Big Cooperative Learning

TL;DR

This work reframes foundation-model training as big cooperative learning, a unified framework in which a universal model learns to match diverse data-sampling demonstrations (joint, marginal, and conditional) across multiple transformed domains to recover the data essence encoded in $\boldsymbol{\theta}^*$. By formalizing the cooperative matching across a set of $(\mathbb{S},\mathbb{T})$ pairs and leveraging both maximum-likelihood and adversarial viewpoints, the approach explains why foundation models succeed and suggests a path to richer data-sampling capabilities. The authors validate the principle with tailored 2-D simulations and a BigLearn-GAN that demonstrates versatile cross-domain generation and completion on MNIST and CelebA, plus preliminary multi-modal capabilities and fine-tuning benefits on NLP benchmarks. Overall, big cooperative learning offers a new dimension for upgrading conventional ML paradigms, enabling a single universal model to support diverse, robust data-sampling tasks across modalities and test scenarios, with practical implications for improved generative and discriminative capabilities.

Abstract

Cooperation plays a pivotal role in the evolution of human intelligence; moreover, it also underlies the recent revolutionary advancement of artificial intelligence (AI) that is driven by foundation models. Specifically, we reveal that the training of foundation models can be interpreted as a form of big cooperative learning (\textit{abbr.} big learning), where massive learning individuals/tasks \emph{cooperate} to approach the unique essence of data from diverse perspectives of data prediction, leveraging a universal model. The presented big learning therefore unifies most training objectives of foundation models within a consistent framework, where their underlying assumptions are exposed simultaneously. We design tailored simulations to demonstrate the principle of big learning, based on which we provide learning-perspective justifications for the successes of foundation models, with interesting side-products. Furthermore, we reveal that big learning is a new dimension for upgrading conventional machine learning paradigms, valuable for endowing reinvigorations to associated applications; as an illustrative example, we propose the BigLearn-GAN, which is a novel adversarially-trained foundation model with versatile data sampling capabilities. Code is available at \texttt{https://github.com/YulaiCong/BigCooperativeLearning}.

Figures (18)

• Figure 1: A single data sample demonstrates versatile data-sampling capabilities in the original domain (a) and diverse transformed domains (b). (a) Given a complete/incomplete data sample, one simultaneously receives a demonstration for each $\boldsymbol{x} _{\mathbb{T} } \sim q(\boldsymbol{x} _{\mathbb{T} }|\boldsymbol{x} _{\mathbb{S} }), \forall (\mathbb{S} ,\mathbb{T} )$. (b) Similarly, various data-sampling demonstrations across plentiful transformed domains (e.g., via a data-level transformation $g(\cdot)$ or a patch-level $h(\cdot)$) are also ready for exploitation.
• Figure 2: Demonstrations of the data distribution and the reverse-KL loss surfaces for for joint, marginal, and conditional matchings in the tailored $2$-D simulations. The first row illustrates the joint distribution $q(\boldsymbol{x} )$ and the marginal/conditional space of interest. The second row shows the corresponding marginal/conditional data distribution. The last row exhibits the surface of $\mathrm{KL} [p_{\boldsymbol{\theta} }(\boldsymbol{x} )||q(\boldsymbol{x} )]$, $\mathrm{KL} [p_{\boldsymbol{\theta} }(x_i)||q(x_i)], i\in\{1,2\}$, and $\mathrm{KL} [p_{\boldsymbol{\theta} }(x_i|x_j)||q(x_i|x_j)], j\neq i$, respectively. The two global optima are marked with red stars. $\sigma^2=0.1$.
• Figure 3: Demonstrations of marginal and conditional matchings in diverse rotationally transformed domains. The joint matching remains the same as in Fig. \ref{['fig:naive_JMC_not_work']} after a rotation transformation. $\sigma^2=0.1$. The local optima unstably vary with different matchings but the global optima are stably the same, laying the foundation for the cooperation among diverse matchings as in Eq. \ref{['eq:big_learning']}.
• Figure 4: Illustrating the exploration power of big learning on the $25$-GMM reverse-KL-minimization simulation. (a) The challenging initialization. (b) Joint matching gets stuck in local optima. (c) Big learning gradually seeks out most components; results of $200$, $800$, $1400$, $6000$ iterations are shown.
• Figure 5: Versatile realistic data-sampling capabilities of the big-learned BigLearn-GAN. (a-b) Data completion with random/initial-portion $\mathbb{S}$, where $\mathbb{S}$s are shown in the first row (light-blue boxed), real images $\boldsymbol{x}$s are given in the rightmost column, generated images with $p_{\boldsymbol{\theta} }(\boldsymbol{x} _{\mathbb{T} }|\boldsymbol{x} _{\mathbb{S} })$ are shown in the rest rows and columns. (c-d) Versatile completion w.r.t. various $\mathbb{S}$s (left) and w.r.t. various noise $\boldsymbol{z}$s but the same $\boldsymbol{x} _{\mathbb{S} }$ (right). The light-blue boxes show $\mathbb{S} /\boldsymbol{z}$s, while the red ones show $\boldsymbol{x}$ (left) or $\boldsymbol{x} _{\mathbb{S} }$ (right).

Theorems & Definitions (6)

• Definition 1: Big cooperative learning
• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5