Continuous Attractor Neural Networks

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9 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Oct 21, 2026

Reconstruction differences rival individual differences in the fly compass connectome and break trained circuit models

Neural network models are increasingly constructed from synapse-resolution connectomes, and the same circuit is now available in reconstructions from other animals and pipelines. We do not know whether such models are dependent on the reconstruction they are built from, and whether connectome differences are biological or measurement errors. We studied the Drosophila head-direction circuit in nine versions: four flies (male CNS, hemibrain, FlyWire, BANC) and five variants of the same fly varying only by thresholds, proofreading or synapse detection. Using wiring-based correspondences validated by anatomical labels, we place all differences on one scale. A change of synapse detection within one fly changed the circuit more than halfway to the smallest between-fly difference on four distance measures; proofreading differences were smaller but depended on the metric, and left and right halves of one fly differed no more than random halves. Networks trained on each wiring to hold a cued heading developed near-perfect ring attractors, but their error increased from below 1 degree to 10-28 degrees when all weights changed by 1%. Training on each wiring did not transfer to any other connectome, including other versions of the same fly; refitting thirty cell-type gains, we repaired filtering-level differences but remaining error depended on wiring distance. Training with noise lowered precision and gave only partial transfer. In imaging data, the fly compass drifted gradually in darkness. Connectome-constrained models should report the reconstruction they were built on and be tested for robustness across reconstructions.

Md Ali Ashraf Yad, Nazifa Tabassum Nabila

Wrocław University of Science and Technology · Comilla University

Continuous Attractor Neural Networks Brain Network Analysis Neural Network Robustness

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Oct 19, 2026

A Spiking Ring-Attractor Architecture for Representation and Control of Revolute Robot Joints

Robotic systems with revolute joints evolve on circular state spaces, yet most control architectures represent these states using Euclidean variables that ignore this underlying geometry. We propose a fully spiking neural control architecture in which ring attractors encode joint states, enforcing representations consistent with the topology of revolute systems. Homeostatic regulation computes goal-state mismatch directly over these distributed representations, and opponent gain-modulated populations convert this mismatch into controlled phase shifts of the activity bump, implementing set-point regulation as motion on the ring. We show that the bump dynamics follow an SO(2) geometry, and that gain asymmetries induce a signed phase velocity on the ring. To interface distributed activity with scalar regulation signals, we derive an analytic Fourier phase decoder and implement its signed components using push-pull spiking populations. For multi-joint systems, we demonstrate that local ring-based Fourier features compose into product representations that linearly decode SO(3) orientations through forward kinematics. Experiments in NEST validate the full SO(2) regulation mechanism and the spiking product-feature decoder for lift, pitch, and yaw. Robot experiments on a Tiago arm show that decoded ring dynamics generate joint velocity commands, producing directed motion with joint-dependent accuracy. Together, these results establish a neuromorphic control framework in which representation, regulation, and action are unified within a ring-attractor substrate aligned with the geometry of revolute systems.

Aung Htet, Alejandro Rodriguez Jimenez, Ruidong Ma +1

Sheffield Hallam University, Sheffield, UK

Continuous Attractor Neural Networks Robotic Control Spiking Neural Networks Recurrent Neural Networks

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Aug 3, 2026

Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory

The ability to robustly maintain and update continuous variables is a hallmark of working memory. While classical continuous attractor networks suffer from severe fine-tuning fragility, standard artificial recurrent neural networks (RNNs) like GRUs and LSTMs typically fail to stably learn continuous manifolds, instead shattering the state space into discretized point attractors. To bridge this gap, we draw inspiration from divisive normalization, a canonical neural computation widely observed across cortical circuits, and propose the Recurrent Divisive Normalization Network (RDNN), a minimal and algebraically isolated model of dynamic division. Through dynamical systems analysis on canonical working memory tasks, we demonstrate that this biophysical constraint allows the network to converge to robust, high-fidelity slow manifolds. Furthermore, we analyze the gradient dynamics of divisive normalization during Backpropagation Through Time (BPTT), showing that it introduces an activity-dependent local gradient scaling. This scaling dampens parameter updates in highly active regimes, which empirically aligns with a significant self-compression of the network's effective rank, confining the recurrent dynamics to a tight, low-dimensional subspace while avoiding the optimization pathologies associated with explicit low-rank factorization. Finally, ablations demonstrate that while subtractive inhibition can maintain static memories, divisive normalization is mathematically essential to prevent manifold shattering under time-varying inputs. Our findings identify divisive normalization not merely as a biological artifact, but as a critical computational mechanism for learning high-fidelity continuous representations.

Zhaotian Gu, Jie Su, Weiwei Wang +3

School of System Science, Beijing Normal University · Qiyuan Laboratory · State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University

Recurrent Neural Networks Continuous Attractor Neural Networks Neural Network Training Dynamics

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Jun 26, 2026

CANNs: A Toolkit for Research on Continuous Attractor Neural Networks

Continuous attractor neural networks (CANNs) are the canonical computational framework for how the brain encodes continuous variables such as spatial position, head direction, and movement direction, and explain the activity of hippocampal place cells, entorhinal grid cells, and head-direction cells. CANN research, however, is fragmented: most results rest on lab-specific implementations, general-purpose simulators lack CANN-specific abstractions, and the path from spike trains to attractor geometry in real recordings lacks a standardized toolkit. Here, we present a comprehensive open-source toolkit that unifies the full CANN research workflow. It combines three tightly integrated components: 1) canns, a Python library on BrainPy/JAX that provides standardized 1D/2D CANNs, spike-frequency-adaptation variants, grid cell networks, hierarchical path-integration models, and brain-inspired attractor architectures, together with curated datasets, task generators, an analyzer module and trainer modules for biologically plausible plasticity; 2) canns-lib, a Rust acceleration backend delivering hundreds-of-times speedups for spatial-navigation workloads and modest gains for Ripser-based persistent homology; 3) ASA (Attractor Structure Analyzer), a PySide6 pipeline applying persistent homology and cohomology to experimental neural recordings to detect ring-like and toroidal attractor signatures in real data. The toolkit ships with full-detail reproducible pipelines that recover recent CANN results including SFA-driven anticipative tracking, theta sweeps in head-direction/place/grid systems, and hierarchical path integration.

Sichao He, Aiersi Tuerhong, Shangjun She +4

School of Psychological and Cognitive Sciences, Peking–Tsinghua Center for Life Sciences, PKU-IDG/McGovern Institute for Brain Research, Center of Quantitative Biology, Peking University, Beijing, China · College of Mathematics and Statistics, Chongqing University, Chongqing, China

Neural Representation Geometry Recurrent Neural Networks Continuous Attractor Neural Networks Neural Encoding

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Jun 21, 2026

A Theory-grounded Hybrid Neural Network Integrating Complementary Estimation Mechanisms for Stable Visual Object TrackingA

Hybrid neural networks (HNNs) that integrate artificial neural networks (ANNs) with brain-inspired neural networks have achieved broad success across perception and control tasks. However, much of the current success is confined to neuron-scale hybridization, where discrete, spike-based coding fundamentally limits applicability to continuous-state estimation tasks. In neuroscience, continuous attractor neural networks (CANNs) represent continuous states through neural ensembles, pointing to a population-scale route for HNNs to address this limitation. Yet, principled methodologies for ANN-CANN integration remain largely underexplored. In this work, we propose a theory-grounded ANN-CANN hybridization framework and instantiate it as a hybrid tracking neural network (HTNN) for visual object tracking, a representative continuous-state estimation task. The framework aligns ANN response maps with CANN dynamics in the same state space, enabling the two heterogeneous branches to interact through the shared state representation. Furthermore, we uncover a functional bias-variance complementarity: data-driven ANNs provide asymptotically unbiased estimates, while CANN estimates are low-variance but temporally lagged. By operationalizing this complementarity, HTNN achieves stable and accurate tracking across nine visual tracking benchmarks, consistently outperforming single-network baselines and existing hybrid models. Notably, these performance gains are robustly maintained even under diverse environmental variations, including occlusion, motion blur, and background interference. Through this proof-of-concept study, our framework offers a generalizable foundation for advancing HNNs toward population-scale hybridization.

Yancheng Zhou, Hanle Zheng, Lei Deng +1

Center for Brain Inspired Computing Research (CBICR), Department of Precision Instrument, Tsinghua University, Beijing, China · Weixian College, Tsinghua University, Beijing, China · Department of Computing, The Hong Kong Polytechnic University, Hong Kong, China

Visual Object Tracking Continuous Attractor Neural Networks

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Jun 13, 2026

Controlled Dynamics Attractor Transformer

Transformer architectures have dramatically advanced representation learning and inference in deep models through self-attention mechanisms. In parallel,associative memory (AM) frameworks map representations onto energy landscapes, offering interpretable retrieval mechanisms. However, their continuous-time inference dynamics lack the biological plausibility of classical Continuous Attractor Neural Networks (CANNs). To bridge this gap, we propose Controlled Dynamics Attractor Transformer (CDAT), which couples a mixture von Mises-Fisher (Mo-vMF) attention energy with a Hopfield refinement energy, while augmenting energy descent with a CANN-inspired excitation-inhibition modulation. CDAT instantiates a topology-constrained dynamical system whose couplings encode relational structure among tokens, thereby linking attractor-style dynamics to modern energy-based attention. We further provide a constructive dissipation analysis to formally establish their controlled inference dynamics. Benefiting from these robust and structured dynamics, CDAT achieves state-of-the-art performance across multiple benchmarks in graph anomaly detection and graph classification.

Cheng Zhang, Minnan Luo, Zesheng Yang +3

School of Computer Science and Technology, MOEK-LINNS Lab, Xi’an Jiaotong University, Xi’an, Shaanxi, China · Department of Computer Science and Technology, Tsinghua University, Beijing, China

Energy-Based Models Continuous Attractor Neural Networks Graph Classification Associative Memory Graph Transformer Anomaly Detection

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May 5, 2026

Symmetry, Defects, and Diffusion in Continuous-memory Recurrent Networks

Continuous-memory recurrent networks must preserve phase, position, or orientation despite model imperfections and state noise. We develop a geometric framework that separates three questions: how many memory coordinates are neutrally transported, how deterministic perturbations alter their finite-horizon stability, and how ambient noise is decoded along them. Exact per-input equivariance transports analytical group tangents pathwise and, on a compact nondegenerate orbit stratum, yields at least

q=\dim(G/H)

zero group-tangent Lyapunov exponents under stationary ergodic driving. For imperfect dynamics, a four-block tangent/normal decomposition gives local and finite-horizon bounds on tangent growth and subspace rotation, distinguishing first-order direct damage from second-order leakage through contracting normal directions. For noisy dynamics, a specified decoder maps ambient covariance

Q

to coordinate covariance

ZQZ^\top

; under isotropic noise and fixed tangent energy, least-squares decoding and scaled-isometric action geometry minimize local diffusion. Local and finite-horizon evaluations include cases both within and outside the sufficient conditions. In a fresh twenty-seed

T^2

replication, a decoder-covariance objective improves noisy horizon-256 memory in every pair while meeting a prespecified clean-error equivalence margin. Direct noise training also improves noisy memory but incurs a clean-error tradeoff. In coupled

T^4/T^8

integrators, the advantage of anisotropic-covariance over isotropic regularization reverses when evaluation noise becomes isotropic. These results connect continuous symmetry to measurable limits and design choices for recurrent memory under explicit dynamical, decoder, and noise assumptions.

Hanson Hanxuan Mo

Equivariant Neural Networks Recurrent Neural Networks Continuous Attractor Neural Networks

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Apr 17, 2026

Impact of leaky dynamics on predictive path integration accuracy in recurrent neural networks

Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To address this question, we introduce adaptive time scales through a leak term in recurrent neural networks (RNNs), forming leaky RNNs discretized from the continuous attractors of firing rate models. Our results demonstrate that leaky RNNs substantially enhance the emergence of well-defined and highly regular hexagonal firing patterns. Compared with vanilla RNNs lacking a leak term, the trained leaky RNNs produce more accurate position estimates while generating reliable grid-cell-like representations. Furthermore, under identical noise conditions, leaky RNNs consistently exhibit more stable dynamics and better-defined grid structures. The learned dynamics also give rise to stable torus attractors with a clear central hole, supporting robust and regular grid-like activity. Overall, the dynamic leak acts as a low-pass filtering mechanism that protects recurrent neural circuitry from noise, stabilizes network dynamics, and improves path-integration accuracy in recurrent neural networks.

Yanlin Zhang, Yan Zhang, Muhua Zheng +1

School of physics and Electronic Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China · Teaching Department, Jiangsu University Jingjiang College, Zhenjiang 212028, Jiangsu, China

Recurrent Neural Networks Continuous Attractor Neural Networks

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Apr 15, 2026

Neuromorphic Spiking Ring Attractor for Proprioceptive Joint-State Estimation

Maintaining stable internal representations of continuous variables is fundamental for effective robotic control. Continuous attractor networks provide a biologically inspired mechanism for encoding such variables, yet neuromorphic realizations have rarely addressed proprioceptive estimation under resource constraints. This work introduces a spiking ring-attractor network representing a robot joint angle through self-sustaining population activity. Local excitation and broad inhibition support a stable activity bump, while velocity-modulated asymmetries drive its translation and boundary conditions confine motion within mechanical limits. The network reproduces smooth trajectory tracking and remains stable near joint limits, showing reduced drift and improved accuracy compared to unbounded models. Such compact hardware-compatible implementation preserves multi-second stability demonstrating a near-linear relationship between bump velocity and synaptic modulation.

Federica Ferrari, Flavia Davidhi, Bernard Maacaron +6

Istituto Italiano di Tecnologia, Genoa, Italy · Department of Neurosurgery, University Hospital Zürich, Switzerland · Institute of Neuroinformatics, Univ. of Zurich and ETH Zurich, Switzerland +3

Continuous Attractor Neural Networks Robot State Estimation Spiking Neural Networks Neuromorphic Computing Recurrent Neural Networks

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