Yi‐Zhuang You

Weitang Liu, Ying-Wai Li, Yi-Zhuang You et al.

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, the Wang-Landau algorithm, by replacing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings - for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.

Artan Sheshmani, Yizhuang You, Wenbo Fu et al.

Following the earlier formalism of the categorical representation learning (arXiv:2103.14770) by the first two authors, we discuss the construction of the "RG-flow based categorifier". Borrowing ideas from theory of renormalization group flows (RG) in quantum field theory, holographic duality, and hyperbolic geometry, and mixing them with neural ODE's, we construct a new algorithmic natural language processing (NLP) architecture, called the RG-flow categorifier or for short the RG categorifier, which is capable of data classification and generation in all layers. We apply our algorithmic platform to biomedical data sets and show its performance in the field of sequence-to-function mapping. In particular we apply the RG categorifier to particular genomic sequences of flu viruses and show how our technology is capable of extracting the information from given genomic sequences, find their hidden symmetries and dominant features, classify them and use the trained data to make stochastic prediction of new plausible generated sequences associated with new set of viruses which could avoid the human immune system. The content of the current article is part of the recent US patent application submitted by first two authors (U.S. Patent Application No.: 63/313.504).

Ruyi Tao, Ningning Tao, Yi-zhuang You et al.

Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. For deterministic dynamics, our framework can discern whether the dynamics are self-similar. For uncertain dynamics, it can compare and determine which parameter set is closer to self-similarity. The framework allows us to extract scale-invariant kernels from the dynamics for modeling at any scale. Moreover, our method can identify the power law exponents in self-similar systems. Preliminary tests on the Ising model yielded critical exponents consistent with theoretical expectations, providing valuable insights for addressing critical phase transitions in non-equilibrium systems.

Wanda Hou, Miao Li, Yi-Zhuang You

Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator valued measurements, replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model's expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces negative log likelihood compared to one hot embeddings, with higher physical dimensions further enhancing single site probabilities and multi site correlations. The model also outperforms GPT2 in single site estimation and achieves competitive correlation modeling, showcasing the potential of trainable POVM embeddings for complex data correlations in quantum inspired sequence modeling.

Weitang Liu, Ying Wai Li, Yuelei Li et al.

Evaluating models on datasets often fails to capture their behavior when faced with unexpected and diverse types of inputs. It would be beneficial if we could evaluate the difference between human annotation and model prediction for an internet number of inputs, or more generally, for an input space that enumeration is computationally impractical. Traditional model evaluation methods rely on precision and recall (PR) as metrics, which are typically estimated by comparing human annotations with model predictions on a specific dataset. This is feasible because enumerating thousands of test inputs is manageable. However, estimating PR across a large input space is challenging because enumeration becomes computationally infeasible. We propose OmniInput, a novel approach to evaluate and compare NNs by the PR of an input space. OmniInput is distinctive from previous works as its estimated PR reflects the estimation of the differences between human annotation and model prediction in the input space which is usually too huge to be enumerated. We empirically validate our method within an enumerable input space, and our experiments demonstrate that OmniInput can effectively estimate and compare precision and recall for (large) language models within a broad input space that is not enumerable.

Artan Sheshmani, Yizhuang You

We provide a construction for categorical representation learning and introduce the foundations of "$\textit{categorifier}$". The central theme in representation learning is the idea of $\textbf{everything to vector}$. Every object in a dataset $\mathcal{S}$ can be represented as a vector in $\mathbb{R}^n$ by an $\textit{encoding map}$ $E: \mathcal{O}bj(\mathcal{S})\to\mathbb{R}^n$. More importantly, every morphism can be represented as a matrix $E: \mathcal{H}om(\mathcal{S})\to\mathbb{R}^{n}_{n}$. The encoding map $E$ is generally modeled by a $\textit{deep neural network}$. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a $\textit{set-theoretic}$ approach. The goal of the current article is to promote the representation learning to a new level via a $\textit{category-theoretic}$ approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Hong-Ye Hu, Yi-Zhuang You

Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. Facing the challenge of realizing deep unitary circuits on near-term quantum devices, we explore the scenario in which the unitary channel can be shallow and is generated by a quantum chaotic Hamiltonian via time evolution. We provide an unbiased estimator of the density matrix for all ranges of the evolution time. We analyze the sample complexity of the Hamiltonian-driven shadow tomography. For Pauli observables, we find that it can be more efficient than the unitary-2-design-based shadow tomography in a sequence of intermediate time windows that range from an order-1 scrambling time to a time scale of $D^{1/6}$, given the Hilbert space dimension $D$. In particular, the efficiency of predicting diagonal Pauli observables is improved by a factor of $D$ without sacrificing the efficiency of predicting off-diagonal Pauli observables.

Hong-Ye Hu, Dian Wu, Yi-Zhuang You et al.

Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has $O(\log L)$ complexity for inpainting of an image with edge length $L$, compared to previous generative models with $O(L^2)$ complexity.

Huitao Shen, Pengfei Zhang, Yi-Zhuang You et al.

The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wavefunction into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information, a quantity recently developed to characterize information scrambling, to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.