Spike-Timing-Dependent Plasticity (STDP)

Hook: 1998's 20 Milliseconds

In 1998 Bi and Poo, in Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type, discovered a precise timing rule in pairs of hippocampal neurons:

If the presynaptic spike arrives BEFORE the postsynaptic spike within 20 ms: the synapse strengthens (LTP).
If the presynaptic spike arrives AFTER the postsynaptic spike within 20 ms: the synapse weakens (LTD).
If the gap exceeds ~50 ms: no change.

This rule is the time-asymmetric version of Hebbian learning: not “cells that fire together wire together” but “the cell that fires first is the cause”.

Intuition: if neuron A is playing a role in firing B in time (A first, then B), then A→B should strengthen. That’s the biological foundation of causal learning.

40 years on: modern reinforcement learning, world models, video-prediction systems — all investigate STDP variants. SIDRA Y100 target: run STDP natively in memristor hardware.

Intuition: An Asymmetric Learning Window

The STDP learning window looks like this:

   Δw
    ↑
+A+ |    ●
    |   ●
    |  ●
    | ●●
    |●
────┼──────●●●●● → Δt (post − pre, ms)
    |        ●
    |          ●
    |            ●
    |              ●
-A- |________________
    -50  -20   0   +20  +50

Right side ( $\Delta t = t_{\text{post}} - t_{\text{pre}} > 0$ ): pre → post order → LTP.
Left side ( $\Delta t < 0$ ): post → pre order → LTD.
Window scale $\tau \approx 20$ ms: typical for the human brain.

Peak values:

LTP peak: $\Delta w \approx +A_+ \approx +0.5$ (normalized weight units).
LTD peak: $\Delta w \approx -A_- \approx -0.5$ (usually slightly bigger than LTP).

Why asymmetric? Cause matters. If A always fires after B, A can’t be B’s cause → weaken the link. If A always fires before B, A might be triggering B → strengthen. STDP teaches the brain causality.

Difference from Hebbian: pure Hebbian is order-independent ( $\Delta w \propto x \cdot y$ ; order doesn’t matter). STDP is order-dependent. Hebbian = statistical correlation; STDP = causal ordered coupling.

Formalism: The STDP Equation and Its Biology

L1 · Başlangıç

Standard STDP equation:

\Delta w(\Delta t) = \begin{cases} +A_+ \cdot e^{-\Delta t / \tau_+} & \text{if } \Delta t > 0 \text{ (pre first, post second)} \\ -A_- \cdot e^{\Delta t / \tau_-} & \text{if } \Delta t < 0 \text{ (post first, pre second)} \\ 0 & \text{if } \Delta t = 0 \end{cases}

$\Delta t = t_{\text{post}} - t_{\text{pre}}$ (ms)
$A_+, A_-$ — peak amplitudes (typically 0.001-0.01, normalized)
$\tau_+, \tau_-$ — time constants (~10-50 ms)

Bi & Poo values:

$\tau_+ \approx 17$ ms
$\tau_- \approx 34$ ms (LTD side is a bit wider)
Often $A_- > A_+$ (LTD dominates → average balance)

L2 · Tam

Biological basis — why this window?

Recall the NMDA receptor (3.2): glutamate + post-depolarization together → Ca²⁺ flows. The amount of Ca²⁺ depends on timing:

Pre first, post second ( $\Delta t > 0$ ):

Pre spike → glutamate released.
Glutamate binds NMDA.
A few ms later, post spike → Mg²⁺ block lifts.
NMDA open + glutamate present → large Ca²⁺ influx.
High, sudden Ca²⁺ → CaMKII → AMPA insertion → LTP.

Post first, pre second ( $\Delta t < 0$ ):

Post spike → membrane depolarized, but no glutamate yet.
Pre spike → glutamate released, binds NMDA.
But post depolarization is already over → Mg²⁺ re-blocks.
Little Ca²⁺ flows (only AMPA), and in a prolonged weak flow → calcineurin → AMPA endocytosis → LTD.

Key: the same NMDA + Ca²⁺ cascade produces both LTP and LTD depending on timing. The gate: $\Delta t$ .

Multi-spike STDP (real):

The above describes single-pre / single-post experiments. Real neurons fire in bursts. Multi-spike STDP:

Triplet STDP (Pfister & Gerstner 2006): specific behavior on pre-post-pre or post-pre-post patterns.
Voltage-based STDP (Clopath et al. 2010): looks at the whole postsynaptic membrane voltage, not just spike times.
Calcium-based STDP (Graupner & Brunel 2012): models Ca²⁺ concentration directly.

All of these generalize BCM (3.3) — multi-timescale plasticity.

L3 · Derin

Functional consequences of STDP:

1. Sequence learning: STDP is naturally suited for temporal sequences. Spiking neural networks (SNNs) use it for language, music, motor learning.

2. Sparse representation: inactive post-neurons receive no LTP; STDP naturally biases toward sparse coding.

3. Unstable dynamics: pure STDP is as unstable as pure Hebbian. Fixes: synaptic scaling, BCM-style normalization, homeostatic STDP variants.

4. Combining with reinforcement learning: a third factor (dopamine) gates STDP → R-STDP. STDP is on at reward moments, otherwise off. The brain’s “reinforce good behavior” mechanism.

STDP implementation on SIDRA:

The natural $\Delta G \propto V_{\text{pre}} \cdot V_{\text{post}}$ behavior of the memristor can deliver STDP — but not directly. It needs time-coded voltage pulse pairs:

Scheme (Y10 target):

Pre spike → short positive pulse on the presynaptic electrode (e.g. +V/2, 10 ns).
Δt later, post spike → short negative pulse on the postsynaptic electrode (-V/2, 10 ns).
If they overlap: the memristor sees V_pre - V_post = +V → SET (LTP).
If post is first and pre is second: memristor sees -V → RESET (LTD).
The overlap window is shaped by pulse width → the STDP τ is emulated.

This approach is used by IBM, Intel, and other neuromorphic groups:

IBM TrueNorth (2014): spike-based but no STDP; weights loaded post-training.
Intel Loihi (2018): spikes + on-chip STDP. CMOS-based.
SpiNNaker (Manchester): software-emulated STDP.
SIDRA Y100 target: native STDP in memristor hardware — potentially the world’s first large-scale analog STDP chip.

Why STDP for online learning?

Backprop needs: error signal, backward pass, global gradient. Hard in hardware (3.6).

STDP needs: pre + post spike coincidence. Local. Works in a memristor cell without extra circuitry.

Training is “slow” but energy is tiny and hardware fits. Ideal for edge AI.

Experiment: 2 Neurons, 5 Spike Pairs, Synaptic Update

One synapse between two neurons. Initial weight $w_0 = 0.5$ . STDP params: $A_+ = 0.1, A_- = 0.12, \tau_+ = \tau_- = 20$ ms.

Observe 5 spike pairs:

Pair	$t_{\text{pre}}$ (ms)	$t_{\text{post}}$ (ms)	$\Delta t$ (ms)	$\Delta w$
1	0	5	+5	$+0.1 e^{-5/20} = +0.078$
2	100	90	-10	$-0.12 e^{-10/20} = -0.073$
3	200	215	+15	$+0.1 e^{-15/20} = +0.047$
4	300	280	-20	$-0.12 e^{-20/20} = -0.044$
5	400	405	+5	$+0.1 e^{-5/20} = +0.078$

Total change: $0.078 - 0.073 + 0.047 - 0.044 + 0.078 = +0.086$ .

New weight: $w = 0.5 + 0.086 = 0.586$ .

Interpretation: 3 of 5 pairs were in the LTP direction (pre first), 2 in LTD (post first). Net gain → connection strengthened. If pre-post were always pre-first, the connection would strengthen far faster.

SIDRA parallel:

5 spike pairs = 5 voltage pulse pairs.
Each pair consumes ~1 pJ in the memristor cell (partial STDP update).
Total 5 pJ. Vs a full SET (~10 pJ), a partial update is much more efficient.
Y100 target: 1 million spike pairs / s / cell → 1 µW per cell. Very low-power edge learning.

Quick Quiz

1/6The core STDP rule?

Lab Exercise

STDP-based sequence learning on the SIDRA Y10 prototype.

Scenario: A 4-input (A, B, C, D), single-output LIF neuron. Each input is tied to one SIDRA memristor (4 synapses). We want to train via STDP to recognize the sequence A → B → C (don’t fire for D).

Data:

4 synapses, initial weights $w_A = w_B = w_C = w_D = 0.25$
STDP: $A_+ = 0.05, A_- = 0.06, \tau = 20$ ms
Training: 100 examples. 50% are A-B-C sequences (each 10 ms apart), followed by a post spike. 50% are random D spikes + random post spikes.
For each synapse, $\Delta w = \sum$ STDP_rule

Questions:

(a) First training example (A-B-C → post at 0/10/20/30 ms): per synapse $\Delta t$ and $\Delta w$ ? (b) Expected weight distribution after 100 examples? Which synapse gains the most? (c) What does the trained neuron do on an A-B-C sequence? On D? (d) Compared to backprop: when is STDP better? (e) How many parallel sequence-recognition nodes can one SIDRA Y10 crossbar (256×256) host?

Solutions

(a) A: $t_{\text{pre}} = 0, t_{\text{post}} = 30$ , $\Delta t = +30$ ms → $\Delta w = +0.05 e^{-30/20} = +0.0112$ . B: $\Delta t = +20$ → $+0.0184$ . C: $\Delta t = +10$ → $+0.0303$ . D: random → ≈ 0. A gains least (farther), C gains most (closest).

(b) 50 of the 100 examples are A-B-C → C’s weight rises fastest (~0.03 × 50 = 1.5 + init 0.25 = 1.75; in practice saturates at 1.0). B: ~1.2. A: ~0.9. D: random → stays ~0.25. Ordering: C > B > A >> D.

(c) On A-B-C: each synapse gets a spike, the membrane depolarizes cumulatively → threshold crossed → post spike. Recognition! On D: one small EPSP, threshold not crossed → no post spike. The neuron has become an “A-B-C detector”.

(d) STDP advantage: no labels during training (unsupervised); just spike coincidences. Backprop needs target labels. STDP is also online (updates on every spike pair), backprop is batch. STDP fits edge AI better.

(e) One crossbar = 256 rows × 256 columns = 256 sequence-recognition neurons. Y1 6400 crossbars → 1.64M sequence-recognition neurons. Each can learn a different sequence → massive unsupervised feature learning. Y10 has 24× → 39M.

Cheat Sheet

STDP rule: pre first, post second → LTP; reverse → LTD. Asymmetric timing window $\tau \approx 20$ ms.
Bi & Poo 1998: precise observation in hippocampal neurons.
Equation: $\Delta w = +A_+ e^{-\Delta t / \tau_+}$ for $\Delta t > 0$ , $-A_- e^{\Delta t / \tau_-}$ for $\Delta t < 0$ .
Biology: NMDA + Ca²⁺ cascade asymmetry.
Upside: time-dependent → learns causal relations (not just correlation).
Reinforcement combo: R-STDP (dopamine modulation).
SIDRA: time-coded pre/post voltage pulse pairs → natural STDP in memristor hardware. Y100 target.

Vision: STDP-Native Hardware and SIDRA's Brain Claim

STDP is the atom of brain-compatible learning. SIDRA’s ultimate claim is to validate that atom in hardware:

Y1 (today): no STDP; weights trained externally on GPU, fixed on chip. Inference-focused.
Y3 (2027): software-emulated STDP (CMOS control circuit sends STDP-shaped pulses to the memristor). Prototype scale.
Y10 (2029): hardware-native STDP — pre/post pulse pairs update the memristor directly with the STDP rule. Multi-spike variants (triplet, voltage-based).
Y100 (2031+): STDP + R-STDP + sparse spike coding + multi-timescale plasticity all at once. Brain-compatible online learning; a GPT-class model trains at the edge.
Y1000 (long horizon): bio-compatible organic STDP device + brain implant. Neuralink’s closed-loop AI.

Strategic signal for Türkiye: no commercial STDP-native chip exists today (Intel Loihi, IBM TrueNorth use digital simulation). Memristor-based, true analog STDP hardware is an open category. If we win that category with the SIDRA Y10 prototype, we could be first in the world. A rare category where Türkiye could plausibly lead in AI.

Unexpected future: the continuously-learning home robot. A robot arrives, meets a child, cat, kitchen — STDP lets it learn from every interaction, offline, no GPU. SIDRA Y100 + STDP could be the first commercial system for this. 2032-2035 horizon; Türkiye has the chance to patent the architecture.

Module 3 wrap-up: we went from biology to algorithm, synapse to memristor, Hebb to STDP. Module 4 (Math Arsenal) covers the algebra, probability, and optimization tools beneath this chain. Module 5 (Chip Hardware) turns it into silicon circuits in the SIDRA.

Spike-Timing-Dependent Plasticity (STDP)

Prerequisites

What you'll learn here

Hook: 1998's 20 Milliseconds

Intuition: An Asymmetric Learning Window

Formalism: The STDP Equation and Its Biology

Experiment: 2 Neurons, 5 Spike Pairs, Synaptic Update

Quick Quiz

Lab Exercise

Cheat Sheet

Vision: STDP-Native Hardware and SIDRA's Brain Claim

Further Reading

Prerequisites

What you'll learn here

🪝 Hook: 1998's 20 Milliseconds

🧭 Intuition: An Asymmetric Learning Window

📐 Formalism: The STDP Equation and Its Biology

🧪 Experiment: 2 Neurons, 5 Spike Pairs, Synaptic Update

📝 Quick Quiz

🛠️ Lab Exercise

🗂️ Cheat Sheet

🔮 Vision: STDP-Native Hardware and SIDRA's Brain Claim

📚 Further Reading

Hook: 1998's 20 Milliseconds

Intuition: An Asymmetric Learning Window

Formalism: The STDP Equation and Its Biology

Experiment: 2 Neurons, 5 Spike Pairs, Synaptic Update

Quick Quiz

Lab Exercise

Cheat Sheet

Vision: STDP-Native Hardware and SIDRA's Brain Claim

Further Reading