Cross-Task Linearity Emerges in the Pretraining-Finetuning Paradigm

The pretraining-finetuning paradigm has become the prevailing trend in modern deep learning. In this work, we discover an intriguing linear phenomenon in models that are initialized from a common pretrained checkpoint and finetuned on different tasks, termed as Cross-Task Linearity (CTL). Specifically, if we linearly interpolate the weights of two finetuned models, the features in the weight-interpolated model are approximately equal to the linear interpolation of features in two finetuned models at each layer. Such cross-task linearity has not been noted in peer literature. We provide comprehensive empirical evidence supporting that CTL consistently occurs for finetuned models that start from the same pretrained checkpoint. We conjecture that in the pretraining-finetuning paradigm, neural networks essentially function as linear maps, mapping from the parameter space to the feature space. Based on this viewpoint, our study unveils novel insights into explaining model merging/editing, particularly by translating operations from the parameter space to the feature space. Furthermore, we delve deeper into the underlying factors for the emergence of CTL, emphasizing the impact of pretraining.

Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theory

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity

Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the spawning and permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.

Defects of Convolutional Decoder Networks in Frequency Representation

In this paper, we prove representation bottlenecks of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we introduce the rule of the forward propagation of such intermediate-layer spectrum maps, which is equivalent to the forward propagation of feature maps through a convolutional layer. Based on this, we find that each frequency component in the spectrum map is forward propagated independently with other frequency components. Furthermore, we prove two bottlenecks in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appears at certain frequencies.

Batch Normalization Is Blind to the First and Second Derivatives of the Loss

In this paper, we prove the effects of the BN operation on the back-propagation of the first and second derivatives of the loss. When we do the Taylor series expansion of the loss function, we prove that the BN operation will block the influence of the first-order term and most influence of the second-order term of the loss. We also find that such a problem is caused by the standardization phase of the BN operation. Experimental results have verified our theoretical conclusions, and we have found that the BN operation significantly affects feature representations in specific tasks, where losses of different samples share similar analytic formulas.

A Unified Game-Theoretic Interpretation of Adversarial Robustness

This paper provides a unified view to explain different adversarial attacks and defense methods, \emph{i.e.} the view of multi-order interactions between input variables of DNNs. Based on the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide a potential method to unify adversarial perturbations and robustness, which can explain the existing defense methods in a principle way. Besides, our findings also make a revision of previous inaccurate understanding of the shape bias of adversarially learned features.

Learning Baseline Values for Shapley Values

This paper aims to formulate the problem of estimating the optimal baseline values for the Shapley value in game theory. The Shapley value measures the attribution of each input variable of a complex model, which is computed as the marginal benefit from the presence of this variable w.r.t.its absence under different contexts. To this end, people usually set the input variable to its baseline value to represent the absence of this variable (i.e.the no-signal state of this variable). Previous studies usually determine the baseline values in an empirical manner, which hurts the trustworthiness of the Shapley value. In this paper, we revisit the feature representation of a deep model from the perspective of game theory, and define the multi-variate interaction patterns of input variables to define the no-signal state of an input variable. Based on the multi-variate interaction, we learn the optimal baseline value of each input variable. Experimental results have demonstrated the effectiveness of our method.

Game-theoretic Understanding of Adversarially Learned Features

This paper aims to understand adversarial attacks and defense from a new perspecitve, i.e., the signal-processing behavior of DNNs. We novelly define the multi-order interaction in game theory, which satisfies six properties. With the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide more insights into and make a revision of previous understanding for the shape bias of adversarially learned features. Besides, the multi-order interaction can also explain the recoverability of adversarial examples.