可能的方向

实验(联合西湖大学)

  1. Integrator dynamics in the cortico-basal ganglia loop for flexible motor timing

  2. An approximate line attractor in the hypothalamus encodes an aggressive state

日期: 2026-05-11   标签: #line attractor 
Summary The hypothalamus regulates innate social behaviors, including mating and aggression. These behaviors can be evoked by optogenetic stimulation of specific neuronal subpopulations within MPOA and VMHvl, respectively. 下丘脑调节着先天的社交行为，包括交配和攻击。这些行为可以通过对 MPOA 和 VMHvl 中特定神经亚群进行光遗传学刺激来引发。 Here, we perform dynamical systems modeling of population neuronal activity in these nuclei during social behaviors. In VMHvl, unsupervised analysis identified a dominant dimension of neural activity with a large time constant (>50 s), generating an approximate line attractor in neural state space. Progression of the neural trajectory along this attractor was correlated with an escalation of agonistic behavior, suggesting that it may encode a scalable state of aggressiveness. ......

  1. A circuit that integrates drive state and social contact to gate mating

  2. A line attractor maintains aggressiveness during feeding in 'hangry' mice

日期: 2026-05-10   标签: #line attractor 
......

  1. Encoding of female mating dynamics by a hypothalamic line attractor

  2. Causal evidence of a line attractor encoding an affective state

日期: 2026-05-11   标签: #line attractor 
Abstract Continuous attractors are an emergent property of neural population dynamics that have been hypothesized to encode continuous variables such as head direction and eye position1–4. In mammals, direct evidence of neural implementation of a continuous attractor has been hindered by the challenge of targeting perturbations to specific neurons within contributing ensembles2,3. 连续吸引子是神经群体动力学的一个涌现属性，被假设为编码连续变量，如头部方向和眼睛位置。在哺乳动物中，直接证据表明连续吸引子的神经实现受到挑战，因为很难针对贡献集合中的特定神经元进行干扰。 ......

meta-learning(biologically plausible learning rule)

  1. The neural computation of affective internal states in the hypothalamus - A dynamical systems perspective

  2. A line attractor encoding a persistent state requires neuropeptide signaling

日期: 2026-05-10   标签: #physics  #numerical calculation 
Summary Internal states drive survival behaviors, but their neural implementation is poorly understood. Recently, we identified a line attractor in the ventromedial hypothalamus (VMH) that represents a state of aggressiveness. Line attractors can be implemented by recurrent connectivity or neuromodulatory signaling, but evidence for the latter is scant. 内部状态驱动生存行为，但其神经实现机制尚不明确。最近，我们在 腹内侧下丘脑（VMH）中识别出一个线性吸引子，它代表了一种攻击性状态。线性吸引子可以通过反馈连接或神经调制信号来实现，但后者的证据很少。 ......

自下而上的方法: 通过病毒和基因编辑, 钙成像神经活动, 研究同一区域(腹内侧下丘脑 VMH)不同神经调节受体(催产素 OXT, 精氨酸加压素 AVP) 局部失活的影响.

社交行为(如攻击性)的神经元集群可构成一个近似线性吸引子.

  1. Integration as a self-organizing process
日期: 2025-11-24   标签: #physics  #numerical calculation 
Integration—the accumulation of information over time—is a fundamental computation in navigation, decisionmaking, and memory. The dominant circuit model, the continuous attractor neural network (CANN), explains integration through finely tuned connectivity that supports marginally stable states. However, data from systems such as Drosophila central complex suggest that real connectivity is heterogeneous, implying that symmetry may only exist in a coarse-grained sense, if at all. One class of models explains this heterogenous connectivity by evoking supervised learning which can enforce coarse-grained symmetry at the expense of extensive trial and error learning or by employing biologically unrealistic learning rules. Another class employs only local learning rules, but this approach typically fails when circuit connectivity or tutoring inputs become sufficiently heterogeneous. 积分——随时间积累信息——是导航、决策和记忆中的基本计算. 主导的回路模型, 连续吸引子神经网络（CANN）, 通过支持边际稳定状态的精细调制连接来解释积分. ......

embeded continuous attractors with random rnn

random rnn(DMFT), random matrix theory

  1. Symmetries and continuous attractors in disordered neural circuits
日期: 2025-10-08   标签: #physics  #numerical calculation 
0. Abstract 经典 cann: 依赖于循环权重 $\mathbb{M}$ 的连续对称性, 调谐曲线也具有平移对称性. 而小鼠头朝向细胞具有异质性. 仍可通过经典 cann 动力学解释哺乳动物神经回路. 通过动力学平均场理论(Dynamical Mean Field Theory) 表明调谐异质性网络(在大 N 下)等效于经典 ring attractor. 随机权重通过特征值简并反映出来. 因此可以对权重进行谱结构分析. ......
面试 PPT 大纲

John Hopfield (Symmetric)

Associative Memory

discrete fixed point

degenerate manifold

Examples

  • occular motor control
  • ring attractors(head direction cells)
  • place cells
  • intrinsic behavior(aggression, mating...)

  1. Existing model/theory

    • Fine tuned connectivity
    • 1996 S.Seung PNAS

    $$ \tau\frac{\mathrm{d}x}{\mathrm{d}t} = Ax + \xi_{\tau} $$

  2. Biological noisyness

问题: 是否存在一套学习规则, 使得神经网络在接受到一些实验数据的时候, 可以在无监督下自组织出对应的连续吸引子网络, 从而将现实世界的某低维变量嵌入到高维的 RNN 相空间中?

  1. 实验数据是否存在低维流形

2020: Manifold GPLVMs for discovering non-Euclidean latent structure in neural data 流形高斯过程隐变量模型: 还原了 Head Direction 的环结构

2018: Learning a latent manifold of odor representations from neural responses in piriform cortex: 不是证明了气味分子在现实世界构成低维流形, 而是从小鼠 piriform cortex 的神经活动中能够反推一个能解释这些响应的潜在嗅觉表征空间

  1. 能否在无监督下自组织, 从而恢复流形的 latent variable

  2. 是否存在某种生物学上可行的学习规则, 使得 RNN 能够将流形映射到自己的相空间中

Oja rule: Discovering plasticity rules that organize and maintain neural circuits

  1. 是否有不同的流形可以拓展应用目前学习的 random RNN 的理论框架?
    • 线性吸引子: 能否构造一个协方差矩阵, 使得生成的调谐曲线能满足 aggression 等表征?
    • 蝙蝠: (目前尚未查到比较完整的数据集) Three-dimensional head-direction coding in the bat brain: 并未构成想象中的球面吸引子, 而更像是一个环面吸引子

meeting notes:

  • $(\cos{\theta}, \sin{\theta})\rightarrow \vec{x}\in\mathbb{R}^{N}\rightarrow \mathrm{bump}$ 设计 $\Delta J_{ij}$, 使得具有一定初始化规则创建的 J0 通过具有一定内在结构的外部输入更新权重, 从而收敛至 optimized J matrix, 并且其更新规则需要是 local 的(而非机器学习中的梯度下降算法这类依赖于全局状态的方法)

  • 线性吸引子: 搞清楚积分变量的累积是否具有方向性, 以及和速度输入的关系, aggression 是否能够用类扩散行为来描述. 比如小鼠的和 aggression 相关存在类似线性吸引子的机制, 攻击性的累积具体是怎样的机制? 这个需要具体确认一下(因为头朝向是一个旋转对称的系统, 而线性吸引子并不具有这个特性: 往一个方向和另一个方向的漂移是代表同一个生理过程吗? 还是往一个方向积分是提高攻击性, 另一个方向是减少攻击性? ...)

  • place cell 是否可以应用于 random RNN 理论框架 (是不是对 $\Gamma$ 协方差函数的 M matrix 进行修改, 以及新的协方差函数应该如何设计从而适应 place cell 单 bump 以及多 bump 的结构, grid cell 是六角晶格分布的 bump 因此两者还是存在神经集群活动模式的区别)

  • 论文阅读:

  • 继续 Follow 有关 3D 蝙蝠 head direction 的相关工作, 对其进行了解

  • 补充的论文阅读材料:

    • Multiscale representation of very large environments in the hippocampus of flying bats
    • Large environments reveal the statistical structure governing hippocampal representations
    • Universal statistics of hippocampal place fields across species and dimensionalities
    • A thalamus-brainstem attractor network drives history-biased decisions

思路:

  1. 通过 universal... 的 place cells 数据集, 使用 symmetries... 中的 random RNN 框架, 先尝试构造 target manifold 以及对应的 weight matrix

    现实世界位置 $\vec{r}\in\Omega\subset\mathbb{R}^{D}$; 单神经元 $i$ 的 place field $\phi_{i}^{*}(\vec{r})$ (在 $\vec{r}$ 的平均放电率)

    文章声称在高阈值条件下, field size, gap, Euler characteristic 等刻画 place field 的参数, 统计对于具体选取哪一个协方差函数并不敏感, 因此可以采用

    $$ \Gamma(\vec{x}-\vec{x}^{\prime}) = A^{2}\exp{\left[-\frac{|\vec{x}-\vec{x}^{\prime}|^{2}}{2l^{2}}\right]} $$

    异质性 place cell 的解码: $\hat{\vec{r}}(t) = \arg\max_{\vec{r}} \mathrm{Match}\left[\vec{\phi}(t), \vec{\phi}(\vec{r})\right]$

    其中匹配算法有多种选择, 比如 Maximum likelihood 的 Poisson 核, overlap parameter (Clark 就是用的这个方法 $m(\theta,t) = \frac{1}{N}\sum_{i}\phi_{i}^{*}(\theta)\phi_{i}(t)$)等等.

  2. 通过 Gaussian process 构造的通性:

    • Clark:
      • 现实状态: 头朝向 $\theta\in [0,2\pi]$
      • 随机变量: 输入电流场 $\vec{x}^{*}_{i}\sim \mathcal{N}(0,\mathbf{\Gamma}^{x}(\theta-\theta^{\prime}))$
      • 非线性激活函数: $\phi(x) = 1 + \mathrm{erf}\left(\frac{\beta\sqrt{\pi}}{2}x\right)$
    • Mainali:
      • 现实状态: 位矢 $\vec{x}\in\mathbb{R}^{D}$,
      • 随机变量: 输入电流场 $h(\vec{x})\sim \mathcal{GP}[\vec{0},\mathbf{r}(\vec{x}-\vec{x}^{\prime})]$
      • 非线性激活函数: $f(\vec{x}) = \left[h(\vec{x}) - q\sqrt{\mathbf{r}(\vec{0})}\right]$
    日期: 2026-06-13   标签: #line attractor 
    Summary Hippocampal place cells have single, bell-shaped place fields in small environments. Recent experiments, however, reveal that, in large environments, place cells have multiple fields with heterogeneous shapes and sizes. 海马体位置细胞在小环境中具有单一的钟形位置场. 然而, 最近的实验表明, 在大环境中, 位置细胞具有多个具有 异质形状和大小 的位置场. We show that this diversity is explained by a surprisingly simple mathematical model, in which place fields are generated by thresholding a realization of a random Gaussian process. The model captures the statistics of field arrangements and generates new quantitative predictions about the statistics of field shapes and topologies. These predictions are quantitatively verified in bats and rodents, in one, two, and three dimensions, in both small and large environments. ......

    随机变量 $\vec{x}\in\mathbb{R}^{d}$, 约束 $E[\vec{x}]=\vec{\mu}$ 和 $\mathrm{Cov}[\vec{x}] =\Sigma$.熵 $h[p(\vec{x})] = -\int p(\vec{x})\log{p(\vec{x})}\mathrm{d}\vec{x}$ 最大的是 $g(\vec{x}) = \frac{1}{(2\pi)^{\frac{d}{2}}|\Sigma|^{\frac{1}{2}}}\exp{\left[-\frac{1}{2}(\vec{x}-\vec{\mu})^T\Sigma^{-1}(\vec{x}-\vec{\mu})\right]}$.

  3. *学习规则: 什么样的学习规则能使 weight matrix 学习到 Gaussian process?

  4. 确认小鼠线性吸引子的具体理论机制

    1. agg 主要的驱动因素是社会交互(male intruder, sniffing, attack...)的相关输入, 而没有考虑类 random walk 的自发性升高机制

    2. 类比眼位 $E$ 的 $v_{i} = v_{i}^{0} + k_{i}E$, aggression 的 $a(t)\in\mathbb{R}$ 是一种一维连续变量, 引入 latent state $x_{1}$ 来描述 integration dimension, $x_{1}$ 越高, 攻击概率和攻击程度越高.

    3. 因此, 即使 $\lambda=0$ 描述刻画了线性吸引子 $\pm$ 增长的 neutral stability, 但是 aggression 仍应被理解为一个具有方向性的积分器: $x_{1}\uparrow$, agg $\uparrow$; $x_{1}\downarrow$, agg $\downarrow$.

    4. aggression 不能简单地被理解为 integrate-and-fire 行为. 以 $a$ 表示 aggression 变量

      $$ \begin{aligned} \dot{a}(t) &= -\frac{a(t)-a_{0}}{\tau} + v_{\mathrm{social}}(t) + v_{\mathrm{state}}(t) + \xi(t)\\ P(\mathrm{attack}) &= \sigma[\beta(a(t)-a_{\mathrm{thresh}})]\end{aligned} $$

      即没有后续社交或饥饿等输入后, aggression 会以很慢的速度往 baseline $a_{0}$ 跌落. 若将其放置于一个短时系统中, 将会表现出 history dependence. 积分总是从当前状态 $a(t)$ 开始

      并且, 在攻击产生之后, $a$ 值也不会立刻归零, 高 $a$ 可持续约 80s, 而单次 attack bout 仅持续 5s. 这也确保了小鼠从攻击到进食行为的切换: 在进食完毕后仍保留较高的 $a$.

Todo:

  1. *阅读 A thamalus-brainstem attractor network drives history-biased decisions, 探索是否有将其和 random RNN 框架结合的可能性

  2. Follow 有关 universal statistics of hippocampal place fields across species and dimensionalities 的工作中和学习规则有关的部分

  3. 做一个小型的 weight matrix learning 实验, 看下能不能通过 local learning rule 逼近 $J_{ij}$ 矩阵

    Clark: 通过 $K^{-1}_{i,\lambda}$ 离线优化 $J$

    切入口: 将伪逆解替换为 online learning rule

meeting notes:

课题:

  1. 目前 Clark 已实现 offline 的 optimized weight matrix 用于产生 ring attractor, 是否存在某种 local learning rule 能够逼近这类 optimized weight matrix?

    $\dot{J}_{ij} = F[\vec{r}(t), J_{ij}]$

  2. 是否可以将 Clark 的方法推广至 place cells 相关数据集?

题目拟定

  1. 复现 Clark disordered ring attractor 的实验平台和动力学

  2. 系统测试 classical local learning rules 是否能从 sensory-clamped heterogeneous activity(感知输入引起的异质性神经活动) 自组织出 quasi-continuous attractor

  3. 使用 meta-learning 在 local rule basis 上搜索最小 plasticity motif, 并解释其与经典 Hebbian/Oja/BCM 等 plasticity 的关系

meeting notes:

课题的艰难探索

  1. 完成 Hebbian 等 learning rule 的 baseline 实现

    • Classical continuous attractor
    • Heterogeneous tuning curve

  2. Literature research

    • CA3 数据集寻找 (dandi...)
    • attractor in hippocampus 相关论文
    • 以及更多...

  3. Proposal 确定

    • 找到感兴趣的方向, 找到自己想要解决的问题 (只是把现有的 random RNN 推广到 place cell 数据集上, 这种缝合行为是一个真正的问题吗? )

神经回路如何在没有 global error signal 的情况下, self-organize 并且 maintain some low-dim dynamical motif

低维神经动力学如何在异质, 随机, 局部可塑的神经网络中形成并且维持? (How can low dimensional dynamical motifs self-organize and maintain in neural circuits without global error signal)

Clark's random RNN: 提供了一套分析逻辑, 用于判断是否出现了 continuous attractor