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Advancing Deep Learning through Probability Engineering: A Pragmatic Paradigm for Modern AI

Jianyi Zhang

TL;DR

This work reframes probabilistic modeling as an engineering practice for modern AI, arguing that probability distributions should be actively designed and manipulated to meet real-world constraints. It introduces Probability Engineering across four domains: Bayesian deep learning (via SPOS and related samplers), edge AI (Fed-CBS and ReAugKD for FL and KD), and generative AI (SLED for LLM factuality and ARTIST for text-rich diffusion). The key contributions include SPOS with non-asymptotic guarantees, Fed-CBS with privacy-preserving QCID-based client selection, ReAugKD with retrieval-augmented distillation, SLED for decoding-time factuality, and ARTIST for disentangled text-visual generation. Collectively, these methods demonstrate robust, efficient, and trustworthy AI capabilities, illustrating how probabilistic reasoning can be integrated into learning, inference, and generation pipelines to tackle non-IID data, evolving knowledge, and multimodal challenges.

Abstract

Recent years have witnessed the rapid progression of deep learning, pushing us closer to the realization of AGI (Artificial General Intelligence). Probabilistic modeling is critical to many of these advancements, which provides a foundational framework for capturing data distributions. However, as the scale and complexity of AI applications grow, traditional probabilistic modeling faces escalating challenges, such as high-dimensional parameter spaces, heterogeneous data sources, and evolving real-world requirements often render classical approaches insufficiently flexible. This paper proposes a novel concept, Probability Engineering, which treats the already-learned probability distributions within deep learning as engineering artifacts. Rather than merely fitting or inferring distributions, we actively modify and reinforce them to better address the diverse and evolving demands of modern AI. Specifically, Probability Engineering introduces novel techniques and constraints to refine existing probability distributions, improving their robustness, efficiency, adaptability, or trustworthiness. We showcase this paradigm through a series of applications spanning Bayesian deep learning, Edge AI (including federated learning and knowledge distillation), and Generative AI (such as text-to-image generation with diffusion models and high-quality text generation with large language models). These case studies demonstrate how probability distributions once treated as static objects can be engineered to meet the diverse and evolving requirements of large-scale, data-intensive, and trustworthy AI systems. By systematically expanding and strengthening the role of probabilistic modeling, Probability Engineering paves the way for more robust, adaptive, efficient, and trustworthy deep learning solutions in today's fast-growing AI era.

Advancing Deep Learning through Probability Engineering: A Pragmatic Paradigm for Modern AI

TL;DR

This work reframes probabilistic modeling as an engineering practice for modern AI, arguing that probability distributions should be actively designed and manipulated to meet real-world constraints. It introduces Probability Engineering across four domains: Bayesian deep learning (via SPOS and related samplers), edge AI (Fed-CBS and ReAugKD for FL and KD), and generative AI (SLED for LLM factuality and ARTIST for text-rich diffusion). The key contributions include SPOS with non-asymptotic guarantees, Fed-CBS with privacy-preserving QCID-based client selection, ReAugKD with retrieval-augmented distillation, SLED for decoding-time factuality, and ARTIST for disentangled text-visual generation. Collectively, these methods demonstrate robust, efficient, and trustworthy AI capabilities, illustrating how probabilistic reasoning can be integrated into learning, inference, and generation pipelines to tackle non-IID data, evolving knowledge, and multimodal challenges.

Abstract

Recent years have witnessed the rapid progression of deep learning, pushing us closer to the realization of AGI (Artificial General Intelligence). Probabilistic modeling is critical to many of these advancements, which provides a foundational framework for capturing data distributions. However, as the scale and complexity of AI applications grow, traditional probabilistic modeling faces escalating challenges, such as high-dimensional parameter spaces, heterogeneous data sources, and evolving real-world requirements often render classical approaches insufficiently flexible. This paper proposes a novel concept, Probability Engineering, which treats the already-learned probability distributions within deep learning as engineering artifacts. Rather than merely fitting or inferring distributions, we actively modify and reinforce them to better address the diverse and evolving demands of modern AI. Specifically, Probability Engineering introduces novel techniques and constraints to refine existing probability distributions, improving their robustness, efficiency, adaptability, or trustworthiness. We showcase this paradigm through a series of applications spanning Bayesian deep learning, Edge AI (including federated learning and knowledge distillation), and Generative AI (such as text-to-image generation with diffusion models and high-quality text generation with large language models). These case studies demonstrate how probability distributions once treated as static objects can be engineered to meet the diverse and evolving requirements of large-scale, data-intensive, and trustworthy AI systems. By systematically expanding and strengthening the role of probabilistic modeling, Probability Engineering paves the way for more robust, adaptive, efficient, and trustworthy deep learning solutions in today's fast-growing AI era.

Paper Structure

This paper contains 84 sections, 3 theorems, 29 equations, 22 figures, 12 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Probability Engineering in Bayesian Deep Learning
  3. Background
  4. Stochastic Gradient MCMC
  5. Stein Variational Gradient Descent
  6. Stochastic Particle-Optimization Sampling (SPOS)
  7. Experimental Results
  8. Summary
  9. Probability Engineering in Edge AI
  10. Federated Learning
  11. Background
  12. Federated Class-balanced Sampling (Fed-CBS)
  13. Summary
  14. Knowledge Distillation
  15. Related Work
  16. ...and 69 more sections

Key Result

Theorem 2

Under Assumption assnew:ass1 and setting $h_k=h_0$, $B_k=B_0$, if we denote the distribution of ${\theta}_{T}^{(i)}$ as $\mu_T$ and our target distribution as $\nu_{\infty}$, ${W}_1(\mu_T, \nu_{\infty})$ is bounded as: where $(c_1, c_2, c_3, c_4, c_5, c_6, \beta)$ are positive constants such that $\frac{1}{\beta} > c_2$ and $\frac{m_F}{\beta} >L_F+2L_K$.

Figures (22)

  • Figure 1: Comparison of SPOS (left) and SVGD (right) on a multi-mode distribution.
  • Figure 2: Policy learning with Bayesian exploration in policy-gradient methods with SVPG and SPOS-PG.
  • Figure 3: An example demonstrating the weakness of greedy method to deal with class imbalance.
  • Figure 4: Three different FL client selection strategies on MNIST. Each client has only one class of data in (a) and (c) and each client has two classes of data in (b) and (d).
  • Figure 5: Test accuracy on Cifar-10 under three heterogeneous settings.
  • ...and 17 more figures

Theorems & Definitions (3)

  • Theorem 2
  • Proposition 3
  • Proposition 4