Add Problem #41: Tanh & Soft-Capping

[ThierryHJ]

Summary

Adds a new Easy-difficulty problem where users implement tanh activation using three parts:

• Forward (my_tanh) — compute tanh from scratch using exp, numerically stable via 2/(1+exp(-2x))-1
• Manual Backward (tanh_backward) — compute gradient using 1 - tanh²(x), note it depends on the output not the input
• Soft-Capping (soft_cap_logits) — cap · tanh(logits/cap), a technique used in Gemma 2 and Griffin to bound logits

Motivation

• Tanh is a classic activation function commonly asked in ML interviews
• Implementing it from scratch tests understanding of exponentials, numerical stability, and the chain rule
• Logit soft-capping is a modern technique (Gemma 2, Griffin) that applies tanh in a practical setting — good bonus context for interviews
• Complements existing activation exercises: ReLU (KV cache MHA inference #1) and GELU (#19)

Files Changed

File	Status	Description
torch_judge/tasks/tanh.py	NEW	Task definition with 6 test cases
templates/41_tanh.ipynb	NEW	Template notebook (blank stubs for 3 functions)
solutions/41_tanh_solution.ipynb	NEW	Reference solution (numerically stable)
README.md	Modified	Added row #41 to Fundamentals table, updated badge 40→41

Test Cases

#	Test Name	What It Verifies
1	Matches torch.tanh	Output matches reference with atol=1e-5
2	tanh(0) = 0 and bounded output	Boundary behavior, output in (-1, 1) for ±100
3	Shape preservation	Multi-dim tensor shape unchanged
4	Gradient flow	backward() succeeds, grad shape correct
5	Manual backward (tanh_backward)	Manual grad matches autograd
6	Soft-capping bounds logits	Output bounded within (-cap, cap), matches reference

Conventions Followed

• Auto-discovery via _registry.py — no manual registration needed
• Standard notebook format (markdown → import → implementation → debug → submit)
• Colab badge on both template and solution notebooks
• {fn} placeholder in all test code
• torch.allclose() for numerical comparison with appropriate tolerances
• Difficulty emoji consistent with existing Easy problems (🟢)

How to Test

# From repo root
python3 -c "
from torch_judge.tasks._registry import TASKS
print('tanh' in TASKS)  # True
"

Open solutions/41_tanh_solution.ipynb in JupyterLab and run all cells — the final check('tanh') should show 6/6 tests passed.