Learning to predict sensory consequences

Preset

Starting posture

Sensed at the start, so already available

Posture q

Motor command

Abstract command strengths

Shoulder drive u₁

Elbow drive u₂

The same command goes to the body and, as an efference copy, to the prediction circuit.

Recoded inputs: granule-cell-inspired features

A simplified population representation supplies different combinations of command and starting state.

Appears at step 2, Recode inputs.

Learned weights

W: 3 × 6 numbers that weight the features

Body

Turns the command into movement with its own mechanics, starting from posture q. Baseline mechanics

Waiting for a command

Trial history

Size of the residual on each compared trial (root mean square of its three components)

Practice

Predicted sensory consequences

Computed from the efference copy and starting posture

Appears at step 3, Predict.

Actual sensory consequences

Later sensory feedback, for the same comparison time as the prediction

Feedback not yet available.

Residual = actual − predicted

Appears at step 5, Compare.

Notes

Five-minute instructor sequence

“A copy of a command is not yet a prediction of sensation.” Choose A learned prediction. Press Next step three times, to Predict. Compare the two command numbers with the three predicted sensory numbers: they are different kinds of quantity.
“Consequences depend on the starting state.” Press New trial (the weights are kept). Leave the command alone and move posture to 0.90. Step to Predict. Three feature tiles and all three predictions change; the “was” labels show the earlier values.
“Feedback tests a prediction that already exists.” Pause at Predict and ask the class what they expect. Then Receive feedback and Compare.
“Learning changes the next prediction.” Choose Improve a prediction. Step to Compare (residual +0.220, +0.152, +0.230). Press Learn from this trial: the trial's own numbers do not change. Press Repeat this trial, then Play trial: the residual has halved.
“Unexpected input can come from the world.” Choose An external disturbance. Step to Compare: the residual equals the disturbance. Turn on Show the cancellation interpretation. Press Observe the residual.

Optional extension: Learning over trials. Run single trials with learning and watch the history chart. Switch to six movements to see a bumpier curve, then test a movement you never practiced.

Keyboard and clicker controls

When focus is not in a number box: N, → or Page Down (most presentation clickers) for the next step; P play or pause; L learn or observe; R repeat; T new trial; C calculation; A anatomy; Esc closes a panel.

Opening the file with #preset=improve (or learned, changed, disturbance, trials) at the end of its address starts in that preset.

Scientific qualifications

Efference copy and prediction. The efference copy carries the two command numbers. The prediction is a different object: three sensory numbers produced by a learned transformation of the command together with the starting state.

Feature tiles. The six features are an illustrative basis set. They do not claim that six granule cells compute these products, or that every granule cell combines command and state. The constant feature is an offset term, not a dedicated “bias neuron”. Granule cells are not necessarily a fixed, learning-free input bank: anticipatory signals can appear at the granule-cell stage (Giovannucci et al., 2017).

Learned weights. W is an effective readout of the circuit, not eighteen identified parallel-fiber synapses. Parallel fibers are excitatory; a negative coefficient here does not imply inhibitory parallel fibers. Negative effective influences can arise elsewhere, for example through molecular-layer interneurons and Purkinje-cell inhibition of the nuclei.

Climbing fibers. Climbing fibers can help instruct changes to a learned response; this demonstration represents that teaching influence with a numerical error signal. Climbing fibers do not carry the efference copy. Not all climbing-fiber activity is a sensory prediction error, error-related activity does not always produce learning (Kimpo et al., 2014), and a zero numerical residual does not mean that Purkinje cells or climbing fibers stop firing.

Negative images. The strongest evidence for learned negative images comes from cerebellum-like electrosensory structures in fish (Requarth & Sawtell, 2014; Kennedy et al., 2014). Predictive models of the cerebellum proper are broader. Purkinje-cell output is not “a negative image” by default, and its inhibitory sign is not the algebraic minus sign used here. The sensory vectors are not literal firing-rate vectors.

Time. The step spacing shows teaching stages, not measured conduction delays. The prediction and the feedback refer to the same later comparison time.

The disturbance preset. Learning is withheld there as a teaching choice for an independent, one-off event. Biological systems have no infallible external-disturbance switch, and a disturbance that recurs predictably could itself become learnable.

Model details

All values are synthetic and dimensionless. Coefficients are illustrative, not fitted to data.

features   φ = [1, u1, u2, q, u1·q, u2·q]
prediction     predicted = W φ
body           actual    = A φ + p
residual       error     = actual − predicted
update         W ← W + η · error φᵀ / (ε + φ·φ)
               η = 0.50,  ε = 1e-8

The body's matrix A is stored and calculated separately from W. The predictor never reads A: a preset may initialize W from A0 once, at setup, but prediction and learning use only W, the trial's inputs, and the revealed feedback. A does not change when W learns.

Body for the current preset ():

External disturbance in the disturbance preset: p = [0.00, −0.12, +0.18]. Changed mechanics: A1 = diag(0.80, 0.80, 1.40) × A0, a deliberately simple change, not a model of a specific load, lesion or disease.

What one trained movement teaches. Repeating one movement drives its residual towards zero (it halves on each update), but only pins down the weights along that one feature pattern. Other movements improve partly, because their features overlap, but are not fully calibrated. The six movements schedule in Learning over trials shows this.

Inputs accept 0 to 1; typed values are rounded to two decimals. Calculations use full floating-point precision; displays round to three decimals. “≈0.000” marks a value that rounds to zero but is not exactly zero.

Text version of the current trial

Sources

These support the biological framing, not the chosen coefficients or this learning rule.

Huang et al. (2013). Convergence of pontine and proprioceptive streams onto multimodal cerebellar granule cells. eLife. doi:10.7554/eLife.00400
Kennedy et al. (2014). A temporal basis for predicting the sensory consequences of motor commands in an electric fish. Nature Neuroscience. doi:10.1038/nn.3650
Requarth & Sawtell (2014). Plastic corollary discharge predicts sensory consequences of movements in a cerebellum-like circuit. Neuron. doi:10.1016/j.neuron.2014.03.025
Giovannucci et al. (2017). Cerebellar granule cells acquire a widespread predictive feedback signal during motor learning. Nature Neuroscience. doi:10.1038/nn.4531
Kimpo, Rinaldi, Kim, Payne & Raymond (2014). Gating of neural error signals during motor learning. eLife. doi:10.7554/eLife.02076