This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can benefit both communities. Our work generalizes popular tensor factorizations within the circuit language, and unifies various circuit learning algorithms under a single, generalized hierarchical factorization framework. Specifically, we introduce a modular "Lego block" approach to build tensorized circuit architectures. This, in turn, allows us to systematically construct and explore various circuit and tensor factorization models while maintaining tractability. This connection not only clarifies similarities and differences in existing models, but also enables the development of a comprehensive pipeline for building and optimizing new circuit/tensor factorization architectures. We show the effectiveness of our framework through extensive empirical evaluations, and highlight new research opportunities for tensor factorizations in probabilistic modeling.

This paper introduces a novel framework for Archetypal Analysis (AA) tailored to ordinal data, particularly from questionnaires. Unlike existing methods, the proposed method, Ordinal Archetypal Analysis (OAA), bypasses the two-step process of transforming ordinal data into continuous scales and operates directly on the ordinal data. We extend traditional AA methods to handle the subjective nature of questionnaire-based data, acknowledging individual differences in scale perception. We introduce the Response Bias Ordinal Archetypal Analysis (RBOAA), which learns individualized scales for each subject during optimization. The effectiveness of these methods is demonstrated on synthetic data and the European Social Survey dataset, highlighting their potential to provide deeper insights into human behavior and perception. The study underscores the importance of considering response bias in cross-national research and offers a principled approach to analyzing ordinal data through Archetypal Analysis.

While memory-augmented neural networks (MANNs) offer an effective solution for few-shot learning (FSL) by integrating deep neural networks with external memory, the capacity requirements and energy overhead of data movement become enormous due to the large number of support vectors in many-class FSL scenarios. Various in-memory search solutions have emerged to improve the energy efficiency of MANNs. NAND-based multi-bit content addressable memory (MCAM) is a promising option due to its high density and large capacity. Despite its potential, MCAM faces limitations such as a restricted number of word lines, limited quantization levels, and non-ideal effects like varying string currents and bottleneck effects, which lead to significant accuracy drops. To address these issues, we propose several innovative methods. First, the Multi-bit Thermometer Code (MTMC) leverages the extensive capacity of MCAM to enhance vector precision using cumulative encoding rules, thereby mitigating the bottleneck effect. Second, the Asymmetric vector similarity search (AVSS) reduces the precision of the query vector while maintaining that of the support vectors, thereby minimizing the search iterations and improving efficiency in many-class scenarios. Finally, the Hardware-Aware Training (HAT) method optimizes controller training by modeling the hardware characteristics of MCAM, thus enhancing the reliability of the system. Our integrated framework reduces search iterations by up to 32 times, and increases overall accuracy by 1.58% to 6.94%.

We present a new perspective on how readers integrate context during real-time language comprehension. Our proposals build on surprisal theory, which posits that the processing effort of a linguistic unit (e.g., a word) is an affine function of its in-context information content. We first observe that surprisal is only one out of many potential ways that a contextual predictor can be derived from a language model. Another one is the pointwise mutual information (PMI) between a unit and its context, which turns out to yield the same predictive power as surprisal when controlling for unigram frequency. Moreover, both PMI and surprisal are correlated with frequency. This means that neither PMI nor surprisal contains information about context alone. In response to this, we propose a technique where we project surprisal onto the orthogonal complement of frequency, yielding a new contextual predictor that is uncorrelated with frequency. Our experiments show that the proportion of variance in reading times explained by context is a lot smaller when context is represented by the orthogonalized predictor. From an interpretability standpoint, this indicates that previous studies may have overstated the role that context has in predicting reading times.

The number of free parameters, or dimension, of a model is a straightforward way to measure its complexity: a model with more parameters can encode more information. However, this is not an accurate measure of complexity: models capable of memorizing their training data often generalize well despite their high dimension. Effective dimension aims to more directly capture the complexity of a model by counting only the number of parameters required to represent the functionality of the model. Singular learning theory (SLT) proposes the learning coefficient $ \lambda $ as a more accurate measure of effective dimension. By describing the rate of increase of the volume of the region of parameter space around a local minimum with respect to loss, $ \lambda $ incorporates information from higher-order terms. We compare $ \lambda $ of models trained using natural gradient descent (NGD) and stochastic gradient descent (SGD), and find that those trained with NGD consistently have a higher effective dimension for both of our methods: the Hessian trace $ \text{Tr}(\mathbf{H}) $, and the estimate of the local learning coefficient (LLC) $ \hat{\lambda}(w^*) $.

Graph Contrastive Learning (GCL) seeks to learn nodal or graph representations that contain maximal consistent information from graph-structured data. While node-level contrasting modes are dominating, some efforts commence to explore consistency across different scales. Yet, they tend to lose consistent information and be contaminated by disturbing features. Here, we introduce MUX-GCL, a novel cross-scale contrastive learning paradigm that utilizes multiplex representations as effective patches. While this learning mode minimizes contaminating noises, a commensurate contrasting strategy using positional affinities further avoids information loss by correcting false negative pairs across scales. Extensive downstream experiments demonstrate that MUX-GCL yields multiple state-of-the-art results on public datasets. Our theoretical analysis further guarantees the new objective function as a stricter lower bound of mutual information of raw input features and output embeddings, which rationalizes this paradigm. Code is available at https://github.com/MUX-GCL/Code.

We propose a prototype-based federated learning method designed for embedding networks in classification or verification tasks. Our focus is on scenarios where each client has data from a single class. The main challenge is to develop an embedding network that can distinguish between different classes while adhering to privacy constraints. Sharing true class prototypes with the server or other clients could potentially compromise sensitive information. To tackle this issue, we propose a proxy class prototype that will be shared among clients instead of the true class prototype. Our approach generates proxy class prototypes by linearly combining them with their nearest neighbors. This technique conceals the true class prototype while enabling clients to learn discriminative embedding networks. We compare our method to alternative techniques, such as adding random Gaussian noise and using random selection with cosine similarity constraints. Furthermore, we evaluate the robustness of our approach against gradient inversion attacks and introduce a measure for prototype leakage. This measure quantifies the extent of private information revealed when sharing the proposed proxy class prototype. Moreover, we provide a theoretical analysis of the convergence properties of our approach. Our proposed method for federated learning from scratch demonstrates its effectiveness through empirical results on three benchmark datasets: CIFAR-100, VoxCeleb1, and VGGFace2.

We study the problem of multiclass classification for settings where data features $\mathbf{x}$ and their labels $\mathbf{y}$ are uncertain. We identify that distributionally robust one-vs-all (OVA) classifiers often struggle in settings with imbalanced data. To address this issue, we use Wasserstein distributionally robust optimization to develop a robust version of the multiclass support vector machine (SVM) characterized by the Crammer-Singer (CS) loss. First, we prove that the CS loss is bounded from above by a Lipschitz continuous function for all $\mathbf{x} \in \mathcal{X}$ and $\mathbf{y} \in \mathcal{Y}$, then we exploit strong duality results to express the dual of the worst-case risk problem, and we show that the worst-case risk minimization problem admits a tractable convex reformulation due to the regularity of the CS loss. Moreover, we develop a kernel version of our proposed model to account for nonlinear class separation, and we show that it admits a tractable convex upper bound. We also propose a projected subgradient method algorithm for a special case of our proposed linear model to improve scalability. Our numerical experiments demonstrate that our model outperforms state-of-the art OVA models in settings where the training data is highly imbalanced. We also show through experiments on popular real-world datasets that our proposed model often outperforms its regularized counterpart as the first accounts for uncertain labels unlike the latter.

Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.

Recent advancements in automatic speaker verification (ASV) studies have been achieved by leveraging large-scale pretrained networks. In this study, we analyze the approaches toward such a paradigm and underline the significance of interlayer information processing as a result. Accordingly, we present a novel approach for exploiting the multilayered nature of pretrained models for ASV, which comprises a layer/frame-level network and two steps of pooling architectures for each layer and frame axis. Specifically, we let convolutional architecture directly processes a stack of layer outputs.Then, we present a channel attention-based scheme of gauging layer significance and squeeze the layer level with the most representative value. Finally, attentive statistics over frame-level representations yield a single vector speaker embedding. Comparative experiments are designed using versatile data environments and diverse pretraining models to validate the proposed approach. The experimental results demonstrate the stability of the approach using multi-layer outputs in leveraging pretrained architectures. Then, we verify the superiority of the proposed ASV backend structure, which involves layer-wise operations, in terms of performance improvement along with cost efficiency compared to the conventional method. The ablation study shows how the proposed interlayer processing aids in maximizing the advantage of utilizing pretrained models.