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Dai Shi

Dai Shi appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.PR Artificial Intelligence astro-ph.HE Computation and Language Machine Learning

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preprint2026arXiv

Cognifold: Always-On Proactive Memory via Cognitive Folding

Existing agent memory remains predominantly reactive and retrieval-based, lacking the capacity to autonomously organize experience into persistent cognitive structure. Toward genuinely autonomous agents, we introduce Cognifold, a brain-inspired "always-on" agent memory designed for the next generation of proactive assistants. CogniFold continuously folds fragmented event streams into self-emerging cognitive structures, bootstrapping progressively higher-level cognition from incoming events and accumulated knowledge. We ground this by extending Complementary Learning Systems (CLS) theory from two layers (hippocampus, neocortex) to three, adding a prefrontal intent layer. Emulating the prefrontal cortex as the locus of intentional control and decision-making, CogniFold achieves this through graph-topology self-organization: cognitive structures proactively assemble under the stream, merge when semantically similar, decay when stale, relink through associative recall, and surface intents when concept-cluster density crosses a threshold. We evaluate structural formation using CogEval-Bench, demonstrating that CogniFold uniquely produces memory structures that match cognitive expectations and concept emergence. Furthermore, across 7 broad-coverage benchmarks spanning five cognitive domains, we validate that CogniFold simultaneously performs robustly on conventional memory benchmarks.

preprint2026arXiv

LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection

Orthogonal parameter-efficient fine-tuning (PEFT) adapts pretrained weights through structure-preserving multiplicative transformations, but existing methods often conflate two distinct design choices: the subspace in which adaptation occurs and the transformation applied within that subspace. This paper introduces LOFT, a low-rank orthogonal fine-tuning framework that explicitly separates these two components. By viewing orthogonal adaptation as a multiplicative subspace rotation, LOFT provides a unified formulation that recovers representative orthogonal PEFT methods, including coordinate-, butterfly-, Householder-, and principal-subspace-based variants. More importantly, this perspective exposes support selection as a central design axis rather than a byproduct of a particular parameterization. We develop a first-order analysis showing that useful adaptation supports should be informed by the downstream training signal, motivating practical task-aware support selection strategies. Across language understanding, visual transfer, mathematical reasoning, and multilingual out-of-distribution adaptation, LOFT recovers principal-subspace orthogonal adaptation while gradient-informed supports improve the efficiency-performance trade-off under matched parameter, memory, and compute budgets. These results suggest that principled support selection is an important direction for improving orthogonal PEFT.

preprint2020arXiv

A Fast Radio Burst discovered in FAST drift scan survey

We report the discovery of a highly dispersed fast radio burst, FRB~181123, from an analysis of $\sim$1500~hr of drift-scan survey data taken using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulse has three distinct emission components, which vary with frequency across our 1.0--1.5~GHz observing band. We measure the peak flux density to be $>0.065$~Jy and the corresponding fluence $>0.2$~Jy~ms. Based on the observed dispersion measure of 1812~cm$^{-3}$~pc, we infer a redshift of $\sim 1.9$. From this, we estimate the peak luminosity and isotropic energy to be $\lesssim 2\times10^{43}$~erg~s$^{-1}$ and $\lesssim 2\times10^{40}$~erg, respectively. With only one FRB from the survey detected so far, our constraints on the event rate are limited. We derive a 95\% confidence lower limit for the event rate of 900 FRBs per day for FRBs with fluences $>0.025$~Jy~ms. We performed follow-up observations of the source with FAST for four hours and have not found a repeated burst. We discuss the implications of this discovery for our understanding of the physical mechanisms of FRBs.

preprint2013arXiv

Asymptotic Joint Distribution of Extreme Sample Eigenvalues and Eigenvectors in the Spiked Population Model

In this paper, we consider a data matrix $X_N\in\mathbb{R}^{N\times p}$ where all the rows are i.i.d. samples in $\mathbb{R}^p$ of mean zero and covariance matrix $Σ\in\mathbb{R}^{p\times p}$. Here the population matrix $Σ$ is of finite rank perturbation of the identity matrix. This is the "spiked population model" first proposed by Johnstone. As $N, p\to\infty$ but $N/p \to γ\in(1, \infty)$, for the sample covariance matrix $S_N := X_NX_N^T/N$, we establish the joint distribution of the largest and the smallest few packs of eigenvalues. Inside each pack, they will behave the same as the eigenvalues drawn from a Gaussian matrix of the corresponding size. Among different packs, we also calculate the covariance between the Gaussian matrices entries. As a corollary, if all the rows of the data matrix are Gaussian, then these packs will be asymptotically independent. Also, the asymptotic behavior of sample eigenvectors are obtained. Their local fluctuation is also Gaussian with covariance explicitly calculated.

preprint2012arXiv

Asymptotic Joint Distribution of Extreme Eigenvalues of the Sample Covariance Matrix in the Spiked Population Model

In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $Σ\in\mathbb{C}^{N\times N}$. Here the population matrix $Σ$ is of finite rank perturbation of the identity matrix. This is the "spiked population model" first proposed by Johnstone in \cite{21}. As $M, N\to\infty$ but $M/N = γ\in(1, \infty)$, we first establish in this paper the asymptotic distribution of the smallest eigenvalue of the sample covariance matrix $S:= XX^*/M$. It also exhibits a phase transition phenomenon proposed in \cite{1} --- the local fluctuation will be the generalized Tracy-Widom or the generalized Gaussian to be defined in the paper. Moreover we prove that the largest and the smallest eigenvalue are asymptotically independent as $M, N\to\infty$.

preprint2012arXiv

Smallest Gaps Between Eigenvalues of Random Matrices With Complex Ginibre, Wishart and Universal Unitary Ensembles

In this paper we study the limiting distribution of the $k$ smallest gaps between eigenvalues of three kinds of random matrices -- the Ginibre ensemble, the Wishart ensemble and the universal unitary ensemble. All of them follow a Poissonian ansatz. More precisely, for the Ginibre ensemble we have a global result in which the $k$-th smallest gap has typical length $n^{-3/4}$ with density $x^{4k-1}e^{-x^4}$ after normalization. For the Wishart and the universal unitary ensemble, it has typical length $n^{-4/3}$ and has density $x^{3k-1}e^{-x^3}$ after normalization.

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