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Nov 11

Perturbation Analysis of Neural Collapse

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

  • 3 authors
·
Oct 29, 2022

Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond

Linear relaxation based perturbation analysis (LiRPA) for neural networks, which computes provable linear bounds of output neurons given a certain amount of input perturbation, has become a core component in robustness verification and certified defense. The majority of LiRPA-based methods focus on simple feed-forward networks and need particular manual derivations and implementations when extended to other architectures. In this paper, we develop an automatic framework to enable perturbation analysis on any neural network structures, by generalizing existing LiRPA algorithms such as CROWN to operate on general computational graphs. The flexibility, differentiability and ease of use of our framework allow us to obtain state-of-the-art results on LiRPA based certified defense on fairly complicated networks like DenseNet, ResNeXt and Transformer that are not supported by prior works. Our framework also enables loss fusion, a technique that significantly reduces the computational complexity of LiRPA for certified defense. For the first time, we demonstrate LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet where previous approaches cannot scale to due to the relatively large number of classes. Our work also yields an open-source library for the community to apply LiRPA to areas beyond certified defense without much LiRPA expertise, e.g., we create a neural network with a probably flat optimization landscape by applying LiRPA to network parameters. Our opensource library is available at https://github.com/KaidiXu/auto_LiRPA.

  • 9 authors
·
Feb 28, 2020

Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery

Automated discovery of physical laws from observational data in the real world is a grand challenge in AI. Current methods, relying on symbolic regression or LLMs, are limited to uni-modal data and overlook the rich, visual phenomenological representations of motion that are indispensable to physicists. This "sensory deprivation" severely weakens their ability to interpret the inherent spatio-temporal patterns within dynamic phenomena. To address this gap, we propose VIPER-R1, a multimodal model that performs Visual Induction for Physics-based Equation Reasoning to discover fundamental symbolic formulas. It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process. The model is trained via a curriculum of Motion Structure Induction (MSI), using supervised fine-tuning to interpret kinematic phase portraits and to construct hypotheses guided by a Causal Chain of Thought (C-CoT), followed by Reward-Guided Symbolic Calibration (RGSC) to refine the formula structure with reinforcement learning. During inference, the trained VIPER-R1 acts as an agent: it first posits a high-confidence symbolic ansatz, then proactively invokes an external symbolic regression tool to perform Symbolic Residual Realignment (SR^2). This final step, analogous to a physicist's perturbation analysis, reconciles the theoretical model with empirical data. To support this research, we introduce PhysSymbol, a new 5,000-instance multimodal corpus. Experiments show that VIPER-R1 consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability, enabling more precise discovery of physical laws. Project page: https://jiaaqiliu.github.io/VIPER-R1/

  • 15 authors
·
Aug 24 2

FailureSensorIQ: A Multi-Choice QA Dataset for Understanding Sensor Relationships and Failure Modes

We introduce FailureSensorIQ, a novel Multi-Choice Question-Answering (MCQA) benchmarking system designed to assess the ability of Large Language Models (LLMs) to reason and understand complex, domain-specific scenarios in Industry 4.0. Unlike traditional QA benchmarks, our system focuses on multiple aspects of reasoning through failure modes, sensor data, and the relationships between them across various industrial assets. Through this work, we envision a paradigm shift where modeling decisions are not only data-driven using statistical tools like correlation analysis and significance tests, but also domain-driven by specialized LLMs which can reason about the key contributors and useful patterns that can be captured with feature engineering. We evaluate the Industrial knowledge of over a dozen LLMs-including GPT-4, Llama, and Mistral-on FailureSensorIQ from different lens using Perturbation-Uncertainty-Complexity analysis, Expert Evaluation study, Asset-Specific Knowledge Gap analysis, ReAct agent using external knowledge-bases. Even though closed-source models with strong reasoning capabilities approach expert-level performance, the comprehensive benchmark reveals a significant drop in performance that is fragile to perturbations, distractions, and inherent knowledge gaps in the models. We also provide a real-world case study of how LLMs can drive the modeling decisions on 3 different failure prediction datasets related to various assets. We release: (a) expert-curated MCQA for various industrial assets, (b) FailureSensorIQ benchmark and Hugging Face leaderboard based on MCQA built from non-textual data found in ISO documents, and (c) LLMFeatureSelector, an LLM-based feature selection scikit-learn pipeline. The software is available at https://github.com/IBM/FailureSensorIQ.

SeFAR: Semi-supervised Fine-grained Action Recognition with Temporal Perturbation and Learning Stabilization

Human action understanding is crucial for the advancement of multimodal systems. While recent developments, driven by powerful large language models (LLMs), aim to be general enough to cover a wide range of categories, they often overlook the need for more specific capabilities. In this work, we address the more challenging task of Fine-grained Action Recognition (FAR), which focuses on detailed semantic labels within shorter temporal duration (e.g., "salto backward tucked with 1 turn"). Given the high costs of annotating fine-grained labels and the substantial data needed for fine-tuning LLMs, we propose to adopt semi-supervised learning (SSL). Our framework, SeFAR, incorporates several innovative designs to tackle these challenges. Specifically, to capture sufficient visual details, we construct Dual-level temporal elements as more effective representations, based on which we design a new strong augmentation strategy for the Teacher-Student learning paradigm through involving moderate temporal perturbation. Furthermore, to handle the high uncertainty within the teacher model's predictions for FAR, we propose the Adaptive Regulation to stabilize the learning process. Experiments show that SeFAR achieves state-of-the-art performance on two FAR datasets, FineGym and FineDiving, across various data scopes. It also outperforms other semi-supervised methods on two classical coarse-grained datasets, UCF101 and HMDB51. Further analysis and ablation studies validate the effectiveness of our designs. Additionally, we show that the features extracted by our SeFAR could largely promote the ability of multimodal foundation models to understand fine-grained and domain-specific semantics.

  • 6 authors
·
Jan 2 2

Fine-Grained Perturbation Guidance via Attention Head Selection

Recent guidance methods in diffusion models steer reverse sampling by perturbing the model to construct an implicit weak model and guide generation away from it. Among these approaches, attention perturbation has demonstrated strong empirical performance in unconditional scenarios where classifier-free guidance is not applicable. However, existing attention perturbation methods lack principled approaches for determining where perturbations should be applied, particularly in Diffusion Transformer (DiT) architectures where quality-relevant computations are distributed across layers. In this paper, we investigate the granularity of attention perturbations, ranging from the layer level down to individual attention heads, and discover that specific heads govern distinct visual concepts such as structure, style, and texture quality. Building on this insight, we propose "HeadHunter", a systematic framework for iteratively selecting attention heads that align with user-centric objectives, enabling fine-grained control over generation quality and visual attributes. In addition, we introduce SoftPAG, which linearly interpolates each selected head's attention map toward an identity matrix, providing a continuous knob to tune perturbation strength and suppress artifacts. Our approach not only mitigates the oversmoothing issues of existing layer-level perturbation but also enables targeted manipulation of specific visual styles through compositional head selection. We validate our method on modern large-scale DiT-based text-to-image models including Stable Diffusion 3 and FLUX.1, demonstrating superior performance in both general quality enhancement and style-specific guidance. Our work provides the first head-level analysis of attention perturbation in diffusion models, uncovering interpretable specialization within attention layers and enabling practical design of effective perturbation strategies.

CellCLIP -- Learning Perturbation Effects in Cell Painting via Text-Guided Contrastive Learning

High-content screening (HCS) assays based on high-throughput microscopy techniques such as Cell Painting have enabled the interrogation of cells' morphological responses to perturbations at an unprecedented scale. The collection of such data promises to facilitate a better understanding of the relationships between different perturbations and their effects on cellular state. Towards achieving this goal, recent advances in cross-modal contrastive learning could, in theory, be leveraged to learn a unified latent space that aligns perturbations with their corresponding morphological effects. However, the application of such methods to HCS data is not straightforward due to substantial differences in the semantics of Cell Painting images compared to natural images, and the difficulty of representing different classes of perturbations (e.g., small molecule vs CRISPR gene knockout) in a single latent space. In response to these challenges, here we introduce CellCLIP, a cross-modal contrastive learning framework for HCS data. CellCLIP leverages pre-trained image encoders coupled with a novel channel encoding scheme to better capture relationships between different microscopy channels in image embeddings, along with natural language encoders for representing perturbations. Our framework outperforms current open-source models, demonstrating the best performance in both cross-modal retrieval and biologically meaningful downstream tasks while also achieving significant reductions in computation time.

  • 4 authors
·
May 16

The Policy Cliff: A Theoretical Analysis of Reward-Policy Maps in Large Language Models

Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal policy. We show that policy brittleness often stems from non-unique optimal actions, a common occurrence when multiple valid traces exist in a reasoning task. This theoretical lens provides a unified explanation for a range of seemingly disparate failures, reframing them as rational outcomes of optimizing rewards that may be incomplete or noisy, especially in the presence of action degeneracy. We extend this analysis from the fundamental single-reward setting to the more realistic multi-reward RL across diverse domains, showing how stability is governed by an "effective reward" aggregation mechanism. We also prove that entropy regularization restores policy stability at the cost of increased stochasticity. Our framework provides a unified explanation for recent empirical findings on deceptive reasoning, instruction-following trade-offs, and RLHF-induced sophistry, and is further validated through perturbation experiments in multi-reward RL. This work advances policy-stability analysis from empirical heuristics towards a principled theory, offering essential insights for designing safer and more trustworthy AI systems.

  • 1 authors
·
Jul 27

Preserving Statistical Validity in Adaptive Data Analysis

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

  • 6 authors
·
Nov 10, 2014

A Novel Bifurcation Method for Observation Perturbation Attacks on Reinforcement Learning Agents: Load Altering Attacks on a Cyber Physical Power System

Components of cyber physical systems, which affect real-world processes, are often exposed to the internet. Replacing conventional control methods with Deep Reinforcement Learning (DRL) in energy systems is an active area of research, as these systems become increasingly complex with the advent of renewable energy sources and the desire to improve their efficiency. Artificial Neural Networks (ANN) are vulnerable to specific perturbations of their inputs or features, called adversarial examples. These perturbations are difficult to detect when properly regularized, but have significant effects on the ANN's output. Because DRL uses ANN to map optimal actions to observations, they are similarly vulnerable to adversarial examples. This work proposes a novel attack technique for continuous control using Group Difference Logits loss with a bifurcation layer. By combining aspects of targeted and untargeted attacks, the attack significantly increases the impact compared to an untargeted attack, with drastically smaller distortions than an optimally targeted attack. We demonstrate the impacts of powerful gradient-based attacks in a realistic smart energy environment, show how the impacts change with different DRL agents and training procedures, and use statistical and time-series analysis to evaluate attacks' stealth. The results show that adversarial attacks can have significant impacts on DRL controllers, and constraining an attack's perturbations makes it difficult to detect. However, certain DRL architectures are far more robust, and robust training methods can further reduce the impact.

  • 3 authors
·
Jul 6, 2024

On the Robustness of Aspect-based Sentiment Analysis: Rethinking Model, Data, and Training

Aspect-based sentiment analysis (ABSA) aims at automatically inferring the specific sentiment polarities toward certain aspects of products or services behind the social media texts or reviews, which has been a fundamental application to the real-world society. Since the early 2010s, ABSA has achieved extraordinarily high accuracy with various deep neural models. However, existing ABSA models with strong in-house performances may fail to generalize to some challenging cases where the contexts are variable, i.e., low robustness to real-world environments. In this study, we propose to enhance the ABSA robustness by systematically rethinking the bottlenecks from all possible angles, including model, data, and training. First, we strengthen the current best-robust syntax-aware models by further incorporating the rich external syntactic dependencies and the labels with aspect simultaneously with a universal-syntax graph convolutional network. In the corpus perspective, we propose to automatically induce high-quality synthetic training data with various types, allowing models to learn sufficient inductive bias for better robustness. Last, we based on the rich pseudo data perform adversarial training to enhance the resistance to the context perturbation and meanwhile employ contrastive learning to reinforce the representations of instances with contrastive sentiments. Extensive robustness evaluations are conducted. The results demonstrate that our enhanced syntax-aware model achieves better robustness performances than all the state-of-the-art baselines. By additionally incorporating our synthetic corpus, the robust testing results are pushed with around 10% accuracy, which are then further improved by installing the advanced training strategies. In-depth analyses are presented for revealing the factors influencing the ABSA robustness.

  • 6 authors
·
Apr 19, 2023

A likelihood approach to nonparametric estimation of a singular distribution using deep generative models

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

  • 4 authors
·
May 9, 2021