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Weifan Wang

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8 papers
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8

AAAI Conference 2026 Conference Paper

Modeling Rapid Contextual Learning in the Visual Cortex with Fast-Weight Deep Autoencoder Networks

  • Yue Li
  • Weifan Wang
  • Tai Sing Lee

Recent neurophysiological studies have revealed that the early visual cortex can rapidly learn global image context, as evidenced by a sparsification of population responses and a reduction in mean activity when exposed to familiar versus novel image contexts. This phenomenon has been attributed primarily to local recurrent interactions, rather than changes in feedforward or feedback pathways—supported by both empirical findings and circuit-level modeling. Recurrent neural circuits capable of simulating these effects have been shown to reshape the geometry of neural manifolds, enhancing robustness and invariance to irrelevant variations. In this study, we employ a Vision Transformer (ViT)-based autoencoder to investigate, from a functional perspective, how familiarity training can induce sensitivity to global context in the early layers of a deep neural network. We hypothesize that rapid learning operates via fast weights, which encode transient or short-term memory traces, and we explore the use of Low-Rank Adaptation (LoRA) to implement such fast weights within each Transformer layer. Our results show that: (1) The proposed ViT-based autoencoder's self-attention circuit is performing a manifold transform similar to a neural circuit developed for modeling the familiarity effect. (2) Familiarity training induces alignment of latent representation in early layers with the top layer that contains global context information. (3) Familiarity training makes self-attention pay attention to a broader scope details in the remembered image context, rather than just the critical features for object recognition. (4) These effects are significantly amplified by the incorporation of LoRA-based fast weights. Together, these findings suggest that familiarity training can introduce global sensitivity to earlier layers in a hierarchical network, and that a hybrid fast-and-slow weight architecture may provide a viable computational model for studying the functional consequences of rapid global context learning in the brain.

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TCS Journal 2017 Journal Article

The entire chromatic number of graphs embedded on the torus with large maximum degree

  • Xiaoxue Hu
  • Ping Wang
  • Yiqiao Wang
  • Weifan Wang

An embedded graph G = ( V, E, F ) on the torus is entirely k-colorable if V ∪ E ∪ F can be colored with k colors such that any two adjacent or incident elements receive different colors. In this paper, we prove that every embedded graph G on the torus with maximum degree Δ ≥ 10 is entirely ( Δ + 2 ) -colorable.

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TCS Journal 2014 Journal Article

The 2-surviving rate of planar graphs without 6-cycles

  • Weifan Wang
  • Stephen Finbow
  • Jiangxu Kong

The firefighter problem models the spread of a fire or virus through a network and the k-surviving rate of G, ρ k ( G ), is the expected proportion of nodes k fire fighters per turn can save. In this paper, we show that if G is a planar graph with at least two vertices and having no 6-cycles, then ρ 2 ( G ) > 1 85.

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TCS Journal 2012 Journal Article

The 2-surviving rate of planar graphs without 4-cycles

  • Weifan Wang
  • Jiangxu Kong
  • Lianzhu Zhang

Let G be a connected graph with n ≥ 2 vertices. Suppose that a fire breaks out at a vertex v of G. A firefighter starts to protect vertices. At each time interval, the firefighter protects two vertices not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbour on fire. Let sn 2 ( v ) denote the maximum number of vertices in G that the firefighter can save when a fire breaks out at vertex v. The surviving rate ρ 2 ( G ) of G is defined to be ∑ v ∈ V ( G ) sn 2 ( v ) / n 2, which is the average proportion of saved vertices. In this paper, we show that if G is a planar graph with n ≥ 2 vertices and without 4-cycles, then ρ 2 ( G ) > 1 76.

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TCS Journal 2012 Journal Article

The surviving rate of planar graphs

  • Jiangxu Kong
  • Weifan Wang
  • Xuding Zhu

Let G be a connected graph with n ≥ 2 vertices. Let k ≥ 1 be an integer. Suppose that a fire breaks out at a vertex v of G. A firefighter starts to protect vertices. At each time interval, the firefighter protects k -vertices not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbor on fire. Let s n k ( v ) denote the maximum number of vertices in G that the firefighter can save when a fire breaks out at vertex v. The k -surviving rate ρ k ( G ) of G is defined to be ∑ v ∈ V ( G ) s n k ( v ) / n 2, which is the average proportion of saved vertices. In this paper, we show that every planar graph G with minimum degree δ satisfies ρ 4 ( G ) > 3 11 if δ = 5, ρ 4 ( G ) > 3 19 if δ = 4, and ρ 4 ( G ) > 1 9 if δ ≤ 3. This improves a result in [W. Wang, S. Finbow, P. Wang, The surviving rate of an infected network, Theoret. Comput. Sci. 411 (2010) 3651–3660].

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TCS Journal 2011 Journal Article

The surviving rate of an outerplanar graph for the firefighter problem

  • Weifan Wang
  • Xubin Yue
  • Xuding Zhu

Let G be a connected graph with n ≥ 2 vertices. Let k ≥ 1 be an integer. Suppose that a fire breaks out at a vertex v of G. A firefighter starts to protect vertices. At each time interval, the firefighter protects k -vertices not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbour on fire. Let sn k ( v ) denote the maximum number of vertices in G that the firefighter can save when a fire breaks out at vertex v. The k -surviving rate ρ k ( G ) of G is defined to be ∑ v ∈ V ( G ) sn k ( v ) / n 2, which is the average proportion of saved vertices. In this paper, we investigate the surviving rate of outerplanar graphs G with n ≥ 2 vertices. The main results are as follows: (1) lim n → ∞ ρ 5 ( G ) = 1; and (2) ρ 1 ( G ) ≥ 43 81 − 5 3 n + 3 n 2 if n ≥ 8, and ρ 1 ( G ) ≥ 1 3 if n ≥ 2, which improves the result in [L. Cai, W. Wang, The surviving rate of a graph for the firefighter problem, SIAM J. Discrete Math. 23 (2009) 1814–1826].

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TCS Journal 2010 Journal Article

The surviving rate of an infected network

  • Weifan Wang
  • Stephen Finbow
  • Ping Wang

Let G be a connected network. Let k ≥ 1 be an integer. Suppose that a vertex v of G becomes infected. A program is then installed on k -nodes not yet infected. Afterwards, the virus spreads to all its unprotected neighbors in each time interval. The virus and the network administrator take turns until the virus can no longer spread further. Let s n k ( v ) denote the maximum number of vertices in G the network administrator can save when a virus infects v. The k -surviving rate ρ k ( G ) of G is defined to be the average value ∑ v ∈ V ( G ) s n k ( v ) / n 2. In particular, we write ρ ( G ) = ρ 1 ( G ). In this paper, we first use a probabilistic method to show that almost all networks have k -surviving rate arbitrarily close to 0. Then, we prove the following results: (1) ρ ( G ) ≥ 2 35 for a planar network G of girth at least 9; (2) ρ 2 ( G ) ≥ 1 16 for a series–parallel network G; and (3) ρ 2 d − 1 ( G ) ≥ 2 5 d for a d -degenerate network G.

Details DOI
v2026.09.13