huashen218/convxai-cia-dataset huggingface dataset:
An Operator Theoretic View On Pruning Deep Neural Networks
Keywords: deep neural network pruning, Koopman operator theory

The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest. While many pruning methods have been developed to this end, the naïve approach of removing parameters based on their magnitude has been found to be as robust as more complex, state-of-the-art algorithms. The lack of theory behind magnitude pruning's success, especially pre-convergence, and its relation to other pruning methods, such as gradient based pruning, are outstanding open questions in the field that are in need of being addressed. We make use of recent advances in dynamical systems theory, namely Koopman operator theory, to define a new class of theoretically motivated pruning algorithms. We show that these algorithms can be equivalent to magnitude and gradient based pruning, unifying these seemingly disparate methods, and find that they can be used to shed light on magnitude pruning's performance during the early part of training.
Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?
Keywords: representation learning, perceptron capacity, perceptual manifolds, equivariance, cover's theorem, vc dimension

Equivariance has emerged as a desirable property of representations of objects subject to identity-preserving transformations that constitute a group, such as translations and rotations. However, the expressivity of a representation constrained by group equivariance is still not fully understood. We address this gap by providing a generalization of Cover's Function Counting Theorem that quantifies the number of linearly separable and group-invariant binary dichotomies that can be assigned to equivariant representations of objects. We find that the fraction of separable dichotomies is determined by the dimension of the space that is fixed by the group action. We show how this relation extends to operations such as convolutions, element-wise nonlinearities, and global and local pooling. While other operations do not change the fraction of separable dichotomies, local pooling decreases the fraction, despite being a highly nonlinear operation. Finally, we test our theory on intermediate representations of randomly initialized and fully trained convolutional neural networks and find perfect agreement.
Tuformer: Data-driven Design of Transformers for Improved Generalization or Efficiency
Keywords: Attention Modules, Transformers, Data-driven Model Design, Trainable Heads, Expressive Power, Tensor Methods.

Transformers are neural network architectures that achieve remarkable performance in many areas. However, the core component of Transformers, multi-head self-attention (MHSA), is mainly derived from heuristics, and the interactions across its components are not well understood. To address the problem, we first introduce a mathematically rigorous and yet intuitive tensor diagram representation of MHSA. Guided by tensor diagram representations, we propose a novel design, namely Tunable Transformers (Tuformers), by allowing data-driven weights across heads, whereas MHSA adopts pre-defined and fixed weights across heads, as will be explained in our paper. Tuformers naturally reveal a flexible design space that a user, depending on the needs, can choose a structure that has either improved performance (generalization error) or higher model efficiency. Any pre-trained Transformer can be an initialization of the corresponding Tuformer with trainable number of heads for efficient training and fine-tuning. Tuformers universally outperform Transformers on various tasks across multiple domains under a wide range of model sizes.
Learning Weakly-supervised Contrastive Representations
Keywords: Self-supervised Learning, Weakly Supervised Learning, Learning with Auxiliary Information, Clustering-based Representation Learning

We argue that a form of the valuable information provided by the auxiliary information is its implied data clustering information. For instance, considering hashtags as auxiliary information, we can hypothesize that an Instagram image will be semantically more similar with the same hashtags. With this intuition, we present a two-stage weakly-supervised contrastive learning approach. The first stage is to cluster data according to its auxiliary information. The second stage is to learn similar representations within the same cluster and dissimilar representations for data from different clusters. Our empirical experiments suggest the following three contributions. First, compared to conventional self-supervised representations, the auxiliary-information-infused representations bring the performance closer to the supervised representations, which use direct downstream labels as supervision signals. Second, our approach performs the best in most cases, when comparing our approach with other baseline representation learning methods that also leverage auxiliary data information. Third, we show that our approach also works well with unsupervised constructed clusters (e.g., no auxiliary information), resulting in a strong unsupervised representation learning approach.
Encoding Weights of Irregular Sparsity for Fixed-to-Fixed Model Compression
Keywords: Sparse Neural Network, Fixed-to-fixed data compression, Unstructured Pruning

Even though fine-grained pruning techniques achieve a high compression ratio, conventional sparsity representations (such as CSR) associated with irregular sparsity degrade parallelism significantly. Practical pruning methods, thus, usually lower pruning rates (by structured pruning) to improve parallelism. In this paper, we study fixed-to-fixed (lossless) encoding architecture/algorithm to support fine-grained pruning methods such that sparse neural networks can be stored in a highly regular structure. We first estimate the maximum compression ratio of encoding-based compression using entropy. Then, as an effort to push the compression ratio to the theoretical maximum (by entropy), we propose a sequential fixed-to-fixed encoding scheme. We demonstrate that our proposed compression scheme achieves almost the maximum compression ratio for the Transformer and ResNet-50 pruned by various fine-grained pruning methods.
An Experimental Design Perspective on Model-Based Reinforcement Learning
Keywords: reinforcement learning, acquisition function, information gain

In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an \emph{acquisition function} that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.
BAM: Bayes with Adaptive Memory
Keywords: Bayesian learning, online learning

Online learning via Bayes' theorem allows new data to be continuously integrated into an agent's current beliefs. However, a naive application of Bayesian methods in non-stationary environments leads to slow adaptation and results in state estimates that may converge confidently to the wrong parameter value. A common solution when learning in changing environments is to discard/downweight past data; however, this simple mechanism of "forgetting" fails to account for the fact that many real-world environments involve revisiting similar states. We propose a new framework, Bayes with Adaptive Memory (BAM), that takes advantage of past experience by allowing the agent to choose which past observations to remember and which to forget. We demonstrate that BAM generalizes many popular Bayesian update rules for non-stationary environments. Through a variety of experiments, we demonstrate the ability of BAM to continuously adapt in an ever-changing world.
Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop
Keywords: Unsupervised Learning, Full-Waveform Inversion, Partial Differential Equation, Physics-Informed Machine Learning

This paper investigates unsupervised learning of Full-Waveform Inversion (FWI), which has been widely used in geophysics to estimate subsurface velocity maps from seismic data. This problem is mathematically formulated by a second order partial differential equation (PDE), but is hard to solve. Moreover, acquiring velocity map is extremely expensive, making it impractical to scale up a supervised approach to train the mapping from seismic data to velocity maps with convolutional neural networks (CNN).We address these difficulties by $\textit{integrating PDE and CNN in a loop}$, thus shifting the paradigm to unsupervised learning that only requires seismic data. In particular, we use finite difference to approximate the forward modeling of PDE as a differentiable operator (from velocity map to seismic data) and model its inversion by CNN (from seismic data to velocity map). Hence, we transform the supervised inversion task into an unsupervised seismic data reconstruction task. We also introduce a new large-scale dataset $\textit{OpenFWI}$, to establish a more challenging benchmark for the community. Experiment results show that our model (using seismic data alone) yields comparable accuracy to the supervised counterpart (using both seismic data and velocity map). Furthermore, it outperforms the supervised model when involving more seismic data.
Conditional Contrastive Learning with Kernel
Keywords: Contrastive Learning, Conditional Sampling, Kernel methods

Conditional contrastive learning frameworks consider the conditional sampling procedure that constructs positive or negative data pairs conditioned on specific variables. Fair contrastive learning constructs negative pairs, for example, from the same gender (conditioning on sensitive information), which in turn reduces undesirable information from the learned representations; weakly supervised contrastive learning constructs positive pairs with similar annotative attributes (conditioning on auxiliary information), which in turn are incorporated into the representations. Although conditional contrastive learning enables many applications, the conditional sampling procedure can be challenging if we cannot obtain sufficient data pairs for some values of the conditioning variable. This paper presents Conditional Contrastive Learning with Kernel (CCL-K) that converts existing conditional contrastive objectives into alternative forms that mitigate the insufficient data problem. Instead of sampling data according to the value of the conditioning variable, CCL-K uses the Kernel Conditional Embedding Operator that samples data from all available data and assigns weights to each sampled data given the kernel similarity between the values of the conditioning variable. We conduct experiments using weakly supervised, fair, and hard negatives contrastive learning, showing CCL-K outperforms state-of-the-art baselines.
ConFeSS: A Framework for Single Source Cross-Domain Few-Shot Learning

Most current few-shot learning methods train a model from abundantly labeled base category data and then transfer and adapt the model to sparsely labeled novel category data. These methods mostly generalize well on novel categories from the same domain as the base categories but perform poorly for distant domain categories. In this paper, we propose a framework for few-shot learning coined as ConFeSS (Contrastive Learning and Feature Selection System) that tackles large domain shift between base and novel categories. The first step of our framework trains a feature extracting backbone with the contrastive loss on the base category data. Since the contrastive loss does not use supervision, the features can generalize better to distant target domains. For the second step, we train a masking module to select relevant features that are more suited to target domain classification. Finally, a classifier is fine-tuned along with the backbone such that the backbone produces features similar to the relevant ones. To evaluate our framework, we tested it on a recently introduced cross-domain few-shot learning benchmark. Experimental results demonstrate that our framework outperforms all meta-learning approaches and produces competitive results against recent cross-domain methods. Additional analyses are also performed to better understand our framework.
Granger causal inference on DAGs identifies genomic loci regulating transcription
Keywords: Granger causality, causal inference, graph neural networks, gene regulation, single-cell genomics, chromatin accessibility, directed acyclic graphs, single-cell multimodal

When a dynamical system can be modeled as a sequence of observations, Granger causality is a powerful approach for detecting predictive interactions between its variables. However, traditional Granger causal inference has limited utility in domains where the dynamics need to be represented as directed acyclic graphs (DAGs) rather than as a linear sequence, such as with cell differentiation trajectories. Here, we present GrID-Net, a framework based on graph neural networks with lagged message passing for Granger causal inference on DAG-structured systems. Our motivating application is the analysis of single-cell multimodal data to identify genomic loci that mediate the regulation of specific genes. To our knowledge, GrID-Net is the first single-cell analysis tool that accounts for the temporal lag between a genomic locus becoming accessible and its downstream effect on a target gene's expression. We applied GrID-Net on multimodal single-cell assays that profile chromatin accessibility (ATAC-seq) and gene expression (RNA-seq) in the same cell and show that it dramatically outperforms existing methods for inferring regulatory locus-gene links, achieving up to 71% greater agreement with independent population genetics-based estimates. By extending Granger causality to DAG-structured dynamical systems, our work unlocks new domains for causal analyses and, more specifically, opens a path towards elucidating gene regulatory interactions relevant to cellular differentiation and complex human diseases at unprecedented scale and resolution.
Energy-Inspired Molecular Conformation Optimization

This paper studies an important problem in computational chemistry: predicting a molecule's spatial atom arrangements, or a molecular conformation. We propose a neural energy minimization formulation that casts the prediction problem into an unrolled optimization process, where a neural network is parametrized to learn the gradient fields of an implicit conformational energy landscape. Assuming different forms of the underlying potential energy function, we can not only reinterpret and unify many of the existing models but also derive new variants of SE(3)-equivariant neural networks in a principled manner. In our experiments, these new variants show superior performance in molecular conformation optimization comparing to existing SE(3)-equivariant neural networks. Moreover, our energy-inspired formulation is also suitable for molecular conformation generation, where we can generate more diverse and accurate conformers comparing to existing baselines.
Towards Deepening Graph Neural Networks: A GNTK-based Optimization Perspective
Keywords: Trainablity, Graph Neural Tangent Kernel, Critical DropEdge

Graph convolutional networks (GCNs) and their variants have achieved great success in dealing with graph-structured data. Nevertheless, it is well known that deep GCNs suffer from the over-smoothing problem, where node representations tend to be indistinguishable as more layers are stacked up. The theoretical research to date on deep GCNs has focused primarily on expressive power rather than trainability, an optimization perspective. Compared to expressivity, trainability attempts to address a more fundamental question: Given a sufficiently expressive space of models, can we successfully find a good solution via gradient descent-based optimizers? This work fills this gap by exploiting the Graph Neural Tangent Kernel (GNTK), which governs the optimization trajectory under gradient descent for wide GCNs. We formulate the asymptotic behaviors of GNTK in the large depth, which enables us to reveal the dropping trainability of wide and deep GCNs at an exponential rate in the optimization process. Additionally, we extend our theoretical framework to analyze residual connection-based techniques, which are found to be merely able to mitigate the exponential decay of trainability mildly. Inspired by our theoretical insights on trainability, we propose Critical DropEdge, a connectivity-aware and graph-adaptive sampling method, to alleviate the exponential decay problem more fundamentally. Experimental evaluation consistently confirms using our proposed method can achieve better results compared to relevant counterparts with both infinite-width and finite-width.
Connectome-constrained Latent Variable Model of Whole-Brain Neural Activity
Keywords: connectome, latent-variable model, variational autoencoder, biophysics, whole-brain, neural activity, calcium imaging, caenorhabditis elegans, voltage, generative model, inference network

The availability of both anatomical connectivity and brain-wide neural activity measurements in C. elegans make the worm a promising system for learning detailed, mechanistic models of an entire nervous system in a data-driven way. However, one faces several challenges when constructing such a model. We often do not have direct experimental access to important modeling details such as single-neuron dynamics and the signs and strengths of the synaptic connectivity. Further, neural activity can only be measured in a subset of neurons, often indirectly via calcium imaging, and significant trial-to-trial variability has been observed. To address these challenges, we introduce a connectome-constrained latent variable model (CC-LVM) of the unobserved voltage dynamics of the entire C. elegans nervous system and the observed calcium signals. We used the framework of variational autoencoders to fit parameters of the mechanistic simulation constituting the generative model of the LVM to calcium imaging observations. A variational approximate posterior distribution over latent voltage traces for all neurons is efficiently inferred using an inference network, and constrained by a prior distribution given by the biophysical simulation of neural dynamics. We applied this model to an experimental whole-brain dataset, and found that connectomic constraints enable our LVM to predict the activity of neurons whose activity were withheld significantly better than models unconstrained by a connectome. We explored models with different degrees of biophysical detail, and found that models with realistic conductance-based synapses provide markedly better predictions than current-based synapses for this system.
T-WaveNet: A Tree-Structured Wavelet Neural Network for Time Series Signal Analysis

Time series signal analysis plays an essential role in many applications, e.g., activity recognition and healthcare monitoring.
        Recently, features extracted with deep neural networks (DNNs) have shown to be more effective than conventional hand-crafted ones.
        However, most existing solutions rely solely on the network to extract information carried in the raw signal, regardless of its inherent physical and statistical properties, leading to sub-optimal performance particularly under a limited amount of training data.
        In this work, we propose a novel tree-structured wavelet neural network for time series signal analysis, namely \emph{T-WaveNet}, taking advantage of an inherent property of various types of signals, known as the \emph{dominant frequency range}. Specifically, with \emph{T-WaveNet}, we first conduct frequency spectrum energy analysis of the signals to get a set of dominant frequency subbands. Then, we construct a tree-structured network that iteratively decomposes the input signal into various frequency subbands with similar energies. Each node on the tree is built with an invertible neural network (INN) based wavelet transform unit. Such a disentangled representation learning method facilitates a more effective extraction of the discriminative features, as demonstrated with the comprehensive experiments on various real-life time series classification datasets.
Trans-Encoder: Unsupervised sentence-pair modelling through self- and mutual-distillations
Keywords: self-supervised learning, sentence embeddings, sentence representations, knowledge distillation

In NLP, a large volume of tasks involve pairwise comparison between two sequences (e.g. sentence similarity and paraphrase identification). Predominantly, two formulations are used for sentence-pair tasks: bi-encoders and cross-encoders. Bi-encoders produce fixed-dimensional sentence representations and are computationally efficient, however, they usually underperform cross-encoders. Cross-encoders can leverage their attention heads to exploit inter-sentence interactions for better performance but they require task fine-tuning and are computationally more expensive. In this paper, we present a completely unsupervised sentence representation model termed as Trans-Encoder that combines the two learning paradigms into an iterative joint framework to simultaneously learn enhanced bi- and cross-encoders. Specifically, on top of a pre-trained Language Model (PLM), we start with converting it to an unsupervised bi-encoder, and then alternate between the bi- and cross-encoder task formulations. In each alternation, one task formulation will produce pseudo-labels which are used as learning signals for the other task formulation. We then propose an extension to conduct such self-distillation approach on multiple PLMs in parallel and use the average of their pseudo-labels for mutual distillation. Trans-Encoder creates, to the best of our knowledge, the first completely unsupervised cross-encoder and also a state-of-the-art unsupervised bi-encoder for sentence similarity. Both the bi-encoder and cross-encoder formulations of Trans-Encoder outperform recently proposed state-of-the-art unsupervised sentence encoders such as Mirror-BERT and SimCSE by up to 5% on the sentence similarity benchmarks.