Skip to main content Startseite Ersteller hiyenwong ai_collection canns-toolkit-attractor-networks
canns-toolkit-attractor-networks Comprehensive open-source toolkit unifying continuous attractor neural network (CANN) research workflow. Three co-designed components (Python/Rust/GUI) for 1D/2D attractor modeling, spike-frequency adaptation, grid cells, path integration, and persistent homology-based attractor detection in neural recordings.
Zur Installation springen Skills Marktplatz Entdecken und erkunden Sie KI-Skills, die von der Community erstellt wurden.
Mit Codex oder Claude installieren Kopieren Sie diesen Prompt, fügen Sie ihn in Codex, Claude oder einen anderen Assistant ein und lassen Sie die Skill-Seite prüfen und installieren.
Prompt-Details anzeigen Ein direkter Befehl überspringt den Prüf-Prompt. Prüfen Sie die Quelle, bevor Sie ihn ausführen.
npx skills add https://github.com/hiyenwong/ai_collection --skill canns-toolkit-attractor-networksDer Befehl bleibt in einer Zeile. Scrollen Sie horizontal, um ihn vor dem Kopieren vollständig zu prüfen.
Sie bevorzugen eine lokale Kopie? Laden Sie die Dateien herunter, die SkillsMP derzeit vorliegen.
ZIP herunterladen Herunterladen... Mehr aus diesem Repository
Verwandte Berufe SOC
Basierend auf der SOC-Berufsklassifikation
name canns-toolkit-attractor-networks description Comprehensive open-source toolkit unifying continuous attractor neural network (CANN) research workflow. Three co-designed components (Python/Rust/GUI) for 1D/2D attractor modeling, spike-frequency adaptation, grid cells, path integration, and persistent homology-based attractor detection in neural recordings. version 1.0.0 tags ["neuroscience","continuous-attractor","grid-cells","place-cells","head-direction","path-integration","persistent-homology","topological-data-analysis","BrainPy","JAX","hippocampus","entorhinal-cortex"] arxiv 2606.27783 authors ["Sichao He","Aiersi Tuerhong","Shangjun She","Tianhao Chu","Yuling Wu","Junfeng Zuo","Si Wu"] institution Peking University published 2026-06-30
CANNs: A Toolkit for Research on Continuous Attractor Neural Networks
Core Methodology
1. What are Continuous Attractor Neural Networks (CANNs)?
Canonical computational framework for how the brain encodes continuous variables:
Spatial position (hippocampal place cells)Head direction (head-direction cells)Movement direction (entorhinal grid cells)
Key properties:
Recurrently connected population with localized "bump" of activity
Bump smoothly translates along low-dimensional manifold
Provides stability, noise robustness, and integration
Manifold topology: ring (S¹) for 1D, torus (T²) for 2D
Biological grounding:
Place cells (O'Keefe & Dostrovsky, 1971)
Grid cells (Hafting et al., 2005)
Head-direction cells (Taube et al., 1990)
2. Mathematical Core (Wu-Amari-Wong Model)
Network architecture:
N neurons on 1D ring or 2D torus
Translation-invariant recurrent connectivity (Gaussian kernel)
Divisive normalization implements global inhibition
Continuum of stable bump states parameterized by continuous variable
Dynamics:
τ du/dt = -u + ∫ J(u,v) r(v) dv + I_ext
r = [u]² / (1 + k ∫ [u]² du) # divisive normalization
Where:
u: internal state
r: firing rate
J: recurrent connectivity kernel (Gaussian)
k: global inhibition strength
I_ext: external input
Energy landscape:
E(r) = -1/2 r^T W r + I^T r
Key behaviors:
Bump can be moved arbitrarily by localized input
When input disappears, bump remains (short-term memory)
Attractor structure provides built-in integrator
3. CANNs Toolkit Architecture
Three co-designed components:
A. canns (Python library on BrainPy/JAX)
Modules:
Models (canns.models): Neural network dynamics
1D ring CANN (head-direction)
2D torus CANN (place fields)
2D grid-cell network (path integration)
Spike-frequency adaptation (SFA) variants
Theta-rhythmic modulation
Hierarchical path integration models
Brain-inspired attractor architectures
Tasks (canns.task): Experimental paradigms
Spatial navigation
Head-direction tracking
Grid cell firing field generation
Parametric working memory
Analyzers (canns.analyzer): Visualization and analysis
Energy landscape computation
Manifold extraction (PCA, UMAP)
Tuning curve fitting
Topological data analysis integration
Trainers (canns.trainer): Biologically plausible learning
Hebbian plasticity
STDP-like rules
Homeostatic mechanisms
Pipeline (canns.pipeline): Orchestration
Full workflow from simulation to analysis
Reproducible experiment scripts
B. canns-lib (Rust acceleration backend) Performance-critical operations:
Ripser-based persistent homology (hundreds-of-times speedup)
Long spatial navigation trajectories
Bulk task generation
Python FFI for seamless integration
C. ASA (Attractor Structure Analyzer - PySide6 GUI) Purpose: Detect attractor topology in experimental neural recordings
Data ingestion (.npz format)
Preprocessing (spike/rate extraction)
Point cloud construction (time-indexed or spatially-indexed)
Persistent homology computation
Shuffle controls (statistical significance)
Persistent cohomology decoding (CohoMap/EcohoMap)
Circular coordinate extraction
Grid score computation
Module-level workflows
GUI + CLI interfaces
Ring (S¹): One dominant H₁ barcode → head-direction cells, band cells, 1D CANNTorus (T² = S¹×S¹): Two stable H₁ features → grid-cell modules, 2D CANN
4. Advanced CANN Variants
A. Spike-Frequency Adaptation (SFA) Mechanism: Activity-dependent negative feedback
Turns static bump into moving wave
Enables anticipative tracking
Models theta sweeps and phase precession
τ_a da/dt = -a + b * r
τ du/dt = -u + ∫ J r dv - g_a * a + I_ext
a: adaptation current
b: adaptation strength
g_a: adaptation conductance
B. Theta-Rhythmic Modulation
Theta sweeps (forward/backward)
Phase precession
Phase procession
theta(t) = sin(2 π f_theta t + φ)
I_mod = I_baseline + A_theta * theta(t)
C. Hierarchical Path Integration Architecture: Multiple grid-cell modules with different spatial scales
Coarse modules: large grid spacing
Fine modules: small grid spacing
Hierarchical combination → precise position coding
5. Topological Data Analysis (TDA) for Attractor Detection
Track topological features (connected components, loops, voids) across scales
Barcode: persistence of features vs. scale parameter
Stable features = true topology; transient = noise
Application to neural data:
from ripser import ripser
r(t) = [r₁(t), r₂(t), ..., rₙ(t)]^T ∈ ℝ^N
X_t = {r(tⱼ) : j = 1 , ..., T} ⊂ ℝ^N
result = ripser(X_t, maxdim=2 )
diagrams = result['dgms' ]
ring_signature = len (diagrams[1 ]) > 0 and diagrams[1 ][0 , 1 ] > threshold
torus_signature = len (diagrams[1 ]) >= 2 and diagrams[1 ][1 , 1 ] > threshold
Persistent Cohomology Decoding:
Extract circular coordinates from cohomology generators
Map high-dimensional activity to S¹ (ring) or T² (torus)
Validate by alignment with behavioral variables
Efficient cohomology computation
Cache-aware result management
Module-level workflows
Surrogate data with destroyed topology
Statistical significance testing
Distinguish true attractor from noise
6. Reproducible Research Pipelines Example: 1D Ring CANN (Head Direction)
from canns.models import CANN1D
from canns.task import HeadDirectionTracking
from canns.analyzer import EnergyLandscape, ManifoldAnalysis
net = CANN1D(N=512 , J0=1.0 , a=0.5 , k=0.1 )
task = HeadDirectionTracking(n_directions=4 , delay=500 )
inputs = task.sample()
outputs, states = net.simulate(inputs, T=2000 )
energy = EnergyLandscape(net.W)
energy.plot()
manifold = ManifoldAnalysis(states)
manifold.pca(n_components=3 )
manifold.umap(n_neighbors=15 )
from canns.analyzer import PersistentHomology
ph = PersistentHomology()
barcode = ph.compute(states)
assert ph.is_ring_attractor(barcode)
Example: Real Neural Recording Analysis with ASA
from asa import AttractorStructureAnalyzer
data = asa.load('mec_grid_cells.npz' )
rates = asa.extract_rates(data, bin_size=50 )
asa_pipeline = AttractorStructureAnalyzer()
result = asa_pipeline.analyze(
rates,
method='persistent_cohomology' ,
maxdim=2 ,
shuffle_controls=100
)
if result.is_torus():
print ("Grid-cell module detected: toroidal topology" )
circular_coords = result.decode_circular_coordinates()
grid_score = result.compute_grid_score(circular_coords)
elif result.is_ring():
print ("Head-direction or band-cell ring attractor" )
phase = result.decode_ring_phase()
7. Key Capabilities
SFA-driven anticipative tracking
Theta sweeps in head-direction/place/grid systems
Hierarchical path integration
Real MEC grid-cell module analysis (heterogeneous topology)
Head-direction cell ring attractor detection
GridScore: quantify hexagonal firing fields
CohoScore: topological signature strength
PathCompare: compare trajectories across conditions
Module-level workflows for common analyses
8. Installation and Usage
pip install canns
pip install canns[gui]
pip install asa-attractor-analyzer
import canns
net = canns.models.GridCellNetwork(module_id=1 )
positions, firing_rates = net.simulate_navigation(
trajectory='random_walk' ,
duration=600
)
from canns.analyzer import GridFieldAnalysis
gfa = GridFieldAnalysis()
grid_score = gfa.compute_score(firing_rates, positions)
gfa.plot_firing_fields(firing_rates, positions)
Key Insights
1. Unification of CANN Research Problem: CANN research fragmented across:
Lab-specific implementations
General-purpose simulators (NEURON, BRIAN) lack CANN-specific abstractions
No standardized path from spike trains to attractor geometry
Solution: Unified toolkit covering:
Modeling (canns)
Acceleration (canns-lib)
Experimental analysis (ASA)
Reproducible pipelines
2. Topological Signatures as Biomarkers Finding: Real MEC grid-cell modules show heterogeneous topology
Some modules: clear toroidal signature
Others: partial or unstable topology
Suggests: not all grid-cell modules are perfect CANNs
Implication: Persistent homology provides quantitative biomarker for:
Attractor quality (how "perfect" is the CANN?)
Disease states (does Alzheimer's degrade toroidal topology?)
Development (how does topology emerge during learning?)
3. Rust Acceleration Matters
Persistent homology: 100-1000× speedup
Spatial navigation: efficient long trajectories
Enables: real-time analysis of large datasets
Memory safety without garbage collection
Zero-cost abstractions
Seamless Python FFI
4. Separation of Concerns
Models: define dynamics
Tasks: generate inputs
Analyzers: visualize/analyze (no state modification)
Trainers: update parameters
Pipeline: orchestrate
Benefit: Modular, extensible, reproducible
Experimental Validation
Predictions for Empirical Testing
Topology heterogeneity: Different grid-cell modules should show varying topological "perfection" (testable with large-scale MEC recordings)
Disease biomarkers: Neurodegenerative diseases should degrade toroidal topology (Alzheimer's → entorhinal cortex degradation)
Development trajectory: Toroidal topology should emerge during learning (young animals → less stable topology)
SFA signature: Theta sweeps and phase precession should correlate with SFA strength (testable via pharmacological manipulation)
Limitations
Rate-based models (most implementations) → cannot capture spike timing
Assumes translation-invariant connectivity → biological networks have variability
Persistent homology computationally expensive for very large populations (>10,000 neurons)
No direct spike-train analysis (requires rate conversion)
Extensions
Spiking CANNs: Implement leaky integrate-and-fire or adaptive exponential integrate-and-fire neuronsLearning rules: Add biologically plausible synaptic plasticity (STDP, homeostatic)Multi-region models: Connect hippocampus, entorhinal cortex, head-direction circuitsBehavioral coupling: Link attractor dynamics to decision-making and navigation behaviorGPU acceleration: JAX backend already supports GPU; extend Rust backend for CUDA
References
arXiv:2606.27783 - Original paper
Amari (1977a) - Lateral-inhibition neural fields
Wu et al. (2008, 2016) - Analytically solvable CANN model
Gardner et al. (2022) - Toroidal population geometry in grid cells
Mi et al. (2014) - Spike-frequency adaptation in CANNs
Chu et al. (2024, 2025) - Theta rhythms and hierarchical path integration
Activation Keywords continuous attractor neural network, CANN, grid cells, place cells, head-direction cells, path integration, persistent homology, topological data analysis, BrainPy, JAX, hippocampus, entorhinal cortex, spatial navigation, ring attractor, torus attractor, spike-frequency adaptation, theta sweeps, phase precession, manifold learning, neural manifold, attractor analysis, ASA toolkit
