Missing or Noisy Data, https://arxiv.org/abs/2508.01101
Joshua Dimasaka, Christian Gei{\ss}, Emily So, 2 Aug 2025, GraphVSSM: Graph Variational State-Space Model for Probabilistic Spatiotemporal Inference of Dynamic Exposure and Vulnerability for Regional Disaster Resilience Assessment, https://arxiv.org/abs/2508.01310
Yeongjong Kim, Yeoneung Kim, Minseok Kim, Namkyeong Cho, 3 Aug 2025, Neural Policy Iteration for Stochastic Optimal Control: A Physics-Informed Approach, https://arxiv.org/abs/2508.01718
Zhuomin Chen, Jingchao Ni, Hojat Allah Salehi, Xu Zheng, Dongsheng Luo, 3 Aug 2025, From Binary to Continuous: Stochastic Re-Weighting for Robust Graph Explanation, https://arxiv.org/abs/2508.01925
Alexander Norcliffe, Changhee Lee, Fergus Imrie, Mihaela van der Schaar, Pietro Lio, 3 Aug 2025, Stochastic Encodings for Active Feature Acquisition, https://arxiv.org/abs/2508.01957
V\"ain\"o Yrj\"an\"ainen, Isac Bostr\"om, M{\aa}ns Magnusson and Johan Jonasson, 4 Aug 2025, Posterior Sampling of Probabilistic Word Embeddings, https://arxiv.org/abs/2508.02337
Yinbin Han, Meisam Razaviyayn, Renyuan Xu, 3 Aug 2025, Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence, https://arxiv.org/abs/2412.18164
Christian Wald and Gabriele Steidl, 2 Aug 2025, Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans, https://arxiv.org/abs/2501.16839
Helin Cao and Sven Behnke, 2 Aug 2025, DiffSSC: Semantic LiDAR Scan Completion using Denoising Diffusion Probabilistic Models, https://arxiv.org/abs/2409.18092
Tasnia Nobi Afee, Jack Hutchins, Md Mazharul Islam, Thomas Kampfe and Ahmedullah Aziz, 2 Aug 2025, Embedding-Enhanced Probabilistic Modeling of Ferroelectric Field Effect Transistors (FeFETs), https://arxiv.org/abs/2508.02737
Eliot Beyler (SIERRA), Francis Bach (SIERRA), 5 Aug 2025, Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance, https://arxiv.org/abs/2508.03210
Md Rakibul Hasan, Md Zakir Hossain, Aneesh Krishna, Shafin Rahman, Tom Gedeon, 5 Aug 2025, UPLME: Uncertainty-Aware Probabilistic Language Modelling for Robust Empathy Regression, https://arxiv.org/abs/2508.03520
Ling-Qi Zhang, Zahra Kadkhodaie, Eero P. Simoncelli, David H. Brainard, 4 Aug 2025, Generalized Compressed Sensing for Image Reconstruction with Diffusion Probabilistic Models, https://arxiv.org/abs/2405.17456
Chengcheng Yan, Jiawei Xu, Zheng Peng, Qingsong Wang, 6 Aug 2025, Neural Network Training via Stochastic Alternating Minimization with Trainable Step Sizes, https://arxiv.org/abs/2508.04193
Justin Lee, Behnaz Moradijamei, Heman Shakeri, 6 Aug 2025, Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points, https://arxiv.org/abs/2508.04351
Hugo Negrel, Florentin Coeurdoux, Michael S. Albergo, Eric Vanden-Eijnden, 6 Aug 2025, Multitask Learning with Stochastic Interpolants, https://arxiv.org/abs/2508.04605
Wei Liu, Anweshit Panda, Ujwal Pandey, Christopher Brissette, Yikang Shen, George M. Slota, Naigang Wang, Jie Chen, Yangyang Xu, 7 Aug 2025, Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization, https://arxiv.org/abs/2508.04950
Hikaru Umeda, Hideaki Iiduka, 7 Aug 2025, Adaptive Batch Size and Learning Rate Scheduler for Stochastic Gradient Descent Based on Minimization of Stochastic First-order Oracle Complexity, https://arxiv.org/abs/2508.05302
Hrithik Suresh, Sahil Sidheekh, Vishnu Shreeram M.P, Sriraam Natarajan, Narayanan C. Krishnan, 7 Aug 2025, Tractable Sharpness-Aware Learning of Probabilistic Circuits, https://arxiv.org/abs/2508.05537
Ashok Cutkosky, Harsh Mehta, Francesco Orabona, 7 Aug 2025, Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion, https://arxiv.org/abs/2302.03775
Helen Jin, Anton Xue, Weiqiu You, Surbhi Goel, Eric Wong, 7 Aug 2025, Probabilistic Stability Guarantees for Feature Attributions, https://arxiv.org/abs/2504.13787
Prateek Chanda, Saral Sureka, Parth Pratim Chatterjee, Krishnateja Killamsetty, Nikhil Shivakumar Nayak, Ganesh Ramakrishnan, 7 Aug 2025, Learning What Matters: Probabilistic Task Selection via Mutual Information for Model Finetuning, https://arxiv.org/abs/2507.12612
Marina Sheshukova, Denis Belomestny, Alain Durmus, Eric Moulines, Alexey Naumov, Sergey Samsonov, 7 Aug 2025, Nonasymptotic Analysis of Stochastic Gradient Descent with the Richardson-Romberg Extrapolation, https://arxiv.org/abs/2410.05106
Haley Stone, Jing Du, Hao Xue, Matthew Scotch, David Heslop, Andreas Z\"ufle, Chandini Raina MacIntyre, Flora Salim, 7 Aug 2025, A Probabilistic Framework for Imputing Genetic Distances in Spatiotemporal Pathogen Models, https://arxiv.org/abs/2506.09076
Alex Glushkovsky, 8 Aug 2025, Dual Signal Decomposition of Stochastic Time Series, https://arxiv.org/abs/2508.05915
Zichun Ye, Runqi Wang, Xutong Liu, Shuai Li, 8 Aug 2025, Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits, https://arxiv.org/abs/2508.06247
Arvind K. Saibaba and Ilse C.F. Ipsen, 7 Aug 2025, Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory, https://arxiv.org/abs/2508.05764
Fran\c{c}ois Bachoc and Nicol\`o Cesa-Bianchi and Tommaso Cesari and Roberto Colomboni, 7 Aug 2025, Stochastic Bandits for Crowdsourcing and Multi-Platform Autobidding, https://arxiv.org/abs/2508.05844
Paulo Shakarian, Gerardo I. Simari, Nathaniel D. Bastian, 8 Aug 2025, Probabilistic Foundations for Metacognition via Hybrid-AI, https://arxiv.org/abs/2502.05398
Kevin Pekepok, Persephone Kirkwood, Esme Christopolous, Florence Braithwaite, and Oliver Nightingale, 8 Aug 2025, Hierarchical Pattern Decryption Methodology for Ransomware Detection Using Probabilistic Cryptographic Footprints, https://arxiv.org/abs/2501.15084
Joshua R. Tempelman, Kevin Mitchell, Adam J. Wachtor, Eric B. Flynn, 5 Aug 2025, Probabilistic Emissivity Retrieval from Hyperspectral Data via Physics-Guided Variational Inference, https://arxiv.org/abs/2508.08291
Jiani Ni, He Zhao, Yibo Yang, Dandan Guo, 12 Aug 2025, Deep Neural Network Calibration by Reducing Classifier Shift with Stochastic Masking, https://arxiv.org/abs/2508.09116
Shady Agwa, Yihan Pan, Georgios Papandroulidakis and Themis Prodromakis, 12 Aug 2025, OISMA: On-the-fly In-memory Stochastic Multiplication Architecture for Matrix-Multiplication Workloads, https://arxiv.org/abs/2508.08822
Jialiang Shi, Yaguang Dou, Tian Qi, 12 Aug 2025, SPARC: Soft Probabilistic Adaptive multi-interest Retrieval Model via Codebooks for recommender system, https://arxiv.org/abs/2508.09090
Johannes Aspman, Vyacheslav Kungurtsev, Reza Roohi Seraji, 12 Aug 2025, Tame Riemannian Stochastic Approximation, https://arxiv.org/abs/2302.00709
Liwei Jiang, Abhishek Roy, Krishna Balasubramanian, Damek Davis, Dmitriy Drusvyatskiy, Sen Na, 12 Aug 2025, Online Covariance Estimation in Nonsmooth Stochastic Approximation, https://arxiv.org/abs/2502.05305
Ziheng Wang, Pedro Reviriego, Farzad Niknia, Zhen Gao, Javier Conde, Shanshan Liu, Fabrizio Lombardi, 5 Aug 2025, Energy-Efficient Stochastic Computing (SC) Neural Networks for Internet of Things Devices With Layer-Wise Adjustable Sequence Length (ASL), https://arxiv.org/abs/2508.09163
Yao Li, Yicheng Liu, Shirou Wang, 13 Aug 2025, DeepWKB: Learning WKB Expansions of Invariant Distributions for Stochastic Systems, https://arxiv.org/abs/2508.09529
Akshay Thakur and Sawan Kumar and Matthew Zahr and Souvik Chakraborty, 13 Aug 2025, Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems, https://arxiv.org/abs/2508.09623
Arpit Agarwal and Rohan Ghuge and Viswanath Nagarajan and Zhengjia Zhuo, 13 Aug 2025, Semi-Bandit Learning for Monotone Stochastic Optimization, https://arxiv.org/abs/2312.15427
Taihei Oki, Shinsaku Sakaue, 13 Aug 2025, No-Regret M${}^{\natural}$-Concave Function Maximization: Stochastic Bandit Algorithms and Hardness of Adversarial Full-Information Setting, https://arxiv.org/abs/2405.12439
Magdalena Tr\k{e}dowicz, Marcin Mazur, Szymon Janusz, Arkadiusz Lewicki, Jacek Tabor, {\L}ukasz Struski, 13 Aug 2025, PrAViC: Probabilistic Adaptation Framework for Real-Time Video Classification, https://arxiv.org/abs/2406.11443
Arnab Ganguly, Riten Mitra, Jinpu Zhou, 15 Aug 2025, Nonparametric learning of stochastic differential equations from sparse and noisy data, https://arxiv.org/abs/2508.11597
Jinwen Xu, Qin Lu, Yaakov Bar-Shalom, 14 Aug 2025, Adaptive Bayesian Optimization for Robust Identification of Stochastic Dynamical Systems, https://arxiv.org/abs/2503.06381
Michael Bereket and Jure Leskovec, 15 Aug 2025, Uncalibrated Reasoning: GRPO Induces Overconfidence for Stochastic Outcomes, https://arxiv.org/abs/2508.11800
Denis Blessing and Julius Berner and Lorenz Richter and Carles Domingo-Enrich and Yuanqi Du and Arash Vahdat and Gerhard Neumann, 17 Aug 2025, Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference, https://arxiv.org/abs/2508.12511
Marcos Abel Zuzu\'arregui, Stefano Carpin, 17 Aug 2025, Solving Stochastic Orienteering Problems with Chance Constraints Using a GNN Powered Monte Carlo Tree Search, https://arxiv.org/abs/2409.04653
Emma Hannula, Arttu H\"akkinen, Antti Solonen, Felipe Uribe, Jana de Wiljes, Lassi Roininen, 18 Aug 2025, Partially stochastic deep learning with uncertainty quantification for model predictive heating control, https://arxiv.org/abs/2504.03350
Wenhao Mu, Zhi Cao, Mehmed Uludag, Alexander Rodr\'iguez, 18 Aug 2025, Counterfactual Probabilistic Diffusion with Expert Models, https://arxiv.org/abs/2508.13355
Zhuang Yang, 19 Aug 2025, Explainable Learning Rate Regimes for Stochastic Optimization, https://arxiv.org/abs/2508.13639
Soumyajit Guin and Shalabh Bhatnagar, 19 Aug 2025, Convergent Reinforcement Learning Algorithms for Stochastic Shortest Path Problem, https://arxiv.org/abs/2508.13963
Yiyang Jia, Zheng Wei, Zheng Yang, Guohong Peng, 16 Aug 2025, Modeling GRNs with a Probabilistic Categorical Framework, https://arxiv.org/abs/2508.13208
Vladimir Berman, 18 Aug 2025, Structural Foundations for Leading Digit Laws: Beyond Probabilistic Mixtures, https://arxiv.org/abs/2508.13237
Federico Nicolas Peccia, Frederik Haxel, Oliver Bringmann, 19 Aug 2025, Tensor Program Optimization for the RISC-V Vector Extension Using Probabilistic Programs, https://arxiv.org/abs/2507.01457
Shigang Li, Tal Ben-Nun, Giorgi Nadiradze, Salvatore Di Girolamo, Nikoli Dryden, Dan Alistarh, Torsten Hoefler, 19 Aug 2025, Breaking (Global) Barriers in Parallel Stochastic Optimization with Wait-Avoiding Group Averaging, https://arxiv.org/abs/2005.00124
Marina Sheshukova, Sergey Samsonov, Denis Belomestny, Eric Moulines, Qi-Man Shao, Zhuo-Song Zhang, Alexey Naumov, 19 Aug 2025, Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent, https://arxiv.org/abs/2502.06719
Swantje Plambeck, Ali Salamati, Eyke Huellermeier, Goerschwin Fey, 20 Aug 2025, Data-Driven Probabilistic Evaluation of Logic Properties with PAC-Confidence on Mealy Machines, https://arxiv.org/abs/2508.14710
Junwei Su, Chuan Wu, 20 Aug 2025, A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations, https://arxiv.org/abs/2508.14351
Junwei Su, Shan Wu, 20 Aug 2025, SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion, https://arxiv.org/abs/2508.14352
Sridhar Mahadevan, 20 Aug 2025, Universal Reinforcement Learning in Coalgebras: Asynchronous Stochastic Computation via Conduction, https://arxiv.org/abs/2508.15128
Mohammed Elmusrati, 21 Aug 2025, Tutorial on the Probabilistic Unification of Estimation Theory, Machine Learning, and Generative AI, https://arxiv.org/abs/2508.15719
Youjia Zhang, Youngeun Kim, Young-Geun Choi, Hongyeob Kim, Huiling Liu, Sungeun Hong, 21 Aug 2025, Backpropagation-Free Test-Time Adaptation via Probabilistic Gaussian Alignment, https://arxiv.org/abs/2508.15568
Kanata Oowada and Hideaki Iiduka, 21 Aug 2025, Faster Convergence of Riemannian Stochastic Gradient Descent with Increasing Batch Size, https://arxiv.org/abs/2501.18164
Grzegorz Dudek, Witold Orzeszko, Piotr Fiszeder, 21 Aug 2025, Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts, https://arxiv.org/abs/2508.15922
Boris N. Oreshkin and Shiv Tavker and Dmitry Efimov, 22 Aug 2025, Probabilistic Pretraining for Neural Regression, https://arxiv.org/abs/2508.16355
Anahita Asadi, Leonid Popryho, Inna Partin-Vaisband, 22 Aug 2025, Fast and Accurate RFIC Performance Prediction via Pin Level Graph Neural Networks and Probabilistic Flow, https://arxiv.org/abs/2508.16403
Madhava Gaikwad, Abhishek Gandhi, 22 Aug 2025, ANSC: Probabilistic Capacity Health Scoring for Datacenter-Scale Reliability, https://arxiv.org/abs/2508.16119
Amirreza Talebi, 24 Aug 2025, Large Language Model-Based Automatic Formulation for Stochastic Optimization Models, https://arxiv.org/abs/2508.17200
Johannes Schmalz, Felipe Trevizan, 24 Aug 2025, Solving Constrained Stochastic Shortest Path Problems with Scalarisation, https://arxiv.org/abs/2508.17446
Tianhua Chen, 18 Aug 2025, From Classical Probabilistic Latent Variable Models to Modern Generative AI: A Unified Perspective, https://arxiv.org/abs/2508.16643
Baozhuo Su, Zhengxian Qu, 22 Aug 2025, Anchor-MoE: A Mean-Anchored Mixture of Experts For Probabilistic Regression, https://arxiv.org/abs/2508.16802
Kiran Madhusudhanan, Vijaya Krishna Yalavarthi, Jonas Sonntag, Maximilian Stubbemann, Lars Schmidt-Thieme, 23 Aug 2025, TabResFlow: A Normalizing Spline Flow Model for Probabilistic Univariate Tabular Regression, https://arxiv.org/abs/2508.17056
Nanfei Jiang, Hoi-To Wai, Mahnoosh Alizadeh, 23 Aug 2025, Stochastic Gradient Descent with Strategic Querying, https://arxiv.org/abs/2508.17144
Xing Wei, Yuqi Ouyang, 24 Aug 2025, GPG-HT: Generalized Policy Gradient with History-Aware Decision Transformer for Probabilistic Path Planning, https://arxiv.org/abs/2508.17218
YongKyung Oh, Seungsu Kam, Dong-Young Lim, Sungil Kim, 24 Aug 2025, Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equations, https://arxiv.org/abs/2508.17521
Novin Shahroudi, Viacheslav Komisarenko, Meelis Kull, 25 Aug 2025, Aligning the Evaluation of Probabilistic Predictions with Downstream Value, https://arxiv.org/abs/2508.18251
Yue-Jane Liu, Malinda Lu, Matthew K. Nock, Yaniv Yacoby, 23 Aug 2025, Neural Stochastic Differential Equations on Compact State-Spaces, https://arxiv.org/abs/2508.17090
Md Rejwanur Rahman, Adrian Rodriguez-Marek, Nina Stark, Grace Massey, Carl Friedrichs, Kelly M. Dorgan, 25 Aug 2025, Probabilistic Classification of Near-Surface Shallow-Water Sediments using A Portable Free-Fall Penetrometer, https://arxiv.org/abs/2410.00225
Ding Huang, Jian Huang, Ting Li, and Guohao Shen, 25 Aug 2025, Conditional Stochastic Interpolation for Generative Learning, https://arxiv.org/abs/2312.05579
Michela Lapenna, Caterina De Bacco, 22 Aug 2025, How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?, https://arxiv.org/abs/2506.11869