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Jingbo Xia

Publications and source records attributed to Jingbo Xia.

4 recordsLinked to original sources

DINO Eats CLIP: Adapting Beyond Knowns for Open-set 3D Object Retrieval

Vision foundation models have shown great promise for open-set 3D object retrieval (3DOR) through efficient adaptation to multi-view images. Leveraging semantically aligned latent space, previous work typically adapts the CLIP encoder to build view-based 3D descriptors. Despite CLIP's strong generalization ability, its lack of fine-grainedness prompted us to explore the potential of a more recent self-supervised encoder-DINO. To address this, we propose DINO Eats CLIP (DEC), a novel framework for dynamic multi-view integration that is regularized by synthesizing data for unseen classes. We first find that simply mean-pooling over view features from a frozen DINO backbone gives decent performance. Yet, further adaptation causes severe overfitting on average view patterns of known classes. To combat it, we then design a module named Chunking and Adapting Module (CAM). It segments multi-view images into chunks and dynamically integrates local view relations, yielding more robust features than the standard pooling strategy. Finally, we propose Virtual Feature Synthesis (VFS) module to mitigate bias towards known categories explicitly. Under the hood, VFS leverages CLIP's broad, pre-aligned vision-language space to synthesize virtual features for unseen classes. By exposing DEC to these virtual features, we greatly enhance its open-set discrimination capacity. Extensive experiments on standard open-set 3DOR benchmarks demonstrate its superior efficacy.

cs.CV

Fock space: A bridge between Fredholm index and the quantum Hall effect

We compute the quantized Hall conductance at various Landau levels by using the classic trace. The computations reduce to the single elementary one for the lowest Landau level. By using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces, the Hall conductance is naturally identified with a Fredholm index. This brings new mathematical insights to the extraordinary precision of quantization observed in quantum Hall measurements.

math-ph

Roots and Logarithms of Multipliers

By now it is a well-known fact that if $f$ is a multiplier for the Drury-Arveson space $H^2_n$, and if there is a $c>0$ such that $|f(z)|\geq c$ for every $z\in B$, then the reciprocal function 1/f is also a multiplier for $H^2_n$. We show that for such an $f$ and for every $t\in \mathbb{R}$, $f^t$ is also a multiplier for $H^2_n$. We do so by deriving a differentiation formula for $R^m(f^th)$.Moreover, by this formula the same result holds for spaces $H_{m,s}$ of the Besov-Dirichlet type. The same technique also gives us the result that for a non-vanishing multiplier $f$ of $H^2_n$, $log f$ is a multiplier of $H^2_n$ if and only if log $f$ is bounded on $B$.

math.FA

Essential Commutants on Strongly Pseudo-convex Domains

Consider a bounded strongly pseudo-convex domain $Ω$ with a smooth boundary in $\mathbb{C}^n$. Let $\mathcal{T}$ be the Toeplitz algebra on the Bergman space $L^2_a(Ω)$. That is, $\mathcal{T}$ is the $C^\ast $-algebra generated by the Toeplitz operators $\{T_f : f \in L^\infty (Ω)\}$. Extending previous work in the special case of the unit ball, we show that on any such $Ω$, $\mathcal{T}$ and $\{T_f : f \in {\text{VO}}_{\text{bdd}}\} + \mathcal{K}$ are essential commutants of each other. On a general $Ω$ considered in this paper, the proofs require many new ideas and techniques. These same techniques also enable us to show that for $A \in \mathcal{T}$, if $\langle Ak_z,k_z\rangle \rightarrow 0$ as $z \rightarrow \partial Ω$, then $A$ is a compact operator.

math.FA