Deep Learning · MT2 · section

Calculator routine

Mathematics revision

You reported a Casio ES-series calculator. The exact model string is not confirmed. The functions below are mathematical entries; use the keys labelled on your model. On fx-991 ES/fx-991 ES PLUS models, eˣ is normally the SHIFT function of ln. Do not confuse eˣ with the × 10ˣ scientific-notation key. Use the function labels on your own calculator for these entries.

Diagram: Calculate the exponential, build the full denominator, then take its reciprocal.. Labels: Build the calculator expression in pieces | Build the calculator expression in pieces | Example: sigmoid at a raw score of 2. | Exponential | e⁻² ≈ 0.135335 | Denominator | 1 + 0.135335 | Reciprocal | 1 ÷ 1.135335 ≈ | 0.880797 | Enter 1 ÷ (1 + e^(−2)). The entire denominator needs brackets.

1. Use ordinary computation mode. Enter complete brackets around a denominator or negative exponent.

2. For sigmoid at z = 2, enter 1 ÷ (1 + e^(−2)). Result: 0.880797078. Keep the full calculator value; write about six decimals during intermediate work.

3. For tanh at z = 1, use the hyperbolic tanh function if available. A universal alternative is (e² − 1) ÷ (e² + 1), giving 0.761594156. Ordinary tan is a different function; do not use it.

4. For cross-entropy with true probability 0.8, enter −ln(0.8), giving 0.223143551.

5. For softmax [2.3, 4.5, 3.2], subtract 4.5 first, then calculate e⁻²·², 1, e⁻¹·³. Add them, then divide each exponential by the same total.

6. If a result displays as a fraction, use your model’s fraction/decimal conversion key, often S⇔D. Do not reset the calculator unnecessarily.

Five-minute warm-up: compute sigmoid(0) = 0.5; sigmoid(−2) ≈ 0.119203; tanh(0) = 0; −ln(0.5) ≈ 0.693147; √0.25 = 0.5. A different result signals an entry mistake, not a reason to memorize a wrong value.