How a Neural Network Learns by Changing Numbers

What changes when a neural network learns? Follow one original, reproducible coordinate-classification experiment: numerical weights and biases, rectifiers, an error measure, gradients, and a separate held-out test. Our small 2-8-1 network has 33 adjustable parameters. In this one synthetic run, 98.5% of 1,600 held-out points were classified correctly. The test points came from the same artificial distribution as the 640 training points. This is not a real-world accuracy claim. Training states are resampled for display; height in the original Blender surface means output score, not physical energy or verified confidence. A two-weight loss slice keeps the other 31 parameters fixed. AI-generated narration: Michael English captions supplied. No music. Original script, generated data, numerical implementation, Blender model, diagrams and editing: Matter Made Clear. Reproducible demonstration: seed 85027, radius 0.55 inside [-1,1]^2, binary cross entropy, full-batch gradient descent, learning rate 0.12, 8,000 updates. All 33 analytic gradients were checked against central finite differences. CHAPTERS 0:00 The dots stay still. The answer changes. 0:44 Choose the task before learning 1:28 One unit is a calculation 2:14 Several simple pieces make a boundary 3:01 An error measure gives direction 3:43 Find how each number affects the loss 4:56 Watch actual training reshape the answer 5:44 Practice is different from a new test 6:53 The same idea can support a larger task 7:48 Learning and using the result are different PRIMARY SCIENTIFIC SOURCES Rumelhart, Hinton & Williams (1986), Learning representations by back-propagating errors: https://doi.org/10.1038/323533a0 Glorot, Bordes & Bengio (2011), Deep Sparse Rectifier Neural Networks: https://proceedings.mlr.press/v15/glo... Hughes & Kennedy (2019), High-Quality Cloud Masking of Landsat 8 Imagery Using Convolutional Neural Networks: https://doi.org/10.3390/rs11212591 MOVING FOOTAGE / CREDITS From Orbit to A.I. - Harnessing Machine Learning with Landsat Data, SVS 14336: NASA's Scientific Visualization Studio; Chris Burns (KBR Wyle Services, LLC), producer/writer. Source: https://svs.gsfc.nasa.gov/14336/ Excerpts retain the full source frame and source playback rate. NASA's orbital illustration and animated cloud-classification workflow explain a different application and architecture from our synthetic coordinate model. They are not recordings of our model's internal activity. Source audio omitted; excerpts and explanatory labels added by Matter Made Clear. SVS reuse terms: https://svs.gsfc.nasa.gov/help/ Cloud-classification research visuals: M. Joseph Hughes and Robert Kennedy (2019), CC BY 4.0: https://creativecommons.org/licenses/... No NASA, USGS or researcher endorsement implied.