Yaoqing Yang

Tianyu Pang, Vignesh Kothapalli, Shenyang Deng et al.

We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions. In particular, we derive the exact closed-form expressions for the gradients and test loss after one and two steps of gradient descent, enabling a precise characterization of early training dynamics. We characterize how learning rates should scale under the gradient approximation in the first two steps, and prove that performing updates with this approximation yields a tractable surrogate loss with a tight, small approximation error. This formulation enables the theoretical analysis of layer-wise learning rates and reveals a distinct early-training regime: test loss can be minimized by unequal learning rates at the initial step, while equal learning rates become optimal in subsequent steps. Our numerical experiments validate the theory and demonstrate the importance of balancing layer-wise learning rates early during training. The code is available at: https://github.com/TDCSZ327/Layer-Balancing.

Zhengming Zhang, Ashwinee Panda, Linyue Song et al. · berkeley

Due to their decentralized nature, federated learning (FL) systems have an inherent vulnerability during their training to adversarial backdoor attacks. In this type of attack, the goal of the attacker is to use poisoned updates to implant so-called backdoors into the learned model such that, at test time, the model's outputs can be fixed to a given target for certain inputs. (As a simple toy example, if a user types "people from New York" into a mobile keyboard app that uses a backdoored next word prediction model, then the model could autocomplete the sentence to "people from New York are rude"). Prior work has shown that backdoors can be inserted into FL models, but these backdoors are often not durable, i.e., they do not remain in the model after the attacker stops uploading poisoned updates. Thus, since training typically continues progressively in production FL systems, an inserted backdoor may not survive until deployment. Here, we propose Neurotoxin, a simple one-line modification to existing backdoor attacks that acts by attacking parameters that are changed less in magnitude during training. We conduct an exhaustive evaluation across ten natural language processing and computer vision tasks, and we find that we can double the durability of state of the art backdoors.

Yuxin Wang, Yuanzhe Hu, Xiaokun Zhong et al.

Neural networks trained under different hyperparameter settings can fall into distinct training "regimes," with consistent behavior within regimes and qualitative differences across regimes. In this paper, we study such multi-regime behavior in scientific machine learning (SciML) models through a regime-aware diagnostic framework that jointly analyzes performance, training dynamics, and loss-landscape geometry. We identify three key findings: (i) a consistent three-regime structure emerges across many standard SciML models, different constraint enforcements, and various optimizer designs; (ii) optimization effectiveness is regime-specific, with no single method performing well across all regimes; and (iii) SciML models can exhibit fine-grained failure modes that can challenge conventional interpretations of standard loss-landscape metrics. Our results provide an approach to establish a unified, task-oblivious perspective on failure modes in SciML and to inform regime-aware guidance for improving robustness. We validate these findings across widely-used SciML models, including physics-informed neural networks, neural operators, and neural ordinary differential equations, on benchmarks spanning representative ordinary and partial differential equations.

Xiaotian Liu, Shuyuan Shang, Xiaopeng Wang et al.

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), which augments pre-trained operators with a learned refinement module iteratively applied via fixed-point iteration. IRNO decomposes the prediction into a coarse initialization followed by successive residual corrections, paralleling classical numerical solvers. Under local assumptions, we establish contraction of the induced operator, ensuring convergence to a unique fixed point. To explicitly target high-frequency errors, we propose a progressive spectral loss that adaptively increases penalty on high-frequency components over refinement steps during training. Across physical systems, IRNO consistently lowers error, with up to 56.05% improvement on turbulent flow. On Active Matter, spectral analysis reveals that, relative to base operator, the normalized error ratios decrease to 27.72-36.10% in low-, 5.07-6.68% in mid-, and 1.48-2.04% in high-frequencies, remaining stable beyond the trained iteration count. Code is available at https://github.com/xiaotianliu-dartmouth/Iterative_Refinement_Neural_Operator

Shenyang Deng, Boyao Liao, Zhuoli Ouyang et al.

The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few dominant eigenvalues are separated from a bulk of smaller ones, to the imbalance in the data covariance matrix. In this work, we challenge this view by demonstrating that such spectral Bifurcation can arise purely from the network architecture, independent of data imbalance. Specifically, we analyze a deep linear network setup and prove that, even when the data covariance is perfectly balanced, the Hessian still exhibits a Bifurcation eigenvalue structure: a dominant cluster and a bulk cluster. Crucially, we establish that the ratio between dominant and bulk eigenvalues scales linearly with the network depth. This reveals that the spectral gap is strongly affected by the network architecture rather than solely by data distribution. Our results suggest that both model architecture and data characteristics should be considered when designing optimization algorithms for deep networks.

Jinglong Xiong, Xiaotian Liu, Ruoxin Wang et al.

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.

Tianyu Pang, Yujie Fang, Zihang Liu et al.

Muon has recently shown promising results in LLM training. In this work, we study how to further improve Muon. We argue that Muon's orthogonalized update rule suppresses the emergence of heavy-tailed weight spectra and over-emphasizes the training along noise-dominated directions. Motivated by the Heavy-Tailed Self-Regularization (HT-SR) theory, we propose HTMuon. HTMuon preserves Muon's ability to capture parameter interdependencies while producing heavier-tailed updates and inducing heavier-tailed weight spectra. Experiments on LLM pretraining and image classification show that HTMuon consistently improves performance over state-of-the-art baselines and can also serve as a plug-in on top of existing Muon variants. For example, on LLaMA pretraining on the C4 dataset, HTMuon reduces perplexity by up to $0.98$ compared to Muon. We further theoretically show that HTMuon corresponds to steepest descent under the Schatten-$q$ norm constraint and provide convergence analysis in smooth non-convex settings. The implementation of HTMuon is available at https://github.com/TDCSZ327/HTmuon.

Shenyang Deng, Zhuoli Ouyang, Tianyu Pang et al.

Preconditioned adaptive methods have gained significant attention for training deep neural networks, as they capture rich curvature information of the loss landscape . The central challenge in this field lies in balancing preconditioning effectiveness with computational efficiency of implementing the preconditioner. Among recent advances, \textsc{Muon} stands out by using Newton-Schulz iteration to obtain preconditioned updates without explicitly constructing the preconditioning matrix. Despite its advantages, the efficiency of \textsc{Muon} still leaves room for further improvement. In this paper, we introduce \textsc{RMNP} (Row Momentum Normalized Preconditioning), an optimizer that replaces Newton-Schulz iteration with a simple row-wise $\ell_2$ normalization operation, motivated by the empirically observed diagonal block structure of the Transformer layerwise Hessian. This substitution reduces the per-iteration computational complexity from $\mathcal{O}(mn\cdot\min(m,n))$ to $\mathcal{O}(mn)$ for an $m\times n$ weight matrix while maintaining comparable optimization performance. Theoretically, we establish convergence guarantees for \textsc{RMNP} in the non-convex setting that match recent results for \textsc{Muon} optimizers, achieving the information-theoretic minimax optimal complexity. Extensive experiments on large language model pretraining show that \textsc{RMNP} delivers competitive optimization performance compared with \textsc{Muon} while substantially reducing preconditioning wall-clock time. Our code is available at \href{https://anonymous.4open.science/r/RMNP-E8E1/}{this link}.

Haiquan Lu, Xiaotian Liu, Yefan Zhou et al.

Recent studies on deep ensembles have identified the sharpness of the local minima of individual learners and the diversity of the ensemble members as key factors in improving test-time performance. Building on this, our study investigates the interplay between sharpness and diversity within deep ensembles, illustrating their crucial role in robust generalization to both in-distribution (ID) and out-of-distribution (OOD) data. We discover a trade-off between sharpness and diversity: minimizing the sharpness in the loss landscape tends to diminish the diversity of individual members within the ensemble, adversely affecting the ensemble's improvement. The trade-off is justified through our theoretical analysis and verified empirically through extensive experiments. To address the issue of reduced diversity, we introduce SharpBalance, a novel training approach that balances sharpness and diversity within ensembles. Theoretically, we show that our training strategy achieves a better sharpness-diversity trade-off. Empirically, we conducted comprehensive evaluations in various data sets (CIFAR-10, CIFAR-100, TinyImageNet) and showed that SharpBalance not only effectively improves the sharpness-diversity trade-off, but also significantly improves ensemble performance in ID and OOD scenarios.

Jiaqing Chen, Nicholas Hadler, Tiankai Xie et al.

Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for arbitrary-dimensional loss landscape analysis. Landscaper combines Hessian-based subspace construction with topological data analysis to reveal geometric structures such as basin hierarchy and connectivity. A key component is the Saddle-Minimum Average Distance (SMAD) for quantifying landscape smoothness. We demonstrate Landscaper's effectiveness across various architectures and tasks, including those involving pre-trained language models, showing that SMAD captures training transitions, such as landscape simplification, that conventional metrics miss. We also illustrate Landscaper's performance in challenging chemical property prediction tasks, where SMAD can serve as a metric for out-of-distribution generalization, offering valuable insights for model diagnostics and architecture design in data-scarce scientific machine learning scenarios.

Haiquan Lu, Yefan Zhou, Shiwei Liu et al.

Recent work on pruning large language models (LLMs) has shown that one can eliminate a large number of parameters without compromising performance, making pruning a promising strategy to reduce LLM model size. Existing LLM pruning strategies typically assign uniform pruning ratios across layers, limiting overall pruning ability; and recent work on layerwise pruning of LLMs is often based on heuristics that can easily lead to suboptimal performance. In this paper, we leverage Heavy-Tailed Self-Regularization (HT-SR) Theory, in particular the shape of empirical spectral densities (ESDs) of weight matrices, to design improved layerwise pruning ratios for LLMs. Our analysis reveals a wide variability in how well-trained, and thus relatedly how prunable, different layers of an LLM are. Based on this, we propose AlphaPruning, which uses shape metrics to allocate layerwise sparsity ratios in a more theoretically principled manner. AlphaPruning can be used in conjunction with multiple existing LLM pruning methods. Our empirical results show that AlphaPruning prunes LLaMA-7B to 80% sparsity while maintaining reasonable perplexity, marking a first in the literature on LLMs. We have open-sourced our code at https://github.com/haiquanlu/AlphaPruning.

Peijun Qing, Chongyang Gao, Yefan Zhou et al.

Parameter-efficient fine-tuning methods, such as Low-Rank Adaptation (LoRA), are known to enhance training efficiency in Large Language Models (LLMs). Due to the limited parameters of LoRA, recent studies seek to combine LoRA with Mixture-of-Experts (MoE) to boost performance across various tasks. However, inspired by the observed redundancy in traditional MoE structures, previous studies identify similar redundancy among LoRA experts within the MoE architecture, highlighting the necessity for non-uniform allocation of LoRA experts across different layers. In this paper, we leverage Heavy-Tailed Self-Regularization (HT-SR) Theory to design a fine-grained allocation strategy. Our analysis reveals that the number of experts per layer correlates with layer training quality, which exhibits significant variability across layers. Based on this, we introduce AlphaLoRA, a theoretically principled and training-free method for allocating LoRA experts to further mitigate redundancy. Experiments on three models across ten language processing and reasoning benchmarks demonstrate that AlphaLoRA achieves comparable or superior performance over all baselines. Our code is available at https://github.com/morelife2017/alphalora.

Zihang Liu, Tianyu Pang, Oleg Balabanov et al.

Recent studies have shown that supervised fine-tuning of LLMs on a small number of high-quality datasets can yield strong reasoning capabilities. However, full fine-tuning (Full FT), while powerful, is computationally expensive and susceptible to overfitting and catastrophic forgetting, particularly when data is limited. Sparse fine-tuning, which previously achieved notable success by updating only a small subset of model parameters, offers a promising trade-off between efficiency and effectiveness. Yet, it has lagged behind in the LLM era due to the difficulty of identifying parameters truly critical for reasoning. In this work, we state that weights with the largest magnitude after low-rank approximation are critical weights for fine-tuning, which we call Principal Weights. Surprisingly, while magnitude-based sparse fine-tuning performs poorly as a baseline on LLM fine-tuning, it becomes highly effective after rank reduction. These insights motivate our method: Low-rank Informed Sparse Fine-Tuning (LIFT). LIFT only updates the top 5% Principal Weights throughout training and consistently achieves better performance on reasoning tasks than Full FT, while maintaining memory efficiency on par with popular parameter-efficient fine-tuning methods. In addition to strong performance on target domains such as arithmetic reasoning, LIFT also retains up to 20% more source-domain knowledge, compared to Full FT and LoRA. Our code is available at: https://github.com/zihanghliu/LIFT.

Yefan Zhou, Jianlong Chen, Qinxue Cao et al.

This paper considers "model diagnosis", which we formulate as a classification problem. Given a pre-trained neural network (NN), the goal is to predict the source of failure from a set of failure modes (such as a wrong hyperparameter, inadequate model size, and insufficient data) without knowing the training configuration of the pre-trained NN. The conventional diagnosis approach uses training and validation errors to determine whether the model is underfitting or overfitting. However, we show that rich information about NN performance is encoded in the optimization loss landscape, which provides more actionable insights than validation-based measurements. Therefore, we propose a diagnosis method called MD tree based on loss landscape metrics and experimentally demonstrate its advantage over classical validation-based approaches. We verify the effectiveness of MD tree in multiple practical scenarios: (1) use several models trained on one dataset to diagnose a model trained on another dataset, essentially a few-shot dataset transfer problem; (2) use small models (or models trained with small data) to diagnose big models (or models trained with big data), essentially a scale transfer problem. In a dataset transfer task, MD tree achieves an accuracy of 87.7%, outperforming validation-based approaches by 14.88%. Our code is available at https://github.com/YefanZhou/ModelDiagnosis.

Yaoqing Yang, Chen Feng, Yiru Shen et al.

Recent deep networks that directly handle points in a point set, e.g., PointNet, have been state-of-the-art for supervised learning tasks on point clouds such as classification and segmentation. In this work, a novel end-to-end deep auto-encoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graph-based enhancement is enforced to promote local structures on top of PointNet. Then, a novel folding-based decoder deforms a canonical 2D grid onto the underlying 3D object surface of a point cloud, achieving low reconstruction errors even for objects with delicate structures. The proposed decoder only uses about 7% parameters of a decoder with fully-connected neural networks, yet leads to a more discriminative representation that achieves higher linear SVM classification accuracy than the benchmark. In addition, the proposed decoder structure is shown, in theory, to be a generic architecture that is able to reconstruct an arbitrary point cloud from a 2D grid. Our code is available at http://www.merl.com/research/license#FoldingNet

Yiru Shen, Chen Feng, Yaoqing Yang et al.

Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets. However, it does not take full advantage of a point's local neighborhood that contains fine-grained structural information which turns out to be helpful towards better semantic learning. In this regard, we present two new operations to improve PointNet with a more efficient exploitation of local structures. The first one focuses on local 3D geometric structures. In analogy to a convolution kernel for images, we define a point-set kernel as a set of learnable 3D points that jointly respond to a set of neighboring data points according to their geometric affinities measured by kernel correlation, adapted from a similar technique for point cloud registration. The second one exploits local high-dimensional feature structures by recursive feature aggregation on a nearest-neighbor-graph computed from 3D positions. Experiments show that our network can efficiently capture local information and robustly achieve better performances on major datasets. Our code is available at http://www.merl.com/research/license#KCNet

Shenyang Deng, Boyao Liao, Zhuoli Ouyang et al.

This paper explores the suspicious alignment phenomenon in stochastic gradient descent (SGD) under ill-conditioned optimization, where the Hessian spectrum splits into dominant and bulk subspaces. This phenomenon describes the behavior of gradient alignment in SGD updates. Specifically, during the initial phase of SGD updates, the alignment between the gradient and the dominant subspace tends to decrease. Subsequently, it enters a rising phase and eventually stabilizes in a high-alignment phase. The alignment is considered ``suspicious'' because, paradoxically, the projected gradient update along this highly-aligned dominant subspace proves ineffective at reducing the loss. The focus of this work is to give a fine-grained analysis in a high-dimensional quadratic setup about how step size selection produces this phenomenon. Our main contribution can be summarized as follows: We propose a step-size condition revealing that in low-alignment regimes, an adaptive critical step size $η_t^*$ separates alignment-decreasing ($η_t < η_t^*$) from alignment-increasing ($η_t > η_t^*$) regimes, whereas in high-alignment regimes, the alignment is self-correcting and decreases regardless of the step size. We further show that under sufficient ill-conditioning, a step size interval exists where projecting the SGD updates to the bulk space decreases the loss while projecting them to the dominant space increases the loss, which explains a recent empirical observation that projecting gradient updates to the dominant subspace is ineffective. Finally, based on this adaptive step-size theory, we prove that for a constant step size and large initialization, SGD exhibits this distinct two-phase behavior: an initial alignment-decreasing phase, followed by stabilization at high alignment.

Zihang Liu, Oleg Balabanov, Yaoqing Yang et al.

We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral information (e.g., eigenvalue estimates and residual norms), and they predict recurrence coefficients for computing or applying a matrix polynomial tailored to a downstream task. The effectiveness of AutoSpec relies on three ingredients: an architecture whose inference pass implements short, executable numerical linear algebra recurrences; efficient training on small synthetic problems with transfer to large-scale real-world operators; and task-defined objectives that enforce the desired approximation or preconditioning behavior across the range of spectral profiles represented in the training set. We apply AutoSpec to discovering algorithms for representative numerical linear algebra tasks: accelerating matrix-function approximation; accelerating sparse linear solvers; and spectral filtering/preconditioning for eigenvalue computations. On real-world matrices, the learned procedures deliver orders-of-magnitude improvements in accuracy and/or reductions in iteration count, relative to basic baselines. We also find clear connections to classical theory: the induced polynomials often exhibit near-equiripple, near-minimax behavior characteristic of Chebyshev polynomials.

Ashwinee Panda, Christopher A. Choquette-Choo, Zhengming Zhang et al. · deepmind

When large language models are trained on private data, it can be a significant privacy risk for them to memorize and regurgitate sensitive information. In this work, we propose a new practical data extraction attack that we call "neural phishing". This attack enables an adversary to target and extract sensitive or personally identifiable information (PII), e.g., credit card numbers, from a model trained on user data with upwards of 10% attack success rates, at times, as high as 50%. Our attack assumes only that an adversary can insert as few as 10s of benign-appearing sentences into the training dataset using only vague priors on the structure of the user data.

Zihang Liu, Yuanzhe Hu, Tianyu Pang et al.

Recent advances in foundation models have emphasized the need to align pre-trained models with specialized domains using small, curated datasets. Studies on these foundation models underscore the importance of low-data training and fine-tuning. This topic, well-known in natural language processing (NLP), has also gained increasing attention in the emerging field of scientific machine learning (SciML). To address the limitations of low-data training and fine-tuning, we draw inspiration from Heavy-Tailed Self-Regularization (HT-SR) theory, analyzing the shape of empirical spectral densities (ESDs) and revealing an imbalance in training quality across different model layers. To mitigate this issue, we adapt a recently proposed layer-wise learning rate scheduler, TempBalance, which effectively balances training quality across layers and enhances low-data training and fine-tuning for both NLP and SciML tasks. Notably, TempBalance demonstrates increasing performance gains as the amount of available tuning data decreases. Comparative analyses further highlight the effectiveness of TempBalance and its adaptability as an "add-on" method for improving model performance.

Lei Hsiung, Tianyu Pang, Yung-Chen Tang et al.

Recent advancements in large language models (LLMs) have underscored their vulnerability to safety alignment jailbreaks, particularly when subjected to downstream fine-tuning. However, existing mitigation strategies primarily focus on reactively addressing jailbreak incidents after safety guardrails have been compromised, removing harmful gradients during fine-tuning, or continuously reinforcing safety alignment throughout fine-tuning. As such, they tend to overlook a critical upstream factor: the role of the original safety-alignment data. This paper therefore investigates the degradation of safety guardrails through the lens of representation similarity between upstream alignment datasets and downstream fine-tuning tasks. Our experiments demonstrate that high similarity between these datasets significantly weakens safety guardrails, making models more susceptible to jailbreaks. Conversely, low similarity between these two types of datasets yields substantially more robust models and thus reduces harmfulness score by up to 10.33%. By highlighting the importance of upstream dataset design in the building of durable safety guardrails and reducing real-world vulnerability to jailbreak attacks, these findings offer actionable insights for fine-tuning service providers.

Konstantin Schürholt, Léo Meynent, Yefan Zhou et al.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Tiankai Xie, Caleb Geniesse, Jiaqing Chen et al.

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but less emphasis has been placed on quantifying and extracting actionable and reproducible insights from these complex representations. Inspired by powerful tools from topological data analysis (TDA) for summarizing the structure of high-dimensional data, here we characterize the underlying shape (or topology) of loss landscapes, quantifying the topology to reveal new insights about neural networks. To relate our findings to the machine learning (ML) literature, we compute simple performance metrics (e.g., accuracy, error), and we characterize the local structure of loss landscapes using Hessian-based metrics (e.g., largest eigenvalue, trace, eigenvalue spectral density). Following this approach, we study established models from image pattern recognition (e.g., ResNets) and scientific ML (e.g., physics-informed neural networks), and we show how quantifying the shape of loss landscapes can provide new insights into model performance and learning dynamics.

Mansi Sakarvadia, Kareem Hegazy, Amin Totounferoush et al.

A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLOs) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform "zero-shot super-resolution," namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.

Caleb Geniesse, Jiaqing Chen, Tiankai Xie et al.

In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights into the local structure of the so-called loss landscape (e.g., smoothness) as well as global properties of the underlying model (e.g., generalization performance). While various methods for visualizing the loss landscape have been proposed, many approaches limit sampling to just one or two directions, ignoring potentially relevant information in this extremely high-dimensional space. This paper introduces a new representation based on topological data analysis that enables the visualization of higher-dimensional loss landscapes. After describing this new topological landscape profile representation, we show how the shape of loss landscapes can reveal new details about model performance and learning dynamics, highlighting several use cases, including image segmentation (e.g., UNet) and scientific machine learning (e.g., physics-informed neural networks). Through these examples, we provide new insights into how loss landscapes vary across distinct hyperparameter spaces: we find that the topology of the loss landscape is simpler for better-performing models; and we observe greater variation in the shape of loss landscapes near transitions from low to high model performance.

Tiankai Xie, Jiaqing Chen, Yaoqing Yang et al.

Modern machine learning often relies on optimizing a neural network's parameters using a loss function to learn complex features. Beyond training, examining the loss function with respect to a network's parameters (i.e., as a loss landscape) can reveal insights into the architecture and learning process. While the local structure of the loss landscape surrounding an individual solution can be characterized using a variety of approaches, the global structure of a loss landscape, which includes potentially many local minima corresponding to different solutions, remains far more difficult to conceptualize and visualize. To address this difficulty, we introduce LossLens, a visual analytics framework that explores loss landscapes at multiple scales. LossLens integrates metrics from global and local scales into a comprehensive visual representation, enhancing model diagnostics. We demonstrate LossLens through two case studies: visualizing how residual connections influence a ResNet-20, and visualizing how physical parameters influence a physics-informed neural network (PINN) solving a simple convection problem.

Yaning Jia, Shenyang Deng, Chiyu Ma et al.

Graph Neural Networks (GNNs) have achieved impressive success across a wide range of graph-based tasks, yet they remain highly vulnerable to small, imperceptible perturbations and adversarial attacks. Although numerous defense methods have been proposed to address these vulnerabilities, many rely on heuristic metrics, overfit to specific attack patterns, and suffer from high computational complexity. In this paper, we propose Kernel Complexity-Based Edge Sanitization (KCES), a training-free, model-agnostic defense framework. KCES leverages Graph Kernel Complexity (GKC), a novel metric derived from the graph's Gram matrix that characterizes GNN generalization via its test error bound. Building on GKC, we define a KC score for each edge, measuring the change in GKC when the edge is removed. Edges with high KC scores, typically introduced by adversarial perturbations, are pruned to mitigate their harmful effects, thereby enhancing GNNs' robustness. KCES can also be seamlessly integrated with existing defense strategies as a plug-and-play module without requiring training. Theoretical analysis and extensive experiments demonstrate that KCES consistently enhances GNN robustness, outperforms state-of-the-art baselines, and amplifies the effectiveness of existing defenses, offering a principled and efficient solution for securing GNNs.

Xuyuan Liu, Lei Hsiung, Yaoqing Yang et al.

Understanding how feature representations evolve across layers in large language models (LLMs) is key to improving their interpretability and robustness. While recent studies have identified critical layers linked to specific functions or behaviors, these efforts typically rely on data-dependent analyses of fine-tuned models, limiting their use to post-hoc settings. In contrast, we introduce a data-oblivious approach to identify intrinsic critical layers in pre-fine-tuned LLMs by analyzing representation dynamics via Centered Kernel Alignment(CKA). We show that layers with significant shifts in representation space are also those most affected during fine-tuning--a pattern that holds consistently across tasks for a given model. Our spectral analysis further reveals that these shifts are driven by changes in the top principal components, which encode semantic transitions from rationales to conclusions. We further apply these findings to two practical scenarios: efficient domain adaptation, where fine-tuning critical layers leads to greater loss reduction compared to non-critical layers; and backdoor defense, where freezing them reduces attack success rates by up to 40%.

Vignesh Kothapalli, Tianyu Pang, Shenyang Deng et al.

Training strategies for modern deep neural networks (NNs) tend to induce a heavy-tailed (HT) empirical spectral density (ESD) in the layer weights. While previous efforts have shown that the HT phenomenon correlates with good generalization in large NNs, a theoretical explanation of its occurrence is still lacking. Especially, understanding the conditions which lead to this phenomenon can shed light on the interplay between generalization and weight spectra. Our work aims to bridge this gap by presenting a simple, rich setting to model the emergence of HT ESD. In particular, we present a theory-informed setup for 'crafting' heavy tails in the ESD of two-layer NNs and present a systematic analysis of the HT ESD emergence without any gradient noise. This is the first work to analyze a noise-free setting, and we also incorporate optimizer (GD/Adam) dependent (large) learning rates into the HT ESD analysis. Our results highlight the role of learning rates on the Bulk+Spike and HT shape of the ESDs in the early phase of training, which can facilitate generalization in the two-layer NN. These observations shed light on the behavior of large-scale NNs, albeit in a much simpler setting.

Yefan Zhou, Yaoqing Yang, Arin Chang et al.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

Ryan Theisen, Hyunsuk Kim, Yaoqing Yang et al.

Ensembling has a long history in statistical data analysis, with many impactful applications. However, in many modern machine learning settings, the benefits of ensembling are less ubiquitous and less obvious. We study, both theoretically and empirically, the fundamental question of when ensembling yields significant performance improvements in classification tasks. Theoretically, we prove new results relating the \emph{ensemble improvement rate} (a measure of how much ensembling decreases the error rate versus a single model, on a relative scale) to the \emph{disagreement-error ratio}. We show that ensembling improves performance significantly whenever the disagreement rate is large relative to the average error rate; and that, conversely, one classifier is often enough whenever the disagreement rate is low relative to the average error rate. On the way to proving these results, we derive, under a mild condition called \emph{competence}, improved upper and lower bounds on the average test error rate of the majority vote classifier. To complement this theory, we study ensembling empirically in a variety of settings, verifying the predictions made by our theory, and identifying practical scenarios where ensembling does and does not result in large performance improvements. Perhaps most notably, we demonstrate a distinct difference in behavior between interpolating models (popular in current practice) and non-interpolating models (such as tree-based methods, where ensembling is popular), demonstrating that ensembling helps considerably more in the latter case than in the former.

Haohui Wang, Yuzhen Mao, Yujun Yan et al.

Non-IID transfer learning on graphs is crucial in many high-stakes domains. The majority of existing works assume stationary distribution for both source and target domains. However, real-world graphs are intrinsically dynamic, presenting challenges in terms of domain evolution and dynamic discrepancy between source and target domains. To bridge the gap, we shift the problem to the dynamic setting and pose the question: given the label-rich source graphs and the label-scarce target graphs both observed in previous T timestamps, how can we effectively characterize the evolving domain discrepancy and optimize the generalization performance of the target domain at the incoming T+1 timestamp? To answer it, we propose a generalization bound for dynamic non-IID transfer learning on graphs, which implies the generalization performance is dominated by domain evolution and domain discrepancy between source and target graphs. Inspired by the theoretical results, we introduce a novel generic framework named EvoluNet. It leverages a transformer-based temporal encoding module to model temporal information of the evolving domains and then uses a dynamic domain unification module to efficiently learn domain-invariant representations across the source and target domains. Finally, EvoluNet outperforms the state-of-the-art models by up to 12.1%, demonstrating its effectiveness in transferring knowledge from dynamic source graphs to dynamic target graphs.

Yaoqing Yang, Ryan Theisen, Liam Hodgkinson et al.

Selecting suitable architecture parameters and training hyperparameters is essential for enhancing machine learning (ML) model performance. Several recent empirical studies conduct large-scale correlational analysis on neural networks (NNs) to search for effective \emph{generalization metrics} that can guide this type of model selection. Effective metrics are typically expected to correlate strongly with test performance. In this paper, we expand on prior analyses by examining generalization-metric-based model selection with the following objectives: (i) focusing on natural language processing (NLP) tasks, as prior work primarily concentrates on computer vision (CV) tasks; (ii) considering metrics that directly predict \emph{test error} instead of the \emph{generalization gap}; (iii) exploring metrics that do not need access to data to compute. From these objectives, we are able to provide the first model selection results on large pretrained Transformers from Huggingface using generalization metrics. Our analyses consider (I) hundreds of Transformers trained in different settings, in which we systematically vary the amount of data, the model size and the optimization hyperparameters, (II) a total of 51 pretrained Transformers from eight families of Huggingface NLP models, including GPT2, BERT, etc., and (III) a total of 28 existing and novel generalization metrics. Despite their niche status, we find that metrics derived from the heavy-tail (HT) perspective are particularly useful in NLP tasks, exhibiting stronger correlations than other, more popular metrics. To further examine these metrics, we extend prior formulations relying on power law (PL) spectral distributions to exponential (EXP) and exponentially-truncated power law (E-TPL) families.

Alan Pham, Eunice Chan, Vikranth Srivatsa et al.

Overparameterization is shown to result in poor test accuracy on rare subgroups under a variety of settings where subgroup information is known. To gain a more complete picture, we consider the case where subgroup information is unknown. We investigate the effect of model size on worst-group generalization under empirical risk minimization (ERM) across a wide range of settings, varying: 1) architectures (ResNet, VGG, or BERT), 2) domains (vision or natural language processing), 3) model size (width or depth), and 4) initialization (with pre-trained or random weights). Our systematic evaluation reveals that increasing model size does not hurt, and may help, worst-group test performance under ERM across all setups. In particular, increasing pre-trained model size consistently improves performance on Waterbirds and MultiNLI. We advise practitioners to use larger pre-trained models when subgroup labels are unknown.

Yefan Zhou, Yiru Shen, Yujun Yan et al.

Neural networks (NN) for single-view 3D reconstruction (SVR) have gained in popularity. Recent work points out that for SVR, most cutting-edge NNs have limited performance on reconstructing unseen objects because they rely primarily on recognition (i.e., classification-based methods) rather than shape reconstruction. To understand this issue in depth, we provide a systematic study on when and why NNs prefer recognition to reconstruction and vice versa. Our finding shows that a leading factor in determining recognition versus reconstruction is how dispersed the training data is. Thus, we introduce the dispersion score, a new data-driven metric, to quantify this leading factor and study its effect on NNs. We hypothesize that NNs are biased toward recognition when training images are more dispersed and training shapes are less dispersed. Our hypothesis is supported and the dispersion score is proved effective through our experiments on synthetic and benchmark datasets. We show that the proposed metric is a principal way to analyze reconstruction quality and provides novel information in addition to the conventional reconstruction score.

Puja Trivedi, Ekdeep Singh Lubana, Yujun Yan et al.

Unsupervised graph representation learning is critical to a wide range of applications where labels may be scarce or expensive to procure. Contrastive learning (CL) is an increasingly popular paradigm for such settings and the state-of-the-art in unsupervised visual representation learning. Recent work attributes the success of visual CL to use of task-relevant augmentations and large, diverse datasets. Interestingly, graph CL frameworks report strong performance despite using orders of magnitude smaller datasets and employing domain-agnostic graph augmentations (DAGAs). Motivated by this discrepancy, we probe the quality of representations learnt by popular graph CL frameworks using DAGAs. We find that DAGAs can destroy task-relevant information and harm the model's ability to learn discriminative representations. On small benchmark datasets, we show the inductive bias of graph neural networks can significantly compensate for this weak discriminability. Based on our findings, we propose several sanity checks that enable practitioners to quickly assess the quality of their model's learned representations. We further propose a broad strategy for designing task-aware augmentations that are amenable to graph CL and demonstrate its efficacy on two large-scale, complex graph applications. For example, in graph-based document classification, we show task-aware augmentations improve accuracy up to 20%.

Yaoqing Yang, Liam Hodgkinson, Ryan Theisen et al.

Viewing neural network models in terms of their loss landscapes has a long history in the statistical mechanics approach to learning, and in recent years it has received attention within machine learning proper. Among other things, local metrics (such as the smoothness of the loss landscape) have been shown to correlate with global properties of the model (such as good generalization performance). Here, we perform a detailed empirical analysis of the loss landscape structure of thousands of neural network models, systematically varying learning tasks, model architectures, and/or quantity/quality of data. By considering a range of metrics that attempt to capture different aspects of the loss landscape, we demonstrate that the best test accuracy is obtained when: the loss landscape is globally well-connected; ensembles of trained models are more similar to each other; and models converge to locally smooth regions. We also show that globally poorly-connected landscapes can arise when models are small or when they are trained to lower quality data; and that, if the loss landscape is globally poorly-connected, then training to zero loss can actually lead to worse test accuracy. Our detailed empirical results shed light on phases of learning (and consequent double descent behavior), fundamental versus incidental determinants of good generalization, the role of load-like and temperature-like parameters in the learning process, different influences on the loss landscape from model and data, and the relationships between local and global metrics, all topics of recent interest.

Siyuan Xiang, Anbang Yang, Yanfei Xue et al.

Spatial reasoning on multi-view line drawings by state-of-the-art supervised deep networks is recently shown with puzzling low performances on the SPARE3D dataset. Based on the fact that self-supervised learning is helpful when a large number of data are available, we propose two self-supervised learning approaches to improve the baseline performance for view consistency reasoning and camera pose reasoning tasks on the SPARE3D dataset. For the first task, we use a self-supervised binary classification network to contrast the line drawing differences between various views of any two similar 3D objects, enabling the trained networks to effectively learn detail-sensitive yet view-invariant line drawing representations of 3D objects. For the second type of task, we propose a self-supervised multi-class classification framework to train a model to select the correct corresponding view from which a line drawing is rendered. Our method is even helpful for the downstream tasks with unseen camera poses. Experiments show that our method could significantly increase the baseline performance in SPARE3D, while some popular self-supervised learning methods cannot.

Yujun Yan, Milad Hashemi, Kevin Swersky et al.

In node classification tasks, graph convolutional neural networks (GCNs) have demonstrated competitive performance over traditional methods on diverse graph data. However, it is known that the performance of GCNs degrades with increasing number of layers (oversmoothing problem) and recent studies have also shown that GCNs may perform worse in heterophilous graphs, where neighboring nodes tend to belong to different classes (heterophily problem). These two problems are usually viewed as unrelated, and thus are studied independently, often at the graph filter level from a spectral perspective. We are the first to take a unified perspective to jointly explain the oversmoothing and heterophily problems at the node level. Specifically, we profile the nodes via two quantitative metrics: the relative degree of a node (compared to its neighbors) and the node-level heterophily. Our theory shows that the interplay of these two profiling metrics defines three cases of node behaviors, which explain the oversmoothing and heterophily problems jointly and can predict the performance of GCNs. Based on insights from our theory, we show theoretically and empirically the effectiveness of two strategies: structure-based edge correction, which learns corrected edge weights from structural properties (i.e., degrees), and feature-based edge correction, which learns signed edge weights from node features. Compared to other approaches, which tend to handle well either heterophily or oversmoothing, we show that {our model, GGCN}, which incorporates the two strategies performs well in both problems.

Zhengming Zhang, Yaoqing Yang, Zhewei Yao et al.

Federated learning (FL) is a promising way to use the computing power of mobile devices while maintaining the privacy of users. Current work in FL, however, makes the unrealistic assumption that the users have ground-truth labels on their devices, while also assuming that the server has neither data nor labels. In this work, we consider the more realistic scenario where the users have only unlabeled data, while the server has some labeled data, and where the amount of labeled data is smaller than the amount of unlabeled data. We call this learning problem semi-supervised federated learning (SSFL). For SSFL, we demonstrate that a critical issue that affects the test accuracy is the large gradient diversity of the models from different users. Based on this, we investigate several design choices. First, we find that the so-called consistency regularization loss (CRL), which is widely used in semi-supervised learning, performs reasonably well but has large gradient diversity. Second, we find that Batch Normalization (BN) increases gradient diversity. Replacing BN with the recently-proposed Group Normalization (GN) can reduce gradient diversity and improve test accuracy. Third, we show that CRL combined with GN still has a large gradient diversity when the number of users is large. Based on these results, we propose a novel grouping-based model averaging method to replace the FedAvg averaging method. Overall, our grouping-based averaging, combined with GN and CRL, achieves better test accuracy than not just a contemporary paper on SSFL in the same settings (>10\%), but also four supervised FL algorithms.

Yaoqing Yang, Rajiv Khanna, Yaodong Yu et al.

Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with and usefulness for model robustness. Thick decision boundaries lead to improved performance, while thin decision boundaries lead to overfitting (e.g., measured by the robust generalization gap between training and testing) and lower robustness. We show that a thicker boundary helps improve robustness against adversarial examples (e.g., improving the robust test accuracy of adversarial training) as well as so-called out-of-distribution (OOD) transforms, and we show that many commonly-used regularization and data augmentation procedures can increase boundary thickness. On the theoretical side, we establish that maximizing boundary thickness during training is akin to the so-called mixup training. Using these observations, we show that noise-augmentation on mixup training further increases boundary thickness, thereby combating vulnerability to various forms of adversarial attacks and OOD transforms. We can also show that the performance improvement in several lines of recent work happens in conjunction with a thicker boundary.

Siheng Chen, Chaojing Duan, Yaoqing Yang et al.

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use lattice-based methods to process and learn 3D spatial information; however, this leads to inevitable discretization errors. In this work, we handle raw 3D points without such compromise. The proposed networks follow the autoencoder framework with a focus on designing the decoder. The encoder adopts similar architectures as in PointNet. The decoder involves three novel modules. The folding module folds a canonical 2D lattice to the underlying surface of a 3D point cloud, achieving coarse reconstruction; the graph-topology-inference module learns a graph topology to represent pairwise relationships between 3D points, pushing the latent code to preserve both coordinates and pairwise relationships of points in 3D point clouds; and the graph-filtering module couples the above two modules, refining the coarse reconstruction through a learnt graph topology to obtain the final reconstruction. The proposed decoder leverages a learnable graph topology to push the codeword to preserve representative features and further improve the unsupervised-learning performance. We further provide theoretical analyses of the proposed architecture. In the experiments, we validate the proposed networks in three tasks, including 3D point cloud reconstruction, visualization, and transfer classification. The experimental results show that (1) the proposed networks outperform the state-of-the-art methods in various tasks; (2) a graph topology can be inferred as auxiliary information without specific supervision on graph topology inference; and (3) graph filtering refines the reconstruction, leading to better performances.