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Notebook 2 — Meet the mice

SWC ENC 2026 · behaviour module

In Notebook 1 we treated make_mouse as a black box. Now we open it. The whole course rests on synthetic mice whose true strategy we choose, so it's worth seeing exactly how a strategy is encoded and what each one looks like in behavior — before we try to infer it by fitting (Notebook 3 onward).

In this notebook you will:

1. See the generative model: a strategy is just a weight vector.
2. Read the behavioral signature of the visual and timing strategies.
3. Recover the timing strategy straight from data, without peeking at truth.
4. Meet the dynamic mouse whose strategy drifts across the session.

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The paper panel this notebook reproduces

Fig. 1B — licking aligned to task events (image changes, omissions, and the number of images since the last bout). Each strategy leaves a different fingerprint here; this notebook builds the intuition for those signatures.

import numpy as np
import matplotlib.pyplot as plt
import swcbehav as sb

1. A strategy is a weight vector

Every mouse licks according to the same rule — the model from the paper, run forward:

$$p(\text{bout starts on image } t) = \sigma\big(w \cdot x_t\big),$$

where $x_t$ is the five-strategy design row from Notebook 1 and $w = [\,\text{bias},\ \text{visual},\ \text{omission},\ \text{post\_omission},\ \text{timing}\,]$ are the strategy weights. A static mouse uses the same $w$ on every image. Different mice are just different $w$:

for name in ["visual", "timing", "mixed"]:
    w = sb.make_mouse(name, seed=0).true_weights[0]   # constant across the session
    print(f"{name:7s}  w = {np.round(w, 1)}")
print("\norder: [bias, visual, omission, post_omission, timing]")

visual   w = [-3.  5.  0.  0.  0.]
timing   w = [-3.  0.  0.  0.  5.]
mixed    w = [-3.  3.  0.  0.  3.]

order: [bias, visual, omission, post_omission, timing]

Read those off: every mouse has a strongly negative bias (licking is rare by default). The visual mouse adds weight only to the visual column; the timing mouse only to the timing column; the mixed mouse to both. That single difference is what we'll be trying to detect for the rest of the day.

2. Behavioral signatures

Before any modeling, how does each strategy look? The two simplest summaries:

• hit rate — fraction of image changes the mouse licked to.
• false-alarm rate — fraction of non-change images it licked on anyway.

Exercise 1 (~4 min · easy). Complete strategy_signature.

Check / unstuck. Expect the visual mouse near 0.88 hits / 0.05 false alarms, the timing mouse near 0.21 / 0.20. Stuck? The solutions copy has it.

def strategy_signature(sess):
    t = sess.table
    change = t["is_change"].to_numpy()
    bout = t["bout_start"].to_numpy()
    hit_rate = bout[change].mean()
    false_alarm = bout[~change].mean()
    return hit_rate, false_alarm

print(f"{'mouse':7s}  {'hit rate':>8s}  {'false alarm':>11s}")
for name in ["visual", "timing", "mixed"]:
    hr, fa = strategy_signature(sb.make_mouse(name, seed=0))
    print(f"{name:7s}  {hr:8.2f}  {fa:11.2f}")

mouse    hit rate  false alarm
visual       0.88         0.05
timing       0.21         0.20
mixed        0.69         0.12

The visual mouse is a crisp detector — high hits, few false alarms. The timing mouse licks on a schedule, so it catches fewer changes and fires often between them (high false-alarm rate). You can see the same thing in the raw rasters: the visual mouse's licks cluster on the blue change lines, while the timing mouse's are spread rhythmically across the stream.

fig, axes = plt.subplots(2, 1, figsize=(11, 4.2), sharex=True)
sb.plotting.plot_session_raster(sb.make_mouse("visual", seed=0), 560, 585, ax=axes[0])
axes[0].set_title("visual mouse"); axes[0].set_xlabel("")
sb.plotting.plot_session_raster(sb.make_mouse("timing", seed=0), 560, 585, ax=axes[1])
axes[1].set_title("timing mouse")
plt.tight_layout(); plt.show()

3. Recovering the timing strategy from data

The signatures above hint at the strategies but don't isolate them. The timing strategy makes a sharp, testable prediction: licking probability should climb with the time waited since the last bout. We can measure that directly from the data — no ground truth needed — by binning images on images since last bout and asking how often a bout starts in each bin.

Exercise 2 (~7 min). Complete lick_prob_by_wait. Hint: sb.images_since_bout(bout_start) gives the waiting count for every image.

Check / unstuck. The timing mouse's curve should climb with waiting time while the visual mouse's stays roughly flat. Stuck? The solutions copy has it.

def lick_prob_by_wait(sess, max_wait=10):
    bout = sess.table["bout_start"].to_numpy()
    since = sb.images_since_bout(bout)
    waits = np.arange(max_wait + 1)
    probs = np.array([bout[since == k].mean() if np.any(since == k) else np.nan
                      for k in waits])
    return waits, probs

plt.figure(figsize=(6, 3.5))
for name in ["visual", "timing"]:
    waits, probs = lick_prob_by_wait(sb.make_mouse(name, seed=0))
    plt.plot(waits, probs, "o-", color=sb.WEIGHT_COLORS[name], label=name)
plt.xlabel("images since last bout"); plt.ylabel("P(bout starts)")
plt.title("the timing strategy, read from behavior"); plt.legend()
plt.show()

There it is: the timing mouse's curve rises steeply with waiting time (the sigmoid we built into the design matrix), while the visual mouse's stays flat — its licking is driven by image changes, not by the clock. This is the essence of what the full model will do, one strategy at a time and all at once.

4. The dynamic mouse

Real mice don't hold one strategy forever. Our dynamic mouse starts visual-dominant and drifts to timing-dominant. Because we generated it, we can look at its true weights over the session (something we'll have to infer for real data — that's the climax in Notebook 7):

dyn = sb.make_mouse("dynamic", seed=1)
sb.plotting.plot_weights(true_weights=dyn.true_weights, col_names=sb.WEIGHT_NAMES)
plt.title("dynamic mouse: true strategy weights drift across the session")
plt.show()

The visual weight falls and the timing weight rises — the dominant strategy flips partway through. A single static fit (Notebooks 3–6) cannot express this; watch what it does to one when we get there. For now, just confirm the drift is visible in behavior by comparing early vs late in the session:

n = len(dyn.table)
early, late = dyn.table.iloc[:n // 3], dyn.table.iloc[-n // 3:]
for label, seg in [("first third", early), ("last third", late)]:
    change = seg["is_change"].to_numpy(); bout = seg["bout_start"].to_numpy()
    print(f"{label:12s}  hit rate {bout[change].mean():.2f}   "
          f"false alarm {bout[~change].mean():.2f}")

fig, axes = plt.subplots(2, 1, figsize=(11, 4.2), sharex=False)
sb.plotting.plot_session_raster(dyn, 40, 65, ax=axes[0])
axes[0].set_title("early: change-locked (visual)")
sb.plotting.plot_session_raster(dyn, 3500, 3525, ax=axes[1])
axes[1].set_title("late: rhythmic (timing)")
plt.tight_layout(); plt.show()

first third   hit rate 0.52   false alarm 0.04
last third    hit rate 0.12   false alarm 0.17

Wrap-up

You've seen that a strategy is nothing more than a weight vector, and that different weights leave different fingerprints in behavior — crisp change-locked licking for the visual mouse, rhythmic licking for the timing mouse, and a moving target for the dynamic mouse.

So far we've peeked at ground truth to know each mouse's strategy. The rest of the day is about inferring it from behavior alone.

Next (Notebook 3): fit the static strategy model — write down its likelihood, maximize it, and recover the weights of a single-strategy mouse.

← 1. From the task to the design matrixmodule indexstudent versionall modules3. Modeling the licks →