THE LEARNING ROADMAP
Equations, data, learning algorithms and intelligent systems—connected through a small experiment you can reproduce.

Opening film: BabyX First Words — University of Auckland Laboratory for Animate Technologies. An expressive interface prompts questions; evidence establishes capability.
01 / THE MODEL
Liquid begins at 80°C in a 25°C room. Assume the room temperature and effective vessel properties remain constant. Temperature changes in proportion to its difference from the room.
t is in minutes; T is in °C; k is in min⁻¹. The structure comes from the physical model. The unknown k comes from fitting observations.
| Time (min) | Observed °C | Data role |
|---|---|---|
| 0 | 80 | Training |
| 5 | 70.2 | Training |
| 10 | 62.4 | Training |
| 15 | 54.9 | Training |
| 20 | 50.1 | Training |
| 25 | 44.9 | Training |
| 30 | 41.8 | Training |
A low error cannot establish that a different cup, liquid or room will follow the same equation.
02 / THE EXPERIMENT
| Quantity | Calculated result |
|---|---|
| Initial training MSE | 175.461 °C² |
| Fitted k after 180 updates | 0.03978592 min⁻¹ |
| Final training MSE | 0.09379 °C² |
| Held-out MAE (two observations) | 0.133°C |
≈ 34.18°C
Changing k is additional training. Changing t while keeping k fixed is inference. This estimate extrapolates beyond the 0–30 minute training interval.
Run the supplied cooling notebook or use the interactive experiment. Training uses learning rate 0.001 and 180 gradient updates.
03 / CHOOSING THE METHOD
The separate campus-energy CSV has 600 fictional independent scenarios. Temperature and expected occupancy each have 24 missing entries. EDA checks meanings, units, ranges, missingness, duplicates, relationships and availability at prediction time.
| Method | Idea | Important distinction |
|---|---|---|
| Linear / logistic | Weighted input relationships | Number / class probability |
| KNN | Nearby labelled cases | Scaling and distance matter |
| SVM | Separating margin, optional kernel | Supervised method |
| Trees / XGBoost | Splits / boosted trees | Often useful for tabular data |
| K-means | K groups without outcome labels | Clusters need interpretation |
| LSTM | Gated state through ordered steps | Sequence neural architecture |
| Transformer | Attention between representations | Architecture used in foundation models |
These are different tasks, methods and architectures. Compare models only after making inputs, timing and evaluation conditions comparable.
Use later-period tests for a real time series. The campus teaching rows are independent fictional scenarios.
04 / INTELLIGENT SYSTEMS
GPT and Gemini are model families. As of 17 October 2026, official catalogues list GPT-6 Astra and Gemini 4 Argon. A typical development story includes pretraining, further tuning, evaluation and deployment; exact proprietary recipes may be only partly public.
Ask which benchmark, dataset, metric, denominator, date and conditions produced the result. A high score does not certify a different local task. Accuracy, MAE, pass rate and human preference measure different things.
A fluent answer can contain an unsupported claim, invented citation or false number. Open the source and verify the exact claim. Use deterministic calculations for arithmetic. Retrieval helps but does not guarantee truth.
A complete agent includes tools, state, permission boundaries, stop rules and review. A safe teaching example reads a synthetic CSV, counts missing entries and drafts a report for a person to approve.
AI can assist with bounded tasks. Engineers still frame the problem, test failures, secure integrations and take responsibility for deployment. Avoid assuming that a capability demonstration predicts job replacement.
Primary references: OpenAI models · Google DeepMind model cards · Attention Is All You Need
05 / WORKSHEET AND RESOURCES
Choose a useful ML application. Write a small plan that another person can test.
Method references: scikit-learn · XGBoost · Keras LSTM. All numerical cooling and campus examples in this guide are synthetic.