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Optimization · Non-Convex

Sixin Zhang

We study min-max algorithms to solve zero-sum differential games onRiemannian manifold.Based on the notions ofdifferential Stackelberg equilibriumand differential Nash equilibrium on Riemannian manifold,we analyze the local convergence of two representative deterministic simultaneous algorithms $\tau$-GDA and $\tau$-SGAto such equilibria.Sufficient conditions are obtained to establish the linear convergence rateof $\tau$-GDA based on the Ostrowski theorem on manifold and spectral analysis. To avoid strong rotational dynamics in $\tau$-GDA, $\tau$-SGA is extended fromthe symplectic gradient-adjustment method in Euclidean space.We analyze an asymptotic approximation of $\tau$-SGA when the learning rate ratio $\tau$ is big. In some cases, it can achieve a faster convergence rate to differential Stackelberg equilibrium compared to $\tau$-GDA. We show numerically how the insights obtained from theconvergence analysis may improvethe training of orthogonal Wasserstein GANs using stochastic $\tau$-GDA and $\tau$-SGA on simple benchmarks.

Applications · Chemistry and Drug Discovery

Yinkai Wang, Xiaohui Chen, Liping Liu, Soha Hassoun

The annotation (assigning structural chemical identities) of MS/MS spectra remains a significant challenge due to the enormous molecular diversity in biological samples and the limited scope of reference databases. Currently, the vast majority of spectral measurements remain in the "dark chemical space" without structural annotations. To improve annotation, we propose MADGEN (Mass-spec Attends to De Novo Molecular GENeration), a scaffold-based method for de novo molecular structure generation guided by mass spectrometry data. MADGEN operates in two stages: scaffold retrieval and spectra-conditioned molecular generation starting with the scaffold. In the first stage, given an MS/MS spectrum, we formulate scaffold retrieval as a ranking problem and employ contrastive learning to align mass spectra with candidate molecular scaffolds. In the second stage, starting from the retrieved scaffold, we employ the MS/MS spectrum to guide an attention-based generative model to generate the final molecule. Our approach constrains the molecular generation search space, reducing its complexity and improving generation accuracy. We evaluate MADGEN on three datasets (NIST23, CANOPUS, and MassSpecGym) and evaluate MADGEN's performance with a predictive scaffold retriever and with an oracle retriever. We demonstrate the effectiveness of using attention to integrate spectral information throughout the generation process to achieve strong results with the oracle retriever.

Deep Learning · Self-Supervised Learning

Shaden Alshammari, John Hershey, Axel Feldmann, William Freeman, Mark Hamilton

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of mod- ern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality re- duction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Shengju Yu, Zhibin Dong, Siwei Wang, Pei Zhang, Yi Zhang, Xinwang Liu, Thomas Guan, Tiejun Li, Yiu-ming Cheung

Most of incomplete multi-view clustering (IMVC) methods typically choose to ignore the missing samples and only utilize observed unpaired samples to construct bipartite similarity. Moreover, they employ a single quantity of prototypes to extract the information of $\textbf{all}$ views. To eliminate these drawbacks, we present a simple yet effective IMVC approach, SIIHPC, in this work. It firstly transforms partial bipartition learning into original sample form by virtue of reconstruction concept to split out of observed similarity, and then loosens traditional non-negative constraints via regularizing samples to more freely characterize the similarity. Subsequently, it learns to recover the incomplete parts by utilizing the connection built between the similarity exclusive on respective view and the consensus graph shared for all views. On this foundation, it further introduces a group of hybrid prototype quantities for each individual view to flexibly extract the data features belonging to each view itself. Accordingly, the resulting graphs are with various scales and describe the overall similarity more comprehensively. It is worth mentioning that these all are optimized in one unified learning framework, which makes it possible for them to reciprocally promote. Then, to effectively solve the formulated optimization problem, we design an ingenious auxiliary function that is with theoretically proven monotonic-increasing properties. Finally, the clustering results are obtained by implementing spectral grouping action on the eigenvectors of stacked multi-scale consensus similarity. Experimental results confirm the effectiveness of SIIHPC.

Reinforcement Learning · Batch/Offline

Gwangpyo Yoo, Honguk Woo

Offline reinforcement learning (RL) is becoming critical in risk-sensitive areas such as finance and autonomous driving, where incorrect decisions can lead to substantial financial loss or compromised safety. However, traditional risk-sensitive offline RL methods often struggle with accurately assessing risk, with minor errors in the estimated return potentially causing significant inaccuracies of risk estimation. These challenges are intensified by distribution shifts inherent in offline RL. To mitigate these issues, we propose a model risk-sensitive offline RL framework designed to minimize the worst-case of risks across a set of plausible alternative scenarios rather than solely focusing on minimizing estimated risk. We present a critic-ensemble criterion method that identifies the plausible alternative scenarios without introducing additional hyperparameters. We also incorporate the learned Fourier feature framework and the IQN framework to address spectral bias in neural networks, which can otherwise lead to severe errors in calculating model risk. Our experiments in finance and self-driving scenarios demonstrate that the proposed framework significantly reduces risk, by $11.2\%$ to $18.5\%$, compared to the most outperforming risk-sensitive offline RL baseline, particularly in highly uncertain environments.

Deep Learning · Generative Models and Autoencoders

Sepehr Dehdashtian, Gautam Sreekumar, Vishnu Boddeti

Images generated by text-to-image (T2I) models often exhibit visual biases and stereotypes of concepts such as culture and profession. Existing quantitative measures of stereotypes are based on statistical parity that does not align with the sociological definition of stereotypes and, therefore, incorrectly categorizes biases as stereotypes. Instead of oversimplifying stereotypes as biases, we propose a quantitative measure of stereotypes that aligns with its sociological definition. We then propose OASIS to measure the stereotypes in a generated dataset and understand their origins within the T2I model. OASIS includes two scores to measure stereotypes from a generated image dataset: **(M1)** Stereotype Score to measure the distributional violation of stereotypical attributes, and **(M2)** WALS to measure spectral variance in the images along a stereotypical attribute. OASISalso includes two methods to understand the origins of stereotypes in T2I models: **(U1)** StOP to discover attributes that the T2I model internally associates with a given concept, and **(U2)** SPI to quantify the emergence of stereotypical attributes in the latent space of the T2I model during image generation. Despite the considerable progress in image fidelity, using OASIS, we conclude that newer T2I models such as FLUX.1 and SDv3 contain strong stereotypical predispositions about concepts and still generate images with widespread stereotypical attributes. Additionally, the quantity of stereotypes worsens for nationalities with lower Internet footprints.

Applications · Computer Vision

Maximilian Weiherer, Bernhard Egger

We propose to use the family of Matérn kernels for implicit surface reconstruction, building upon the recent success of kernel methods for 3D reconstruction of oriented point clouds. As we show from a theoretical and practical perspective, Matérn kernels have some appealing properties which make them particularly well suited for surface reconstruction---outperforming state-of-the-art methods based on the arc-cosine kernel while being significantly easier to implement, faster to compute, and scalable. Being stationary, we demonstrate that Matérn kernels allow for tunable surface reconstruction in the same way as Fourier feature mappings help coordinate-based MLPs overcome spectral bias. Moreover, we theoretically analyze Matérn kernels' connection to SIREN networks as well as their relation to previously employed arc-cosine kernels. Finally, based on recently introduced Neural Kernel Fields, we present data-dependent Matérn kernels and conclude that especially the Laplace kernel (being part of the Matérn family) is extremely competitive, performing almost on par with state-of-the-art methods in the noise-free case while having a more than five times shorter training time.

Social Aspects · Fairness, Equity, Justice and Safety

Lena Krieger, Anna Beer, Pernille Matthews, Anneka Thiesson, Ira Assent

Fairness in data mining tasks like clustering has recently become an increasingly important aspect. However, few clustering algorithms exist that focus on fair groupings of data with sensitive attributes. Including fairness in the clustering objective is especially hard for density-based clustering, as it does not directly optimize a closed form objective like centroid-based or spectral methods. This paper introduces FairDen, the first fair, density-based clustering algorithm.We capture the dataset's density-connectivity structure in a similarity matrix that we manipulate to encourage a balanced clustering. In contrast to state-of-the-art, FairDen inherently handles categorical attributes, noise, and data with several sensitive attributes or groups.We show that FairDen finds meaningful and fair clusters in extensive experiments.

Applications · Time Series

Hao Wang, zhengnan li, Haoxuan Li, Xu Chen, Mingming Gong, BinChen, Zhichao Chen

Missing data imputation through distribution alignment has demonstrated advantages for non-temporal datasets but exhibits suboptimal performance in time-series applications. The primary obstacle is crafting a discrepancy measure that simultaneously (1) captures temporal patterns—accounting for periodicity and temporal dependencies inherent in time-series—and (2) accommodates non-stationarity, ensuring robustness amidst multiple coexisting temporal patterns. In response to these challenges, we introduce the Proximal Spectrum Wasserstein (PSW) discrepancy, a novel discrepancy tailored for comparing two \textit{sets} of time-series based on optimal transport. It incorporates a pairwise spectral distance to encapsulate temporal patterns, and a selective matching regularization to accommodate non-stationarity. Subsequently, we develop the PSW for Imputation (PSW-I) framework, which iteratively refines imputation results by minimizing the PSW discrepancy. Extensive experiments demonstrate that PSW-I effectively accommodates temporal patterns and non-stationarity, outperforming prevailing time-series imputation methods. Code is available at https://github.com/FMLYD/PSW-I.

Optimization · Everything Else

Cheng Zhang, Jeffrey T. H. Wong, Can Xiao, George Constantinides, Yiren Zhao

The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment.Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms.The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2.Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error,minimizing the Frobenius and spectral norms of the weight approximation error.Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results.However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms.In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA),and offer a closed-form solution to the problem.We show QERA benefits both existing low-precision fine-tuning and inference methods --QERA achieves a fine-tuned accuracy gain of $\Delta_{\text{acc}}$ = 6.05\% of 2-bit RoBERTa-base on GLUE compared to LoftQ;and obtains $\Delta_{\text{acc}}$ = 2.97\% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and $\Delta_{\text{ppl}}$ = $-$ 0.28 lower perplexity on WikiText2 than LQER.

Applications · Computer Vision

Taesun Yeom, Sangyoon Lee, Jaeho Lee

Neural fields are an emerging paradigm that represent data as continuous functions parameterized by neural networks. Despite many advantages, neural fields often have a high training cost, which prevents a broader adoption. In this paper, we focus on a popular family of neural fields, called sinusoidal neural fields (SNFs), and study how it should be initialized to maximize the training speed. We find that the standard initialization scheme for SNFs---designed based on the signal propagation principle---is suboptimal. In particular, we show that by simply multiplying each weight (except for the last layer) by a constant, we can accelerate SNF training by 10$\times$. This method, coined _weight scaling_, consistently provides a significant speedup over various data domains, allowing the SNFs to train faster than more recently proposed architectures. To understand why the weight scaling works well, we conduct extensive theoretical and empirical analyses which reveal that the weight scaling not only resolves the spectral bias quite effectively but also enjoys a well-conditioned optimization trajectory.

Deep Learning · Large Language Models

Ayan Sengupta, Siddhant Chaudhary, Tanmoy Chakraborty

The ever-increasing size of large language models (LLMs) presents significant challenges for deployment due to their heavy computational and memory requirements. Current model pruning techniques attempt to alleviate these issues by relying heavily on external calibration datasets to determine which parameters to prune or compress, thus limiting their flexibility and scalability across different compression ratios. Moreover, these methods often cause severe performance degradation, particularly in downstream tasks, when subjected to higher compression rates. In this paper, we propose *PruneNet*, a novel model compression method that addresses these limitations by reformulating model pruning as a policy learning process. PruneNet decouples the pruning process from the model architecture, eliminating the need for calibration datasets. It learns a stochastic pruning policy to assess parameter importance solely based on intrinsic model properties while preserving the spectral structure to minimize information loss. PruneNet can compress the LLaMA-2-7B model in just 15 minutes, achieving over 80\% retention of its zero-shot performance with a 30\% compression ratio, outperforming existing methods that retain only 75\% performance. Furthermore, on complex multitask language understanding tasks, PruneNet demonstrates its robustness by preserving up to 80\% performance of the original model, proving itself a superior alternative to conventional structured compression techniques.

Jonas Linkerhägner, Cheng Shi, Ivan Dokmanić

When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to **j**ointly **d**enoise the features and **r**ewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.

Deep Learning · Graph Neural Networks

Jonas Linkerhägner, Cheng Shi, Ivan Dokmanić

When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to **j**ointly **d**enoise the features and **r**ewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.

Theory · Optimization

Yuki Takezawa, Sebastian Stich

Decentralized SGD can run with low communication costs, but its sparse communication characteristics deteriorate the convergence rate, especially when the number of nodes is large. In decentralized learning settings, communication is assumed to occur on only a given topology, while in many practical cases, the topology merely represents a preferred communication pattern, and connecting to arbitrary nodes is still possible. Previous studies have tried to alleviate the convergence rate degradation in these cases by designing topologies with large spectral gaps. However, the degradation is still significant when the number of nodes is substantial. In this work, we propose TELEPORTATION. TELEPORTATION activates only a subset of nodes, and the active nodes fetch the parameters from previous active nodes. Then, the active nodes update their parameters by SGD and perform gossip averaging on a relatively small topology comprising only the active nodes. We show that by activating only a proper number of nodes, TELEPORTATION can completely alleviate the convergence rate degradation. Furthermore, we propose an efficient hyperparameter-tuning method to search for the appropriate number of nodes to be activated. Experimentally, we showed that TELEPORTATION can train neural networks more stably and achieve higher accuracy than Decentralized SGD.

Deep Learning · Generative Models and Autoencoders

GIORGIA MINELLO, Alessandro Bicciato, Luca Rossi, Andrea Torsello, Luca Cosmo

In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and eigenvalues from which we can reconstruct the graph Laplacian and adjacency matrix. Using the Laplacian spectrum allows us to naturally capture the structural characteristics of the graph and work directly in the node space while avoiding the quadratic complexity bottleneck that limits the applicability of other diffusion-based methods. This, in turn, is accomplished by truncating the spectrum, which, as we show in our experiments, results in a faster yet accurate generative process, and by designing a novel transformer-based architecture linear in the number of nodes. Our permutation invariant model can also handle node features by concatenating them to the eigenvectors of each node. An extensive set of experiments on both synthetic and real-world graphs demonstrates the strengths of our model against state-of-the-art alternatives.

Deep Learning · Robustness

Róisín Luo, James McDermott, Colm O'Riordan

Perturbation robustness evaluates the vulnerabilities of models, arising from a variety of perturbations, such as data corruptions and adversarial attacks. Understanding the mechanisms of perturbation robustness is critical for global interpretability. We present a model-agnostic, global mechanistic interpretability method to interpret the perturbation robustness of image models. This research is motivated by two key aspects. First, previous global interpretability works, in tandem with robustness benchmarks, *eg.* mean corruption error (mCE), are not designed to directly interpret the mechanisms of perturbation robustness within image models. Second, we notice that the spectral signal-to-noise ratios (SNR) of perturbed natural images exponentially decay over the frequency. This power-law-like decay implies that: Low-frequency signals are generally more robust than high-frequency signals -- yet high classification accuracy can not be achieved by low-frequency signals alone. By applying Shapley value theory, our method axiomatically quantifies the predictive powers of robust features and non-robust features within an information theory framework. Our method, dubbed as **I-ASIDE** (**I**mage **A**xiomatic **S**pectral **I**mportance **D**ecomposition **E**xplanation), provides a unique insight into model robustness mechanisms. We conduct extensive experiments over a variety of vision models pre-trained on ImageNet, including both convolutional neural networks (*eg.* *AlexNet*, *VGG*, *GoogLeNet/Inception-v1*, *Inception-v3*, *ResNet*, *SqueezeNet*, *RegNet*, *MnasNet*, *MobileNet*, *EfficientNet*, *etc.*) and vision transformers (*eg.* *ViT*, *Swin Transformer*, and *MaxViT*), to show that **I-ASIDE** can not only **measure** the perturbation robustness but also **provide interpretations** of its mechanisms.

Miscellaneous Aspects of Machine Learning · Representation Learning

Zeyu Yun, Juexiao Zhang, Yann LeCun, Yubei Chen

Unsupervised representation learning has seen tremendous progress. However, it is constrained by its reliance on domain specific stationarity and topology, a limitation not found in biological intelligence systems. For instance, unlike computer vision, human vision can process visual signals sampled from highly irregular and non-stationary sensors. We introduce a novel framework that learns from high-dimensional data without prior knowledge of stationarity and topology. Our model, abbreviated as URLOST, combines a learnable self-organizing layer, spectral clustering, and a masked autoencoder (MAE). We evaluate its effectiveness on three diverse data modalities including simulated biological vision data, neural recordings from the primary visual cortex, and gene expressions. Compared to state-of-the-art unsupervised learning methods like SimCLR and MAE, our model excels at learning meaningful representations across diverse modalities without knowing their stationarity or topology. It also outperforms other methods that are not dependent on these factors, setting a new benchmark in the field. We position this work as a step toward unsupervised learning methods capable of generalizing across diverse high-dimensional data modalities.

Applications · Computer Vision

Onkar Susladkar, Jishu Sen Gupta, Chirag Sehgal, Sparsh Mittal, Rekha Singhal

The spatio-temporal complexity of video data presents significant challenges in tasks such as compression, generation, and inpainting. We present four key contributions to address the challenges of spatiotemporal video processing. First, we introduce the 3D Mobile Inverted Vector-Quantization Variational Autoencoder (3D-MBQ-VAE), which combines Variational Autoencoders (VAEs) with masked modeling to enhance spatiotemporal video compression. The model achieves superior temporal consistency and state-of-the-art (SOTA) reconstruction quality by employing a novel training strategy with full frame masking. Second, we present MotionAura, a text-to-video generation framework that utilizes vector-quantized diffusion models to discretize the latent space and capture complex motion dynamics, producing temporally coherent videos aligned with text prompts. Third, we propose a spectral transformer-based denoising network that processes video data in the frequency domain using the Fourier Transform. This method effectively captures global context and long-range dependencies for high-quality video generation and denoising. Lastly, we introduce a downstream task of Sketch Guided Video Inpainting. This task leverages Low-Rank Adaptation (LoRA) for parameter-efficient fine-tuning. Our models achieve SOTA performance on a range of benchmarks. Our work offers robust frameworks for spatiotemporal modeling and user-driven video content manipulation.

Probabilistic Methods · Gaussian Processes

Ameer Qaqish, Didong Li

Gaussian processes (GPs) are widely recognized for their robustness and flexibility across various domains, including machine learning, time series, spatial statistics, and biomedicine. In addition to their common usage in regression tasks, GP kernel parameters are frequently interpreted in various applications. For example, in spatial transcriptomics, estimated kernel parameters are used to identify spatial variable genes, which exhibit significant expression patterns across different tissue locations. However, before these parameters can be meaningfully interpreted, it is essential to establish their identifiability. Existing studies of GP parameter identifiability have focused primarily on Mat\'ern-type kernels, as their spectral densities allow for more established mathematical tools. In many real-world applications, particuarly in time series analysis, other kernels such as the squared exponential, periodic, and rational quadratic kernels, as well as their combinations, are also widely used. These kernels share the property of being holomorphic around zero, and their parameter identifiability remains underexplored.In this paper, we bridge this gap by developing a novel theoretical framework for determining kernel parameter identifiability for kernels holomorphic near zero. Our findings enable practitioners to determine which parameters are identifiable in both existing and newly constructed kernels, supporting application-specific interpretation of the identifiable parameters, and highlighting non-identifiable parameters that require careful interpretation.