arXiv subjects

Qingping Zeng

Publications and source records attributed to Qingping Zeng.

6 recordsLinked to original sources

arXiv2026

Encoder Winners Do Not Reliably Transfer Across VLA Backbone Scale: A Frozen-Backbone Grafting Diagnostic

Vision-language-action (VLA) policies typically inherit their vision encoder from upstream VLM releases, but it is unclear whether an encoder choice validated on a small VLA transfers to a larger backbone. We introduce a frozen-backbone grafting diagnostic: the vision tower of a released VLA is replaced by a candidate encoder under a fixed protocol (adaptive average pooling, LayerNorm, and a single trainable linear projector), with the language model and action expert frozen. Across four encoders, two LIBERO suites, two backbones (SmolVLA-450M and $\pi_{0.5}$-3.3B), and two-to-three seeds per cell (40 main grafting runs plus native, LoRA, pooling, and zero-/shuffled-image controls, all scored by offline action MSE), the small-backbone winner does not reliably select the large-backbone top tier: SigLIP is best on SmolVLA across both suites, while on $\pi_{0.5}$ DINOv2-small leads the spatial suite and the object suite is a seed-sensitive near-tie band; three of the four backbone-suite comparisons (and 11 of 12 seed-level cells) support backbone-dependent rankings. The grafting wrapper is itself non-neutral with opposite sign across backbones (+45-56% MSE on the SmolVLA native tower, -50-52% on $\pi_{0.5}$), so all conclusions are conditional on the fixed grafting protocol. We position frozen grafting as a cheap target-backbone diagnostic to run before committing to an encoder at scale, not as a closed-loop deployment claim.

cs.CV↗

arXiv2024

B-Fredholm theory in Banach algebras

The aim of this paper is to develop a systematic B-Fredholm theory in semiprime Banach algebras. We first generalize Smyth's important punctured neighbourhood theorem to B-Fredholm elements. Then using this result, we investigate the local spectral theory of B-Fredholm elements, including the localized left (resp. right) SVEP and a classification of components of B-Fredholm resolvent set. Finally, in semisimple Banach algebra context, we characterize element $f$ such that $f^{n}$ belongs to the socle for some $n \in \mathbb{N}$ from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation $f$, the other is the Rieszness and the B-Fredholmness of $f$.

math.FA↗

arXiv2013

Common properties of bounded linear operators $AC$ and $BA$: Spectral theory

Let $X,Y$ be Banach spaces, $A:X \longrightarrow Y$ and $B,C:Y \longrightarrow X$ be bounded linear operators satisfying operator equation $ABA=ACA$. Recently, as extensions of Jacobson's lemma, Corach, Duggal and Harte studied common properties of $AC-I$ and $BA-I$ in algebraic viewpoint and also obtained some topological analogues. In this note, we continue to investigate common properties of $AC$ and $BA$ from the viewpoint of spectral theory. In particular, we give an affirmative answer to one question posed by Corach et al. by proving that $AC - I$ has closed range if and only if $BA - I$ has closed range.

math.FA↗

arXiv2012

On $(n,k)$-quasi-*-paranormal operators

For nonnegative integers $n$ and $k$, we introduce in this paper a new class of $(n,k)$-quasi-*-paranormal operators satisfying $$||T^{1+n}(T^{k}x)||^{1/(1+n)}||T^{k}x||^{n/(1+n)} \geq ||T^*(T^{k}x)|| \makebox{\ for all} x \in H.$$ This class includes the class of $n$-*-paranormal operators and the class of $(1,k)$-quasi-*-paranormal operators contains the class of $k$-quasi-*-class $A$ operators. We study basic properties of $(n,k)$-quasi-*-paranormal operators: (1) inclusion relations and examples; (2) a matrix representation; (3) joint (approximate) point spectrum and single valued extension property.

math.FA↗

arXiv2012

Spectra originated from semi-B-Fredholm theory and commuting perturbations

Burgos, Kaidi, Mbekhta and Oudghiri provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator $F$ is power finite rank if and only if $σ_{dsc}(T+F) =σ_{dsc}(T)$ for every operator $T$ commuting with $F$. Later, several authors extended this result to the essential descent spectrum, the left Drazin spectrum and the left essentially Drazin spectrum. In this paper, using the theory of operator with eventual topological uniform descent and the technique used in Burgos, Kaidi, Mbekhta, and Oudghiri, we generalize this result to various spectra originated from seni-B-Fredholm theory. As immediate consequences, we give affirmative answers to several questions posed by Berkani, Amouch and Zariouh. Besides, we provide a general framework which allows us to derive in a unify way commuting perturbational results of Weyl-Browder type theorems and properties (generalized or not). These commuting perturbational results, in particular, improve many recent results of Berkani and Amouch, Berkani and Zariouh, and Rashid by removing certain extra assumptions.

math.FA↗

arXiv2012

A note on property (gb) and perturbations

An operator $T \in \mathcal{B}(X)$ defined on a Banach space $X$ satisfies property $(gb)$ if the complement in the approximate point spectrum $σ_{a}(T)$ of the upper semi-B-Weyl spectrum $σ_{SBF_{+}^{-}}(T)$ coincides with the set $Π(T)$ of all poles of the resolvent of $T$. In this note we continue to study property $(gb)$ and the stability of it, for a bounded linear operator $T$ acting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators commuting with $T$. Two counterexamples show that property $(gb)$ in general is not preserved under commuting quasi-nilpotent perturbations or commuting finite rank perturbations.

math.FA↗