Large language models exhibit intelligence without genuine epistemic understanding, exposing a key gap: the absence of epistemic architecture. This paper introduces the Structured Cognitive Loop (SCL) as an executable epistemological framework for emergent intelligence. Unlike traditional AI research asking "what is intelligence?" (ontological), SCL asks "under what conditions does cognition emerge?" (epistemological). Grounded in philosophy of mind and cognitive phenomenology, SCL bridges conceptual philosophy and implementable cognition. Drawing on process philosophy, enactive cognition, and extended mind theory, we define intelligence not as a property but as a performed process -- a continuous loop of judgment, memory, control, action, and regulation. SCL makes three contributions. First, it operationalizes philosophical insights into computationally interpretable structures, enabling "executable epistemology" -- philosophy as structural experiment. Second, it shows that functional separation within cognitive architecture yields more coherent and interpretable behavior than monolithic prompt based systems, supported by agent evaluations. Third, it redefines intelligence: not representational accuracy but the capacity to reconstruct its own epistemic state through intentional understanding. This framework impacts philosophy of mind, epistemology, and AI. For philosophy, it allows theories of cognition to be enacted and tested. For AI, it grounds behavior in epistemic structure rather than statistical regularity. For epistemology, it frames knowledge not as truth possession but as continuous reconstruction within a phenomenologically coherent loop. We situate SCL within debates on cognitive phenomenology, emergence, normativity, and intentionality, arguing that real progress requires not larger models but architectures that realize cognitive principles structurally.

Such assumptions are necessary for exact recovery to be information-theoretically possible.

Clustering based on vibration responses, such as transmissibility functions (TFs), is promising in structural anomaly detection, but most existing approaches struggle with determining the optimal cluster number and handling high-dimensional streaming data, while their shallow structures also make them sensitive to manually-engineered feature quality. To bridge this gap, this work proposes the Dirichlet process-deep generative model-integrated incremental learning (DPGIIL) for clustering by combining the advantages of deep generative models (DGMs) in representation learning and the Dirichlet process mixture model (DPMM) in identifying distinct patterns in observed data. By introducing a DPMM prior into the latent space of DGMs, DPGIIL automatically captures dissimilarities in extracted latent representations, enabling both generative modeling and clustering. Within the context of variational Bayesian inference, a lower bound on the log marginal likelihood of DPGIIL, tighter than the evidence lower bound given sufficient training data, is derived analytically, which enables the joint optimization of DGM and DPMM parameters, thereby allowing the DPMM to regularize the DGM's feature extraction process. Additionally, a greedy split-merge scheme-based coordinate ascent variational inference method is devised to accelerate the optimization. The summary statistics of the DPMM, along with the network parameters, are used to retain information about previous data for incremental learning. Notably, this study uses variational autoencoder (VAE) within DPGIIL as an illustrative example, while this framework is adaptable to other DGMs. Two case studies show that the proposed method outperforms some state-of-the-art approaches in structural anomaly detection and clustering, while also dynamically generating new clusters to indicate the emergence of new structural conditions for online monitoring.

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where $\tilde A=SA$. This phenomenon, which we call inversion bias, arises, e.g., in statistics and distributed optimization, when averaging multiple independently constructed estimates of quantities that depend on the inverse covariance. We develop a framework for analyzing inversion bias, based on our proposed concept of an $(\epsilon,\delta)$-unbiased estimator for random matrices. We show that when the sketching matrix $S$ is dense and has i.i.d. sub-gaussian entries, then after simple rescaling, the estimator $(\frac m{m-d}\tilde A^\top\tilde A)^{-1}$ is $(\epsilon,\delta)$-unbiased for $(A^\top A)^{-1}$ with a sketch of size $m=O(d+\sqrt d/\epsilon)$. This implies that for $m=O(d)$, the inversion bias of this estimator is $O(1/\sqrt d)$, which is much smaller than the $\Theta(1)$ approximation error obtained as a consequence of the subspace embedding guarantee for sub-gaussian sketches. We then propose a new sketching technique, called LEverage Score Sparsified (LESS) embeddings, which uses ideas from both data-oblivious sparse embeddings as well as data-aware leverage-based row sampling methods, to get $\epsilon$ inversion bias for sketch size $m=O(d\log d+\sqrt d/\epsilon)$ in time $O(\text{nnz}(A)\log n+md^2)$, where nnz is the number of non-zeros. The key techniques enabling our analysis include an extension of a classical inequality of Bai and Silverstein for random quadratic forms, which we call the Restricted Bai-Silverstein inequality; and anti-concentration of the Binomial distribution via the Paley-Zygmund inequality, which we use to prove a lower bound showing that leverage score sampling sketches generally do not achieve small inversion bias.

Statistical tests are a crucial tool in scientific endeavors to analyze data: We routinely model data to be a set of samples from an unknown distribution, and use statist ical tests to infer or verify the properties of the underlying distribution. While these tests typically oper ate under the assumption that data points are drawn from a single underlying distribution, in applications, usually the dat a is gathered from multiple sources. Furthermore in many situations, it is the case that the datas et contains only a few data points from each source. For example, an online shop may have the purchase his tory of thousands of customers while each customer may shop at the store a small number of times. Altern atively, a medical dataset might record the lifestyle behaviors of patients of a particular disease whi le only having few data points from any specific demographic (such as age). On the other hand, data that comes from multiple sources may r esult in a dataset consisting of a collection of unconnected and unrelated data points.

Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simple, iterative, sketching-based algorithm for RFDA that comes with provable accuracy guarantees when compared to the conventional approach. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized linear algebra. We analyze the behavior of RFDA when the ridge leverage and the standard leverage scores are used to select predictor variables and we prove that accurate approximations can be achieved by a sample whose size depends on the effective degrees of freedom of the RFDA problem. Our results yield significant improvements over existing approaches and our empirical evaluations support our theoretical analyses.

We propose Progressive Structure-conditional Generative Adversarial Networks (PSGAN), a new framework that can generate full-body and high-resolution character images based on structural information. Recent progress in generative adversarial networks with progressive training has made it possible to generate high-resolution images. However, existing approaches have limitations in achieving both high image quality and structural consistency at the same time. Our method tackles the limitations by progressively increasing the resolution of both generated images and structural conditions during training. In this paper, we empirically demonstrate the effectiveness of this method by showing the comparison with existing approaches and video generation results of diverse anime characters at 1024x1024 based on target pose sequences. We also create a novel dataset containing full-body 1024x1024 high-resolution images and exact 2D pose keypoints using Unity 3D Avatar models.

This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference framework, and establish sufficient conditions on the required sample complexities under which these methods succeed (with high probability) in accurately locating the outliers for each task. Comprehensive numerical experimental results are provided to verify the theoretical bounds and demonstrate the computational efficiency of the proposed algorithm.