Deep hierarchical variational autoencoders (VAEs) are powerful latent variable generative models. In this paper, we introduce Hierarchical VAE with Diffusion-based Variational Mixture of the Posterior Prior (VampPrior). We apply amortization to scale the VampPrior to models with many stochastic layers. The proposed approach allows us to achieve better performance compared to the original VampPrior work and other deep hierarchical VAEs, while using fewer parameters. We empirically validate our method on standard benchmark datasets (MNIST, OMNIGLOT, CIFAR10) and demonstrate improved training stability and latent space utilization.

This paper proposes an online environment poisoning algorithm tailored for reinforcement learning agents operating in a black-box setting, where an adversary deliberately manipulates training data to lead the agent toward a mischievous policy. In contrast to prior studies that primarily investigate white-box settings, we focus on a scenario characterized by \textit{unknown} environment dynamics to the attacker and a \textit{flexible} reinforcement learning algorithm employed by the targeted agent. We first propose an attack scheme that is capable of poisoning the reward functions and state transitions. The poisoning task is formalized as a constrained optimization problem, following the framework of \cite{ma2019policy}. Given the transition probabilities are unknown to the attacker in a black-box environment, we apply a stochastic gradient descent algorithm, where the exact gradients are approximated using sample-based estimates. A penalty-based method along with a bilevel reformulation is then employed to transform the problem into an unconstrained counterpart and to circumvent the double-sampling issue. The algorithm's effectiveness is validated through a maze environment.

As opaque black-box predictive models become more prevalent, the need to develop interpretations for these models is of great interest. The concept of variable importance and Shapley values are interpretability measures that applies to any predictive model and assesses how much a variable or set of variables improves prediction performance. When the number of variables is large, estimating variable importance presents a significant computational challenge because re-training neural networks or other black-box algorithms requires significant additional computation. In this paper, we address this challenge for algorithms using gradient descent and gradient boosting (e.g. neural networks, gradient-boosted decision trees). By using the ideas of early stopping of gradient-based methods in combination with warm-start using the dropout method, we develop a scalable method to estimate variable importance for any algorithm that can be expressed as an iterative kernel update equation. Importantly, we provide theoretical guarantees by using the theory for early stopping of kernel-based methods for neural networks with sufficiently large (but not necessarily infinite) width and gradient-boosting decision trees that use symmetric trees as a weaker learner. We also demonstrate the efficacy of our methods through simulations and a real data example which illustrates the computational benefit of early stopping rather than fully re-training the model as well as the increased accuracy of our approach.

Low-rank adapters have become a standard approach for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a trainable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90x fewer parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

Clustering is a long-standing problem area in data mining. The centroid-based classical approaches to clustering mainly face difficulty in the case of high dimensional inputs such as images. With the advent of deep neural networks, a common approach to this problem is to map the data to some latent space of comparatively lower dimensions and then do the clustering in that space. Network architectures adopted for this are generally autoencoders that reconstruct a given input in the output. To keep the input in some compact form, the encoder in AE's learns to extract useful features that get decoded at the reconstruction end. A well-known centroid-based clustering algorithm is K-means. In the context of deep feature learning, recent works have empirically shown the importance of learning the representations and the cluster centroids together. However, in this aspect of joint learning, recently a continuous variant of K-means has been proposed; where the softmax function is used in place of argmax to learn the clustering and network parameters jointly using stochastic gradient descent (SGD). However, unlike K-means, where the input space stays constant, here the learning of the centroid is done in parallel to the learning of the latent space for every batch of data. Such batch updates disagree with the concept of classical K-means, where the clustering space remains constant as it is the input space itself. To this end, we propose to alternatively learn a clustering-friendly data representation and K-means based cluster centers. Experiments on some benchmark datasets have shown improvements of our approach over the previous approaches.

Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance generalization performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

Binary Neural Networks (BNNs) hold the potential for significantly reducing computational complexity and memory demand in machine and deep learning. However, most successful training algorithms for BNNs rely on quantization-aware floating-point Stochastic Gradient Descent (SGD), with full-precision hidden weights used during training. The binarized weights are only used at inference time, hindering the full exploitation of binary operations during the training process. In contrast to the existing literature, we introduce, for the first time, a multi-layer training algorithm for BNNs that does not require the computation of back-propagated full-precision gradients. Specifically, the proposed algorithm is based on local binary error signals and binary weight updates, employing integer-valued hidden weights that serve as a synaptic metaplasticity mechanism, thereby establishing it as a neurobiologically plausible algorithm. The binary-native and gradient-free algorithm proposed in this paper is capable of training binary multi-layer perceptrons (BMLPs) with binary inputs, weights, and activations, by using exclusively XNOR, Popcount, and increment/decrement operations, hence effectively paving the way for a new class of operation-optimized training algorithms. Experimental results on BMLPs fully trained in a binary-native and gradient-free manner on multi-class image classification benchmarks demonstrate an accuracy improvement of up to +13.36% compared to the fully binary state-of-the-art solution, showing minimal accuracy degradation compared to the same architecture trained with full-precision SGD and floating-point weights, activations, and inputs. The proposed algorithm is made available to the scientific community as a public repository.

Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that the prediction error of FGD is, however, by a factor $d$ slower than the prediction error of stochastic gradient descent (SGD). In this paper we show that by computing $\ell$ FGD steps based on each training sample, this suboptimality factor becomes $d/(\ell \wedge d)$ and thus the suboptimality of the rate disappears if $\ell \gtrsim d.$ We also show that FGD with repeated sampling can adapt to low-dimensional structure in the input distribution. The main mathematical challenge lies in controlling the dependencies arising from the repeated sampling process.

These authors contributed equally to this work. Noisy labels pose a substantial challenge in machine learning, often resulting in overfitting and poor generalization. Sharpness-Aware Minimization (SAM), as demonstrated by Foret et al. (2021), improves generalization over traditional Stochastic Gradient Descent (SGD) in classification tasks with noisy labels by implicitly slowing noisy learning. While SAM's ability to generalize in noisy environments has been studied in several simplified settings, its full potential in more realistic training settings remains underexplored. In this work, we analyze SAM's behavior at each iteration, identifying specific components of the gradient vector that contribute significantly to its robustness against noisy labels. Based on these insights, we propose SANER (Sharpness-Aware Noise-Explicit Reweighting), an effective variant that enhances SAM's ability to manage noisy fitting rate. Our experiments on CIFAR-10, CIFAR-100, and Mini-WebVision demonstrate that SANER consistently outperforms SAM, achieving up to an 8% increase on CIFAR-100 with 50% label noise. The issue of noisy labels due to human error annotation has been commonly observed in many largescale datasets such as CIFAR-10N, CIFAR-100N (Wei et al., 2022), Clothing1M (Xiao et al., 2015), and WebVision (Li et al., 2017). Over-parameterized deep neural networks, which have enough capacity to memorize entire large datasets, can easily overfit such noisy label data, leading to poor generalization performance (Zhang et al., 2021). Moreover, the lottery ticket hypothesis (Frankle & Carbin, 2019) indicates that only a subset of the network's parameters is crucial for generalization. This highlights the importance of noise-robust learning, where the goal is to train a robust classifier despite the presence of inaccurate or noisy labels in the training dataset. Sharpness-Aware Minimization (SAM), introduced by Foret et al. (2021), is an optimizer designed to find better generalization by searching for flat minima. It has shown superior performance over SGD in various tasks, especially in classification tasks involving noisy labels Baek et al. (2024). Understanding the mechanisms behind the success of SAM is crucial for further improvements in handling label noise.

The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing complex costs remains a significant challenge. Neural Networks (NNs), known for their expressivity, can be leveraged to parametrize control policies that yield good performance. However, NNs' sensitivity to small input changes poses a risk of destabilizing the closed-loop system. Many existing approaches enforce constraints on the controllers' parameter space to guarantee closed-loop stability, leading to computationally expensive optimization procedures. To address these problems, we leverage the framework of port-Hamiltonian systems to design continuous-time distributed control policies for nonlinear systems that guarantee closed-loop stability and finite $\mathcal{L}_2$ or incremental $\mathcal{L}_2$ gains, independent of the optimzation parameters of the controllers. This eliminates the need to constrain parameters during optimization, allowing the use of standard techniques such as gradient-based methods. Additionally, we discuss discretization schemes that preserve the dissipation properties of these controllers for implementation on embedded systems. The effectiveness of the proposed distributed controllers is demonstrated through consensus control of non-holonomic mobile robots subject to collision avoidance and averaged voltage regulation with weighted power sharing in DC microgrids.