In this work, we provide a comparative analysis of the learning dynamics for the Euclidean and cosine-based asymmetric losses in the eigenspace of the closed-form predictor DirectPred.

Each mini-batch consists of half 2D and half 3D samples. S7, S8) are used for training and two subjects (S9, S11) for evaluation. The output of the last layer is a per-point probability map for each keypoint. Furthermore, our method is an improvement of existing capabilities but does not introduce a radically new capability in machine learning. Theoretically, the underlying density function cannot be perfectly reconstructed since the proposed basis distributions are fixed.

Training diffusion models requires large datasets. However, acquiring large volumes of high-quality data can be challenging, for example, collecting large numbers of high-resolution images and long videos. On the other hand, there are many complementary data that are usually considered corrupted or partial, such as low-resolution images and short videos. Other examples of corrupted data include videos that contain subtitles, watermarks, and logos. In this study, we investigate the theoretical problem of whether the above partial data can be utilized to train conventional diffusion models. Motivated by our theoretical analysis in this study, we propose a straightforward approach of training diffusion models utilizing partial data views, where we consider each form of complementary data as a view of conventional data. Our proposed approach first trains one separate diffusion model for each individual view, and then trains a model for predicting the residual score function. We prove generalization error bounds, which show that the proposed diffusion model training approach can achieve lower generalization errors if proper regularizations are adopted in the residual score function training. In particular, we prove that the difficulty in training the residual score function scales proportionally with the signal correlations not captured by partial data views. Consequently, the proposed approach achieves near first-order optimal data efficiency.

Non-contrastive SSL methods like BYOL and SimSiam rely on asymmetric predictor networks to avoid representational collapse without negative samples. Yet, how predictor networks facilitate stable learning is not fully understood. While previous theoretical analyses assumed Euclidean losses, most practical implementations rely on cosine similarity. To gain further theoretical insight into non-contrastive SSL, we analytically study learning dynamics in conjunction with Euclidean and cosine similarity in the eigenspace of closed-form linear predictor networks. We show that both avoid collapse through implicit variance regularization albeit through different dynamical mechanisms.

This paper studies stable learning methods for generative models that enable high-quality data generation. Noise injection is commonly used to stabilize learning. However, selecting a suitable noise distribution is challenging. Diffusion-GAN, a recently developed method, addresses this by using the diffusion process with a timestep-dependent discriminator. We investigate Diffusion-GAN and reveal that data scaling is a key component for stable learning and high-quality data generation. Building on our findings, we propose a learning algorithm, Scale-GAN, that uses data scaling and variance-based regularization. Furthermore, we theoretically prove that data scaling controls the bias-variance trade-off of the estimation error bound. As a theoretical extension, we consider GAN with invertible data augmentations. Comparative evaluations on benchmark datasets demonstrate the effectiveness of our method in improving stability and accuracy.

Non-contrastive self-supervised learning (SSL) methods like BYOL and SimSiam rely on asymmetric predictor networks to avoid representational collapse without negative samples. Yet, how predictor networks facilitate stable learning is not fully understood. While previous theoretical analyses assumed Euclidean losses, most practical implementations rely on cosine similarity. To gain further theoretical insight into non-contrastive SSL, we analytically study learning dynamics in conjunction with Euclidean and cosine similarity in the eigenspace of closed-form linear predictor networks. We show that both avoid collapse through implicit variance regularization albeit through different dynamical mechanisms. Moreover, we find that the eigenvalues act as effective learning rate multipliers and propose a family of isotropic loss functions (IsoLoss) that equalize convergence rates across eigenmodes. Empirically, IsoLoss speeds up the initial learning dynamics and increases robustness, thereby allowing us to dispense with the exponential moving average (EMA) target network typically used with non-contrastive methods. Our analysis sheds light on the variance regularization mechanisms of non-contrastive SSL and lays the theoretical grounds for crafting novel loss functions that shape the learning dynamics of the predictor's spectrum.

Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations, thus introducing fundamental finite-sampling noise even on error-free quantum computers. We reduce this noise by introducing the variance regularization, a technique for reducing the variance of the expectation value during the quantum model training. This technique requires no additional circuit evaluations if the QNN is properly constructed. Our empirical findings demonstrate the reduced variance speeds up the training and lowers the output noise as well as decreases the number of necessary evaluations of gradient circuits. This regularization method is benchmarked on the regression of multiple functions. We show that in our examples, it lowers the variance by an order of magnitude on average and leads to a significantly reduced noise level of the QNN. We finally demonstrate QNN training on a real quantum device and evaluate the impact of error mitigation. Here, the optimization is feasible only due to the reduced number of necessary shots in the gradient evaluation resulting from the reduced variance.

Multi-task learning (MTL) has achieved great success in various research domains, such as CV, NLP and IR etc. Due to the complex and competing task correlation, naive training all tasks may lead to inequitable learning, i.e. some tasks are learned well while others are overlooked. Multi-task optimization (MTO) aims to improve all tasks at same time, but conventional methods often perform poor when tasks with large loss scale or gradient norm magnitude difference. To solve the issue, we in-depth investigate the equity problem for MTL and find that regularizing relative contribution of different tasks (i.e. value of task-specific loss divides its raw gradient norm) in updating shared parameter can improve generalization performance of MTL. Based on our theoretical analysis, we propose a novel multi-task optimization method, named EMTL, to achieve equitable MTL. Specifically, we efficiently add variance regularization to make different tasks' relative contribution closer. Extensive experiments have been conduct to evaluate EMTL, our method stably outperforms state-of-the-art methods on the public benchmark datasets of two different research domains. Furthermore, offline and online A/B test on multi-task recommendation are conducted too. EMTL improves multi-task recommendation significantly, demonstrating the superiority and practicability of our method in industrial landscape.