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Bohan Fang

Publications and source records attributed to Bohan Fang.

At least 19 recordsLinked to original sources

Exploring Diffusion Transformers for Cross-Modal Augmentation in Multimodal Brain State Decoding

Multimodal brain state decoding has largely focused on fusing paired modalities for prediction, but has rarely explored how their correspondence can be further exploited to enrich training data and improve multimodal representation learning. To address this gap, we propose CoMA-DiT, a bidirectional cross-modal Diffusion Transformer for latent augmentation that treats paired modalities as sources of mutual generative supervision rather than merely as inputs to be fused. CoMA-DiT conditions velocity prediction on the paired modality through cross-modal attention and adaptively injects the resulting variation via a reliability-gated residual mechanism. Experiments on multimodal auditory attention decoding and emotion recognition showed that CoMA-DiT consistently outperformed 20 representative baselines, achieving absolute gains of 4.28% and 6.70% in accuracy and macro-F1 over the no-augmentation baseline, respectively. Extensive ablation, sensitivity, visualization, and interpretability analyses further demonstrated its robustness, generalizability, and ability to capture functionally relevant cross-modal interactions. These findings support a broader view of multimodal learning: Paired modalities can serve not only as inputs for fusion but also as supervision sources that augment one another.

cs.AI

Conifold Gap Theorem for Topological Recursion

We prove a conifold gap theorem for the topological recursion of toric mirror curves: for every local analytic family acquiring a generic one-node degeneration and every fixed genus at least two, the conifold-polarized free energy has one universal polar term, and the remainder is jointly holomorphic in the transverse and spectator parameters. The result covers separating and nonseparating nodes and allows general family deformations beyond the pure filling-fraction case.

math.AG

Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold

We prove a closed-string remodeling statement for the affine binary dihedral Calabi--Yau orbifold threefold $\mathcal X=[\mathbb C^2/\Gamma\times\mathbb C]$, where $\Gamma$ is a binary dihedral subgroup of $SU(2)$. This target lies outside the toric setting of the Bouchard--Klemm--Mari\~{n}o--Pasquetti remodeling conjecture: the toric mirror curve is replaced by the type-$D_l$ logarithmic Toda curve of Brini--Ma--Strachan, and the Chekhov--Eynard--Orantin topological recursion is replaced by the $\mathbb Z_2$-equivariant topological recursion of Giacchetto--Kramer--Lewa\'nski, run in the sign sector of the Toda-curve involution with the Prym kernel as its two-point input. We identify the equivariant orbifold quantum cohomology Frobenius manifold of $\mathcal X$ with the invariant Jacobian Frobenius structure of the Toda curve, and we prove that the B-model $R$-matrix, defined by regularized stationary phase, equals the A-side normalized canonical Givental--Teleman $R$-matrix on the smooth oscillatory chamber; this equality is anchored at the orbifold point through a semistable degeneration of the Toda curve. Comparing the resulting Givental--Teleman and Dunin-Barkowski--Orantin--Shadrin--Spitz graph sums then identifies, after a parity-twisted leaf substitution, the sign-sector recursion with the descendant Gromov--Witten generating functions of $\mathcal X$ in the stable range ($2g-2+n>0$ with $n>0$), and identifies the recursion free energies with the equivariant Gromov--Witten free energies of $\mathcal X$ for $g\geq2$.

math.AG

Homological Mirror Symmetry for Conic Bundle

We study the homological mirror symmetry statement where A-side is the conic bundle Hori--Vafa mirror $\mathcal{Y} = \{uv = f(z)\} \subset \mathbb{C}^2 \times (\mathbb{C}^\ast)^n$ for a Laurent polynomial $f$ in $(\mathbb{C}^\ast)^n$, and B-side is some a toric Calabi--Yau $(n+2)$-fold with a smooth anti-canonical divisor removed $\mathcal{X}^\circ = \mathcal{X} \setminus w^{-1}(-1)$. We show that when $\mathcal{X}$ is the canonical bundle of a toric Fano $n$-orbifold $S$ and $f$ is its Givental superpotential, the strong deformation retraction skeleton $\mathsf{L}$ of $\mathcal{Y}$ in the sense of RSTZ (Ruddat--Sibilla--Treumann--Zaslow in Geom. Topol. 18(3):1343--1395, 2014) has a Weinstein neighborhood $U$, such that the wrapped microlocal sheaf category $\mu\mathrm{Sh}^w_{\mathsf{L}}(\mathsf{L}) \cong \mathrm{Coh}(\mathcal{X}^\circ)$. This proves a microlocal categorical version of the SYZ mirror in (Abouzaid--Auroux--Katzarkov in Publ. math. IH\'ES 123(1):199--282, 2016, Thm. 1.7). We also extend the definition of characteristic cycles for constructible sheaves in cotangent bundles from (Kashiwara--Schapira in Sheaves on Manifolds, Grundlehren math. Wiss. 292, Springer, 1990, Ch. IX) to finite-rank objects in $\mu\mathrm{Sh}^w_{\mathsf{L}}(\mathsf{L})$, and describe the characteristic cycles for objects mirror to a coherent sheaf supported on $S$.

math.AG

RefDecoder: Enhancing Visual Generation with Conditional Video Decoding

Video generation powers a vast array of downstream applications. However, while the de facto standard, i.e., latent diffusion models, typically employ heavily conditioned denoising networks, their decoders often remain unconditional. We observe that this architectural asymmetry leads to significant loss of detail and inconsistency relative to the input image. To address this, we argue that the decoder requires equal conditioning to preserve structural integrity. We introduce RefDecoder, a reference-conditioned video VAE decoder by injecting high-fidelity reference image signal directly into the decoding process via reference attention. Specifically, a lightweight image encoder maps the reference frame into the detail-rich high-dimensional tokens, which are co-processed with the denoised video latent tokens at each decoder up-sampling stage. We demonstrate consistent improvements across several distinct decoder backbones (e.g., Wan 2.1 and VideoVAE+), achieving up to +2.1dB PSNR over the unconditional baselines on the Inter4K, WebVid, and Large Motion reconstruction benchmarks. Notably, RefDecoder can be directly swapped into existing video generation systems without additional fine-tuning, and we report across-the-board improvements in subject consistency, background consistency, and overall quality scores on the VBench I2V benchmark. Beyond I2V, RefDecoder generalizes well to a wide range of visual generation tasks such as style transfer and video editing refinement.

cs.CV

MolmoAct: Action Reasoning Models that can Reason in Space

Reasoning is central to purposeful action, yet most robotic foundation models map perception and instructions directly to control, which limits adaptability, generalization, and semantic grounding. We introduce Action Reasoning Models (ARMs), a class of robotic foundation models that integrate perception, planning, and control through a structured three-stage pipeline. Our model, MolmoAct, encodes observations and instructions into depth-aware perception tokens, generates mid-level spatial plans as editable trajectory traces, and predicts precise low-level actions, enabling explainable and steerable behavior. MolmoAct-7B-D achieves strong performance across simulation and real-world settings: 70.5% zero-shot accuracy on SimplerEnv Visual Matching tasks, surpassing closed-source Pi-0 and GR00T N1.5; 86.6% average success on LIBERO, including an additional 6.3% gain over ThinkAct on long-horizon tasks; and in real-world fine-tuning, an additional 10% (single-arm) and an additional 22.7% (bimanual) task progression over Pi-0-FAST. It also outperforms baselines by an additional 23.3% on out-of-distribution generalization and achieves top human-preference scores for open-ended instruction following and trajectory steering. Furthermore, we release, for the first time, the MolmoAct Dataset -- a mid-training robot dataset comprising over 10,000 high quality robot trajectories across diverse scenarios and tasks. Training with this dataset yields an average 5.5% improvement in general performance over the base model. We release all model weights, training code, our collected dataset, and our action reasoning dataset, establishing MolmoAct as both a state-of-the-art robotics foundation model and an open blueprint for building ARMs that transform perception into purposeful action through structured reasoning. Blogpost: https://allenai.org/blog/molmoact

cs.RO

Remodeling Conjecture with Descendants

We formulate and prove the Remodeling Conjecture with descendants, which is a version of all-genus equivariant descendant mirror symmetry for semi-projective toric Calabi-Yau 3-orbifolds with integral structures. We construct an isomorphism between the $K$-group of equivariant coherent sheaves on the toric Calabi-Yau 3-orbifold with support bounded in a direction and a certain integral relative first homology group of the equivariant mirror curve. Under this isomorphism, we prove the equivariant mirror symmetric Gamma conjecture which equates quantum cohomology central charges of coherent sheaves and oscillatory integrals along corresponding relative 1-cycles. As a consequence in the non-equivariant setting, we prove a conjecture of Hosono which equates central charges of compactly supported coherent sheaves and period integrals of integral 3-cycles on the Hori-Vafa mirror 3-fold. Furthermore, we establish a correspondence between all-genus equivariant descendant Gromov-Witten invariants with $K$-theoretic framings and oscillatory integrals (Laplace transforms) of the Chekhov-Eynard-Orantin topological recursion invariants along relative 1-cycles on the equivariant mirror curve.

math.AG

Mirror symmetric Gamma conjecture for toric GIT quotients via Fourier transform

Let $\mathcal X=[(\mathbb C^r\setminus Z)/G]$ be a toric Fano orbifold. We compute the Fourier transform of the $G$-equivariant quantum cohomology central charge of any $G$-equivariant line bundle on $\mathbb C^r$ with respect to certain choice of parameters. This gives the quantum cohomology central charge of the corresponding line bundle on $\mathcal X$, while in the oscillatory integral expression it becomes the oscillatory integral in the mirror Landau-Ginzburg mirror of $\mathcal X$. Moving these parameters to real numbers simultaneously deforms the integration cycle to the mirror Lagrangian cycle of that line bundle. This computation produces a new proof the mirror symmetric Gamma conjecture for $\mathcal X$.

math.AG

Mirror symmetric Gamma conjecture for del Pezzo surfaces

For a del Pezzo surface of degree $\geq 3$, we compute the oscillatory integral for its mirror Landau-Ginzburg model in the sense of Gross-Hacking-Keel [Mark Gross, Paul Hacking, and Sean Keel, "Mirror symmetry for log Calabi-Yau surfaces I". In: Publ. Math. Inst. Hautes Etudes Sci. 122 (2015), pp. 65-168]. We explicitly construct the mirror cycle of a line bundle and show that the leading order of the integral on this cycle involves the twisted Chern character and the Gamma class. This proves a version of the Gamma conjecture for non-toric Fano surfaces with an arbitrary K-group insertion.

math.AG

Topological Fukaya category and mirror symmetry for toric Calabi-Yau 3-orbifolds

We prove a version of homological mirror symmetry statement for toric Calabi-Yau $3$-orbifolds, thus extending arXiv:1604.06448 to the case of orbifolds under the mirror symmetry setting considered in arXiv:1604.07123. The B-model is the matrix factorization category for the toric Calabi-Yau $3$-orbifold with a superpotential; while the A-model is a topologically defined Fukaya-type category on its mirror curve.

math.AT

Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry

In this paper we consider the oscillatory integrals on Lefschetz thimbles in the Landau-Ginzburg model as the mirror of a toric Fano manifold. We show these thimbles represent the same relative homology classes as the characteristic cycles of the corresponding constructible sheaves under the equivalence of \cite{GPS18-2}. Then the oscillatory integrals on such thimbles are the same as the integrals on the characteristic cycles and relate to genus $0$ Gromov-Witten descendant potential for $X$, and this leads to a proof of Gamma II conjecture for toric Fano manifolds.

math.SG

Graph sums in the Remodeling Conjecture

The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.

math.AG

Open Gromov-Witten Theory of $K_{\mathbb P^2}, K_{{\mathbb P^1}\times {\mathbb P^1}}, K_{W\mathbb P[1,1,2]}, K_{\mathbb F_1}$ and Jacobi Forms

It was known through the efforts of many works that the generating functions in the closed Gromov-Witten theory of $K_{\mathbb P^2}$ are meromorphic quasi-modular forms basing on the B-model predictions. In this article, we extend the modularity phenomenon to $K_{{\mathbb P^1}\times {\mathbb P^1}}, K_{W\mathbb P[1,1,2]}, K_{\mathbb F_1}$. More importantly, we generalize it to the generating functions in the open Gromov-Witten theory using the theory of Jacobi forms where the open Gromov-Witten parameters are transformed into elliptic variables.

math.AG

Central charges of T-dual branes for toric varieties

Given any equivariant coherent sheaf $\mathcal L$ on a compact semi-positive toric orbifold $\mathcal X$, its SYZ T-dual mirror dual is a Lagrangian brane in the Landau-Ginzburg mirror. We prove the oscillatory integral of the equivariant superpotential in the Landau Ginzburg mirror over this Lagrangian brane is the genus-zero $1$-descendant Gromov-Witten potential with a Gamma-type class of $\mathcal L$ inserted.

math.AG

The SYZ mirror symmetry and the BKMP remodeling conjecture

The Remodeling Conjecture proposed by Bouchard-Klemm-Mari\~{n}o-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (open and closed Gromov-Witten invariants) of a symplectic toric Calabi-Yau 3-fold to Eynard-Orantin invariants of its mirror curve. The Remodeling Conjecture can be viewed as a version of all genus open-closed mirror symmetry. The SYZ conjecture explains mirror symmetry as $T$-duality. After a brief review on SYZ mirror symmetry and mirrors of symplectic toric Calabi-Yau 3-orbifolds, we give a non-technical exposition of our results on the Remodeling Conjecture for symplectic toric Calabi-Yau 3-orbifolds. In the end, we apply SYZ mirror symmetry to obtain the descendent version of the all genus mirror symmetry for toric Calabi-Yau 3-orbifolds.

math.AG

Topological recursion for the conifold transition of a torus knot

In this paper we prove a mirror symmetry conjecture based on the work of Brini-Eynard-Mari\~no \cite{BEM} and Diaconescu-Shende-Vafa \cite{DSV}. This conjecture relates open Gromov-Witten invariants of the conifold transition of a torus knot to the topological recursion on the B-model spectral curve.

math.AG

On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds

The Remodeling Conjecture proposed by Bouchard-Klemm-Mari\~{n}o-Pasquetti (BKMP) [arXiv:0709.1453, arXiv:0807.0597] relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants) of a semi-projective toric Calabi-Yau 3-manifold/3-orbifold to the Eynard-Orantin invariants of its mirror curve. It is an all genus open-closed mirror symmetry for toric Calabi-Yau 3-manifolds/3-orbifolds. In this paper, we present a proof of the BKMP Remodeling Conjecture for all genus open-closed orbifold Gromov-Witten invariants of an arbitrary semi-projective toric Calabi-Yau 3-orbifold relative to an outer framed Aganagic-Vafa Lagrangian brane. We also prove the conjecture in the closed string sector at all genera.

math.AG

The Eynard-Orantin recursion and equivariant mirror symmetry for the projective line

We study the equivariantly perturbed mirror Landau-Ginzburg model of the projective line. We show that the Eynard-Orantin recursion on this model encodes all genus all descendants equivariant Gromov-Witten invariants of the projective line. The non-equivariant limit of this result is the Norbury-Scott conjecture, while by taking large radius limit we recover the Bouchard-Marino conjecture on simple Hurwitz numbers.

math.AG