Diverse Neural Sequences in QIF Networks: An Analytically Tractable Framework for Synfire Chains and Hippocampal Replay

TL;DR

The paper tackles how diverse, precisely timed neural sequences can emerge under biological constraints. It introduces a minimal yet powerful framework of Quadratic Integrate-and-Fire neurons with temporally asymmetric Hebbian learning, enabling exact low-dimensional firing-rate reductions. The authors show that this framework supports both stable synfire-chain propagation and replay-like transient sequences with intra-ripple frequency accommodation, and that these dynamics are robust to synaptic heterogeneity and pattern overlap. The work provides mechanistic insight through the FREs, linking network structure to bifurcations that govern sequence generation, and positions QIF networks as a tractable, biologically plausible platform for studying neural sequences.

Abstract

Sequential neural activity is fundamental to cognition, yet how diverse sequences are recalled under biological constraints remains a key question. Existing models often struggle to balance biophysical realism and analytical tractability. We address this problem by proposing a parsimonious network of Quadratic Integrate-and-Fire (QIF) neurons with sequences embedded via a temporally asymmetric Hebbian (TAH) rule. Our findings demonstrate that this single framework robustly reproduces a spectrum of sequential activities, including persistent synfire-like chains and transient, hippocampal replay-like bursts exhibiting intra-ripple frequency accommodation (IFA), all achieved without requiring specialized delay or adaptation mechanisms. Crucially, we derive exact low-dimensional firing-rate equations (FREs) that provide mechanistic insight, elucidating the bifurcation structure governing these distinct dynamical regimes and explaining their stability. The model also exhibits strong robustness to synaptic heterogeneity and memory pattern overlap. These results establish QIF networks with TAH connectivity as an analytically tractable and biologically plausible platform for investigating the emergence, stability, and diversity of sequential neural activity in the brain.

Figures (5)

• Figure 1: Phase-plane structure and linear stability of the firing-rate equations.A Single-population FREs \ref{['eq:FRE_single']} are bistable, with a low-rate node $(r^{*}_{\mathrm{node}},v^{*}_{\mathrm{node}})$ (bottom left) and a high-rate focus $(r^{*}_{\mathrm{fc}},v^{*}_{\mathrm{fc}})$ (upper right). B Eigenvalue spectrum of the full Jacobian at $(r_k, v_k) = (r^{*}_{\mathrm{fc}},v^{*}_{\mathrm{fc}})$. Solid dots show the discrete spectrum for a finite network with $P=8$ populations; the central dot corresponds to the spatially homogeneous mode ($k=0$), which matches the single-population eigenvalue. The grey dotted curve depicts the continuum envelope obtained as $P\rightarrow\infty$. C Same conventions as in (b) but for $(r^{*}_{\mathrm{node}},v^{*}_{\mathrm{node}})$, illustrating that the node remains stable while the focus becomes unstable when $J_{1}\approx J_{2}$. Parameters shared across panels: $J_{1}=15$, $J_{2}=15$, $\bar{\eta}=-5$, $\Delta=1$.
• Figure 2: Stable synfire propagation in a QIF network with TAH connectivity.A Spike raster: synchronized bursts travel successively among populations. B Population firing rate; solid lines are FRE predictions, dashed lines are full simulations. C Median membrane potential, same conventions as in B. Parameters: $J_1=15$, $J_2=15$, $\bar{\eta}=-5$, $\Delta=1$, $P=8$.
• Figure 3: Single-population response explains stability of synfire propagation.A Response to a Gaussian input ($A_{\text{in}},\sigma_{\text{in}}$). Before stimulation, the population rested at the low-rate node. B State-space analysis of the response. Two fixed points exist: the origin (quiescent state) and a bursting attractor (black dot). Purple and yellow shading indicate their basins of attraction; grey trajectories lead to the high-rate focus. Arrows show the vector field. Parameters: $J_2=15$, $\bar{\eta}=-5$, $\Delta=1$.
• Figure 4: Transient replay and ripple oscillations under slow modulatory drive.A Representative SWR event. Solid lines: FRE prediction; dashed lines: full simulation. B Within each burst, sequential activity propagates several times through the populations before fading (same conventions as in A). C Wavelet spectrogram; the white curve traces the instantaneous peak frequency, revealing IFA. Parameters: $J_{1}=1.8$, $J_{2}=15$, $\bar{\eta}=-5$, $\Delta=1$, $P=10$.
• Figure 5: Robustness of sequential propagation.A Lognormal synaptic noise ($\sigma_{\text{syn}}=1.0$, dotted; $2.0$, dashed) broadens and slows volleys but does not halt them. B Pattern overlap (sparsity $f=0.01$, dotted; $f=0.1$, dashed) likewise preserves the sequence. Solid lines: unperturbed FRE prediction.

Theorems & Definitions (2)

• lemma thmcounterlemma
• proof