Language Setup
Not saved to repo files yet.
Build Alphabet Dataset
Draw Symbol For A
Collect samples to begin.
Letter Progress
Alien Alphabet Reference
Translation key used by this language
Train Letter CNN
Validation Confusion Matrix
Zoogle Translate
Loaded alphabet reference
Alien Input (Unnamed Language)
→
English Output
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Tip: Hover decoded letters for posterior diagnostics.
Test Single Letter
Draw Test Symbol
Visual Diagnostics
Normalized 24×24
Saliency Map
Conv Filter Contributions
About Zoogle Translate
A CS109-driven walkthrough of the full probabilistic pipeline, from labeled data to posterior inference.
Process Breakdown
1
Labeling: You create a dataset of pairs \((x_i, y_i)\), where \(x_i\) is a normalized symbol image and \(y_i\in\{A,\dots,Z\}\).
2
Modeling: A CNN parameterized by \(\theta\) produces class posteriors \(p_{\theta}(Y\mid X)\) over all letters.
3
Learning: Training minimizes \(\mathcal{L}_{\mathrm{CE}}=-\log p_{\theta}(y\mid x)\), equivalent to maximum-likelihood estimation.
4
Decision Rule: Decoding uses MAP inference \(\hat{y}=\arg\max_y p_{\theta}(y\mid X)\) for each symbol token.
5
Uncertainty + Diagnostics: The app reports entropy \(H(Y\mid X)\), MAP margin \(\Delta p\), and evidence ratio \(\frac{p(Y\mid X)}{p(Y)}\).
Posterior Update \(p(Y\mid X)\)
Visual comparison of prior \(p(Y)\) and posterior \(p(Y\mid X)\) for top classes. MAP picks the largest posterior bar.
Uncertainty \(H(Y\mid X)\)
Binary entropy curve \(H_2(p)\). Larger posterior concentration typically lowers uncertainty.
CS109 Concepts Applied
Random Variables + Conditionals: \(X\) is the observed symbol image, \(Y\) is the letter label, and prediction uses \(p_{\theta}(Y\mid X)\).
Bayes Theorem: Evidence is interpreted through \(\frac{p(Y\mid X)}{p(Y)}\), contrasting posterior mass against a prior baseline.
MAP Inference: Classification uses \(\arg\max_y p_{\theta}(y\mid X)\), the standard posterior decision rule.
Entropy: \(H(Y\mid X)\) quantifies uncertainty in bits; high entropy flags ambiguous symbols.
Likelihood + MLE: Cross-entropy training minimizes \(-\log p_{\theta}(y\mid x)\), i.e., negative log-likelihood over labeled data.