arXiv subjects

Yoshinari Takeishi

Publications and source records attributed to Yoshinari Takeishi.

7 recordsLinked to original sources

arXiv2026

Improving the Robustness/Accuracy Tradeoff Against Adversarial Attacks Using Information Bottleneck Distillation Through Dual Teachers

Deep neural networks (DNNs) have achieved remarkable success in classical machine learning problems. However, they are known to be vulnerable to adversarial attacks. Countermeasures proposed in the literature, notably Information Bottleneck Distillation (IBD) introduced by Kuang et al., degrade the classification accuracy on clean inputs while improving the robustness to adversarial inputs. In this work, we extend the IBD framework by introducing an extra teacher model (clean teacher) trained with only clean inputs, into the distillation process from a robust teacher model trained by adversarial training. The features of both clean and robust teachers are transferred to the student through a cross-layer attention matrix. Experimental results on the CIFAR-10 and CIFAR-100 datasets show that the proposed method improves classification accuracy on clean samples compared to the original IBD, while maintaining similar accuracy on adversarial samples. Furthermore, our methods are competitive with state-of-the-art approaches, including the recent dual-teacher distillation framework B-MTARD, particularly in terms of the harmonic mean between clean and robust accuracy. We also analyze the impact of different training settings that have different influences on the attention module.

cs.LG↗

arXiv2026

Approximating Simple ReLU Networks based on Spectral Decomposition of Fisher Information

Properties of Fisher information matrices of 2-layer neural ReLU networks with random hidden weights are studied. For these networks, it is known that the eigenvalue distribution highly concentrates on several eigenspaces approximately. In particular, the eigenvalues for the first three eigenspaces account for 97.7% of the trace of the Fisher information matrix, independently of the number of parameters. In this paper, we identify the function spaces which correspond to those major eigenspaces. This function space consists of the spherical harmonic functions whose orders are not greater than 2. This result relates to the Mercer decomposition of the neural tangent kernels.

stat.ML↗

arXiv2025

Neural Tangent Kernels and Fisher Information Matrices for Simple ReLU Networks with Random Hidden Weights

Fisher information matrices and neural tangent kernels (NTK) for 2-layer ReLU networks with random hidden weight are argued. We discuss the relation between both notions as a linear transformation and show that spectral decomposition of NTK with concrete forms of eigenfunctions with major eigenvalues. We also obtain an approximation formula of the functions presented by the 2-layer neural networks.

cs.LG↗

arXiv2025

Sparse Superposition Codes with Binomial Dictionary are Capacity-Achieving with Maximum Likelihood Decoding

It is known that sparse superposition codes asymptotically achieve the channel capacity over the additive white Gaussian noise channel with both maximum likelihood decoding and efficient decoding (Joseph and Barron in 2012, 2014). Takeishi et al. (in 2014, 2019) demonstrated that these codes can also asymptotically achieve the channel capacity with maximum likelihood decoding when the dictionary is drawn from a Bernoulli distribution. In this paper, we extend these results by showing that the dictionary distribution can be naturally generalized to the binomial distribution.

cs.IT↗

arXiv2024

Risk Bounds on MDL Estimators for Linear Regression Models with Application to Simple ReLU Neural Networks

To investigate the theoretical foundations of deep learning from the viewpoint of the minimum description length (MDL) principle, we analyse risk bounds of MDL estimators based on two-stage codes for simple two-layers neural networks (NNs) with ReLU activation. For that purpose, we propose a method to design two-stage codes for linear regression models and establish an upper bound on the risk of the corresponding MDL estimators based on the theory of MDL estimators originated by Barron and Cover (1991). Then, we apply this result to the simple two-layers NNs with ReLU activation which consist of $d$ nodes in the input layer, $m$ nodes in the hidden layer and one output node. Since the object of estimation is only the $m$ weights from the hidden layer to the output node in our setting, this is an example of linear regression models. As a result, we show that the redundancy of the obtained two-stage codes is small owing to the fact that the eigenvalue distribution of the Fisher information matrix of the NNs is strongly biased, which was shown by Takeishi et al. (2023) and has been refined in this paper. That is, we establish a tight upper bound on the risk of our MDL estimators. Note that our risk bound for the simple ReLU networks, of which the leading term is $O(d^2 \log n /n)$, is independent of the number of parameters $m$.

cs.IT↗

arXiv2023

Approximate Spectral Decomposition of Fisher Information Matrix for Simple ReLU Networks

We argue the Fisher information matrix (FIM) of one hidden layer networks with the ReLU activation function. For a network, let $W$ denote the $d \times p$ weight matrix from the $d$-dimensional input to the hidden layer consisting of $p$ neurons, and $v$ the $p$-dimensional weight vector from the hidden layer to the scalar output. We focus on the FIM of $v$, which we denote as $I$. Under certain conditions, we characterize the first three clusters of eigenvalues and eigenvectors of the FIM. Specifically, we show that 1) Since $I$ is non-negative owing to the ReLU, the first eigenvalue is the Perron-Frobenius eigenvalue. 2) For the cluster of the next maximum values, the eigenspace is spanned by the row vectors of $W$. 3) The direct sum of the eigenspace of the first eigenvalue and that of the third cluster is spanned by the set of all the vectors obtained as the Hadamard product of any pair of the row vectors of $W$. We confirmed by numerical calculation that the above is approximately correct when the number of hidden nodes is about 10000.

cs.LG↗

arXiv2018

An Improved Analysis of Least Squares Superposition Codes with Bernoulli Dictionary

For the additive white Gaussian noise channel with average power constraint, sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. While the codewords of the original sparse superposition codes are made with a dictionary matrix drawn from a Gaussian distribution, we consider the case that it is drawn from a Bernoulli distribution. We show an improved upper bound on its block error probability with least squares decoding, which is fairly simplified and tighter bound than our previous result in 2014.

cs.IT↗