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with a header title (metadata). □ Access through identifiers, i.e., each object can be retrieved by a query through key values. 3/78", "keywords": [], "retrievalText": "Data and Supervised Learning Recap. Tabular Data ■ Data is structured in a tabular form. ■ Data elements are arranged in vertical columns a...
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is described with hundreds (or thousands) of features → visualization is a common problem. ■ Idea: Reduce dimensionality of the data set, while still preserving as much information as possible. ■ Popular algorithms are PCA (principal component analysis) or t-SNE (t-distributed stochastic neighbor embedding). ■ Can redu...
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most important model for colored images. ■ 3 channels: red, green, blue ■ Adding up the 3 color channels results in the final image. 10/78", "keywords": [ "image", "rgb" ], "retrievalText": "Convolutional Networks. RGB Model ■ The RGB (red, green, blue) model is the most important mode...
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ordered in a useful way. What is useful depends on task . . . 13/78" }, { "id": "unit-01-p015", "sourceId": "unit-01", "lectureId": "unit-01", "page": 15, "title": "Unit 1: Recap of Hands-on AI I page 15", "text": "Sequences ■ Time series: Ordered in time, e.g., weather, fina...
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"title": "Unit 1: Recap of Hands-on AI I page 19", "text": "Hierarchical Clustering - Dendrogram 0 20 40 60 80 100 120 18/78", "keywords": [], "retrievalText": "Data and Supervised Learning Recap. Hierarchical Clustering - Dendrogram 0 20 40 60 80 100 120 18/78" }, { "id": "unit-01-p020"...
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parameter values (e.g., a trained neural network) ■ Model class: the class of models in which we search for the model (e.g., neural networks, SVMs, . . . ) ■ Parameters: what is adjusted during training (e.g., network weights) ■ Hyperparameters: settings controlling model complexity or the training procedure (e.g., net...
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"Data and Supervised Learning Recap. Introductory Example: Fish Recognition ■ Example from R. O. Duda, P . E. Hart, and D. G. Stork. Pattern Classification. 2nd edition. John Wiley & Sons, 2001. ISBN 0-471-05669-3. ■ Automated system to sort fish in a fish-packing company: salmons must be distinguished from sea bass op...
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: "unit-01", "page": 32, "title": "Unit 1: Recap of Hands-on AI I page 32", "text": "Input Representation ■ Assume our data set consists of n objects with feature vectors x1, . . . ,xn of length d, and each object has a corresponding label y1, . . . , yn. ■ Then, we can write the feature vectors of al...
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: □ modelA: brightness < 0.18 → Salmon □ modelB: brightness < 0.5 → Salmon □ modelC: brightness < 0.8 → Salmon ■ How do we get the “best” model? □ How does our model perform on our data? – Loss function □ How will it perform on (unseen) future data? – Generalization error/risk 30/78" }, { "id": "unit-01-p...
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(=Empirical Risk Minimization (ERM)): RE(g(.; w), (X, y)) = 1 n · nP i=1 L(yi, g(xi; w)) 32/78" }, { "id": "unit-01-p037", "sourceId": "unit-01", "lectureId": "unit-01", "page": 37, "title": "Unit 1: Recap of Hands-on AI I page 37", "text": "Back to Our Data ■ How do we get t...
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to get a better estimate for the (true) risk. 37/78", "keywords": [], "retrievalText": "Data and Supervised Learning Recap. The Problem of Overfitting 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ■ With ERM, we can optimize our model by minimizing the loss on our data set. ■ Problem: We might fit our par...
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feature vector □ yi: corresponding label □ n: number of samples (dataset size) ■ Find model g(x; w) such that ∀i : g(xi; w) ≈ yi. ■ Simplest approach: use something linear: g(xi; w) = g(xi; a, b) = a + b · xi ■ Idea: Minimize mean-squared error loss: L = 1 n nX i=1 (yi − g(xi; w))2 40/78", "keywords": [], "...
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■ Logistic regression is a regression model because it estimates the probability of class membership (output y is a real numeric value, i.e., y ∈ [0, 1] ∈ R). ■ Classification: Use some decision rule (e.g., threshold). 45/78", "keywords": [ "sigmoid" ], "retrievalText": "Neural Networks and Op...
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KX j=1 ezj where z = (z1, . . . , zK) is the vector of “raw” model outputs, i.e., there is an output for each class (see example later). ■ While not necessary, as a regular sigmoid function would suffice, this also works for binary classification, i.e., K = 2. 47/78" }, { "id": "unit-01-p052", "sour...
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, "keywords": [ "pytorch" ], "retrievalText": "Neural Networks and Optimization. PyTorch 51/78" }, { "id": "unit-01-p056", "sourceId": "unit-01", "lectureId": "unit-01", "page": 56, "title": "Unit 1: Recap of Hands-on AI I page 56", "text": "Overview...
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", "lectureId": "unit-01", "page": 58, "title": "Unit 1: Recap of Hands-on AI I page 58", "text": "Visualization and Output Calculation 𝑜𝑥 OutputInput 𝑤 𝑏 Loss or ො𝑦 ■ The above is a simplified visualization of the data flow through our model: o = σ(z) = σ(a + b · x). ■ The output o can the...
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", "sourceId": "unit-01", "lectureId": "unit-01", "page": 60, "title": "Unit 1: Recap of Hands-on AI I page 60", "text": "Visualization and Output Calculation 𝑥1 𝑥2 𝑥3 𝑥4 𝑤1 𝑤2 𝑤3 𝑤4 𝑜 𝑏 Loss or ො𝑦 Input Output ■ The above is a simplified visualization of the data flow through o...
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where x ∈ R1 and y ∈ {1, . . . , K}. ■ Recall that the softmax function is suitable for multi-class classification, so we replace our logistic function σ(z) with the softmax function σ(z)i, where i means the i-th class and z = (z1, . . . , zK)⊤ is the vector of “raw” model outputs. ■ A matching logistic regression mode...
hands-on-ai
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RM and y ∈ {1, . . . , K}. ■ A matching logistic regression model would look like o = (o1, . . . , oK)⊤ = g(x; {b, W }) = ( σ(z)1, . . . , σ(z)K)⊤, where o is the final vector of K class probabilities for some given input x and the model parameters b and W . ■ Note that the parameter b is now a vector and the parameter...
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  x1 x2 x3 x4   , z =   z1 z2 z3   = b + W x =   b1 + P4 i=1 w1ixi b2 + P4 i=1 w2ixi b3 + P4 i=1 w3ixi   ■ Final model output o (class probability vector): o =   o1 o2 o3   =   σ(z)1 σ(z)2 σ(z)3   63/78 𝑥1 𝑥2 𝑥3 𝑥4 𝑤11 𝑤12 𝑤13 𝑤14 Input Loss or ො𝑦 𝑏1 𝑜1 𝑜2 𝑜3 Output" }, { ...
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"Unit 1: Recap of Hands-on AI I page 70", "text": "Non-linearity ■ Simply stacking linear layers does not work, since multiple linear transformations can be collapsed into a single linear transformation. ■ To get rid of this problem, we thus add a non-linear function f after each layer (same idea we had when goin...
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neural network, a hidden neuron is only connected to a few neurons in the previous layer. Input Neurons Hidden Neuron CNN Input Neurons Hidden Neuron FNN 68/78" }, { "id": "unit-01-p073", "sourceId": "unit-01", "lectureId": "unit-01", "page": 73, "title": "Unit 1: Recap of Hands-on...
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0 0 0 0 0 0.4 0.4 0 0 0 0 0 0 0 0 0.5 0.5 0 0 0 0 0 0 0.5 kernel outputinput 0.5 0.2 70/78 0 · 0 + 0 · 0 + 0 .5 · 0 + 0 · 1.0 + 0 .5 · 0 + 0 · 0 + 0 · 0 + 0 · 0 + 0 .5 · 0.4 = 0.2", "keywords": [ "kernel" ], "retrievalText": "Convolutional Networks. Weight Sharing (k: 3 × 3, i: 6 × 6, o: 4 × 4...
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+ 0 · 0 + 0 · 0.4 + 0 · 0 + 0 .5 · 0 = 0.2" }, { "id": "unit-01-p078", "sourceId": "unit-01", "lectureId": "unit-01", "page": 78, "title": "Unit 1: Recap of Hands-on AI I page 78", "text": "Weight Sharing (k: 3 × 3, i: 6 × 6, o: 4 × 4) 0 0 0 0 0 0 0 1.0 0.4 0 0.4 0.4 0 0 0 0 ...
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" ], "retrievalText": "Convolutional Networks. Weight Sharing (k: 3 × 3, i: 6 × 6, o: 4 × 4) 0 0 0 0 0 0 0 1.0 0.4 0 0.4 0.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0.4 0 0 0 0 0 0 0 0 0.5 0.5 0 0 0 0 0 0 0.5 kernel outputinput 0.5 0.6 0 0.2 0.2 0 0 0 0.6 0 0 0 0 0.4 0.2 0 70/78" }, { "id": "unit-01-p...
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, i.e., there are no parameters to learn. 73/78", "keywords": [ "convolution", "stride", "pooling", "image" ], "retrievalText": "Convolutional Networks. Pooling ■ Another way of downsampling images is pooling. ■ There are different ways to perform pooling. Most popular:...
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0 0 0 0 input (3 channels) 0 0 0 0 0 0 0 1.0 0.4 0 0.4 0.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0.4 0 0 0 0 0 0 0 0 75/78" }, { "id": "unit-01-p086", "sourceId": "unit-01", "lectureId": "unit-01", "page": 86, "title": "Unit 1: Recap of Hands-on AI I page 86", "text": "Inputs in CN...
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0 0 0 0 0 0 0 0.5 0.6 0 0.2 0.2 0 0 0 0.6 0 0 0 0 0.4 0.2 0 75/78" }, { "id": "unit-01-p088", "sourceId": "unit-01", "lectureId": "unit-01", "page": 88, "title": "Unit 1: Recap of Hands-on AI I page 88", "text": "Outputs in CNNs ■ We usually want to apply multiple kernels to ...
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0.5 kernel 1 input (3 channels) 0 0 0 0 0 0 0 1.0 0.4 0 0.4 0.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0.4 0 0 0 0 0 0 0 0 0.5 0 0 0 0 0 0.5 0 0 0.5 0 0 0 0 0 0 0.5 0 0.5 0.5 0 0 0 0 0 0 0.5 kernel 2 0.5 0.6 0 0.2 0.2 0 0 0 0.6 0 0 0 0 0.4 0.2 0 output (2 channels) 77/78", "keywords": [ "cnn", "kernel" ...
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HANDS-ON AI II Model Optimization in Neural Networks Rainer Dangl Institute for Machine Learning" }, { "id": "unit-02-p002", "sourceId": "unit-02", "lectureId": "unit-02", "page": 2, "title": "Unit 2: Model Optimization in Neural Networks page 2", "text": "Copyright Statement...
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"lectureId": "unit-02", "page": 6, "title": "Unit 2: Model Optimization in Neural Networks page 6", "text": "Dropout drop 20% drop 50% W1 · 1.25 W2 · 2.0 ■ For each training example, randomly omit p% of the units and scale the remaining weights with 1 1−p to compensate. □ Units cannot rely on all neig...
hands-on-ai
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page": 10, "title": "Unit 2: Model Optimization in Neural Networks page 10", "text": "Batch Normalization W1 W2 ■ Can we also standardize data for the hidden layers? □ Cannot precompute once, data distribution changes with each weight update. □ Cannot afford a full pass over the training set after each weig...
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34", "keywords": [ "hts", "neural" ], "retrievalText": "Neural Networks and Optimization. Regularization ■ Technique to prevent overfitting where we add a regularization term to the loss function. □ L1 regularization adds the sum of the absolute weights to the loss function (λ is a hyp...
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s input to its output creates a gradient shortcut, He et al. (2015): Deep Residual Learning for Image Recognition 7/34", "keywords": [ "image", "gradient" ], "retrievalText": "Convolutional Networks. Deep Networks ■ Residual Connections: Adding a layer’s input to its output creates a g...
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a “Model Zoo” of pretrained models. 8/34" }, { "id": "unit-02-p021", "sourceId": "unit-02", "lectureId": "unit-02", "page": 21, "title": "Unit 2: Model Optimization in Neural Networks page 21", "text": "Learning Rate Schedules Li et al. (2017): Visualizing the Loss Landscape ...
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"id": "unit-02-p025", "sourceId": "unit-02", "lectureId": "unit-02", "page": 25, "title": "Unit 2: Model Optimization in Neural Networks page 25", "text": "Gradient Descent ■ Given: a function f (x) ■ Task: find x that maximizes (or minimizes) f (x) ■ Idea: start at some value x0, and take...
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text": "Forward Pass x1 x2 x3 x4 Input layer h(1) 1 h(1) 2 h(1) 3 h(1) 4 h(1) 5 Hidden layer 1 h(2) 1 h(2) 2 h(2) 3 h(2) 4 h(2) 5 Hidden layer 2 h(3) 1 h(3) 2 h(3) 3 h(3) 4 h(3) 5 Hidden layer 3 ˆy Output layer ˆy = g  h(3)(h(2)(h(1)( x|{z} Input layer ; W1); W2); W3); W4   14/34", "keywords": [ "forw...
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= g  h(3)(h(2)(h(1)(x; W1); W2)| {z } Hidden layer 2 ; W3); W4   16/34", "keywords": [ "forward pass" ], "retrievalText": "Neural Networks and Optimization. Forward Pass x1 x2 x3 x4 Input layer h(1) 1 h(1) 2 h(1) 3 h(1) 4 h(1) 5 Hidden layer 1 h(2) 1 h(2) 2 h(2) 3 h(2) 4 h(2) 5 Hidden la...
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1) 4 h(1) 5 Hidden layer 1 h(2) 1 h(2) 2 h(2) 3 h(2) 4 h(2) 5 Hidden layer 2 h(3) 1 h(3) 2 h(3) 3 h(3) 4 h(3) 5 Hidden layer 3 ˆy Output layer ˆy = g  h(3)(h(2)(h(1)(x; W1); W2); W3); W4| {z } Input to output layer   18/34" }, { "id": "unit-02-p033", "sourceId": "unit-02", "lectureId": "...
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p035", "sourceId": "unit-02", "lectureId": "unit-02", "page": 35, "title": "Unit 2: Model Optimization in Neural Networks page 35", "text": "Interlude: Chain Rule ■ Derivative is product of derivatives: “outer derivative” times “inner derivative” y = f (u) = f (g(x)) → ∂y ∂x |x=c = ∂f ∂u |...
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x2 x3 x4 Input layer h(1) 1 h(1) 2 h(1) 3 h(1) 4 h(1) 5 Hidden layer 1 h(2) 1 h(2) 2 h(2) 3 h(2) 4 h(2) 5 Hidden layer 2 h(3) 1 h(3) 2 h(3) 3 h(3) 4 h(3) 5 Hidden layer 3 ˆy Output layer W4 ← W4 − η ∂L ∂ ˆy ∂ ˆy ∂W4 23/34" }, { "id": "unit-02-p038", "sourceId": "unit-02", "lectureId": "unit-02...
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"text": "Backward Pass x1 x2 x3 x4 Input layer h(1) 1 h(1) 2 h(1) 3 h(1) 4 h(1) 5 Hidden layer 1 h(2) 1 h(2) 2 h(2) 3 h(2) 4 h(2) 5 Hidden layer 2 h(3) 1 h(3) 2 h(3) 3 h(3) 4 h(3) 5 Hidden layer 3 ˆy Output layer W1 ← W1 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂h(2) ∂h(2) ∂h(1) ∂h(1) ∂W1 26/34", "keywords": [], "retri...
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Gradients of Logistic Regression ■ g(x) = ˆy = σ (wx) with w being the weight vector ■ Example loss: mean-squared error: L = 1 n P(y − ˆy)2 ■ Example of chain rule: ∂L ∂w = 2 n X (y − ˆy) | {z } outer derivative · σ′(wx) | {z } inner derivative 1 · ∂(wx) ∂w| {z } inner derivative 2 with σ′(wx) = σ(wx) · (1 − σ(wx)), se...
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(x) = ˆy = σ (wx) with w being the weight vector ■ Example loss: mean-squared error: L = 1 n P(y − ˆy)2 ■ Example of chain rule: ∂L ∂w = 2 n X (y − ˆy) | {z } outer derivative · σ′(wx) | {z } inner derivative 1 · ∂(wx) ∂w| {z } inner derivative 2 with σ′(wx) = σ(wx) · (1 − σ(wx)), see next slide 27/34", "keywords...
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X (y − ˆy) | {z } outer derivative · σ′(wx) | {z } inner derivative 1 · ∂(wx) ∂w| {z } inner derivative 2 with σ′(wx) = σ(wx) · (1 − σ(wx)), see next slide 27/34" }, { "id": "unit-02-p048", "sourceId": "unit-02", "lectureId": "unit-02", "page": 48, "title": "Unit 2: Model Optimizat...
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"unit-02", "page": 50, "title": "Unit 2: Model Optimization in Neural Networks page 50", "text": "Chain Rule in Deep Neural Networks ■ Remember the nested structure of our neural network: ˆy = g \u0010 h(3)(h(2)(h(1)(x; W1); W2); W3); W4 \u0011 ■ Let’s write out the individual output calculations, usi...
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to compute the final model output (in g): h(1)(x; W1) = h(1) = σ (W1x) h(2)(h(1); W2) = h(2) = σ \u0010 W2h(1) \u0011 h(3)(h(2); W3) = h(3) = σ \u0010 W3h(2) \u0011 g(h(3); W4) = ˆy = σ \u0010 W4h(3) \u0011 ■ Given the final model output, we define the loss = L(ˆy, y) 29/34" }, { "id": "unit-02-p052", ...
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W3h(2) \u0011 g(h(3); W4) = ˆy = σ \u0010 W4h(3) \u0011 ■ Given the final model output, we define the loss = L(ˆy, y) 29/34", "keywords": [ "neural", "activation" ], "retrievalText": "Neural Networks and Optimization. Chain Rule in Deep Neural Networks ■ Remember the nested structure o...
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in Deep Neural Networks ■ Remember the nested structure of our neural network: ˆy = g \u0010 h(3)(h(2)(h(1)(x; W1); W2); W3); W4 \u0011 ■ Let’s write out the individual output calculations, usingσ as our activation function (in h(i)) and also as our final function to compute the final model output (in g): h(1)(x; W1) =...
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′ ■ σ′ are ≤ 1 4 → product tends to become very small! 30/34" }, { "id": "unit-02-p057", "sourceId": "unit-02", "lectureId": "unit-02", "page": 57, "title": "Unit 2: Model Optimization in Neural Networks page 57", "text": "Chain Rule in Deep Neural Networks ■ Given the loss, ...
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W1 ← W1 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) |{z} ∼σ′ ∂h(3) ∂h(2) |{z} ∼σ′ ∂h(2) ∂h(1) |{z} ∼σ′ ∂h(1) ∂W1|{z} ∼σ′ ■ σ′ are ≤ 1 4 → product tends to become very small! 30/34 ˆy = σ \u0010 W4h(3) \u0011 ∂ ˆy ∂W4 = σ′ \u0010 W4h(3) \u0011 · h(3)" }, { "id": "unit-02-p059", "sourceId": "unit-02", "lectureId": "...
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become very small! 30/34", "keywords": [ "neural" ], "retrievalText": "Neural Networks and Optimization. Chain Rule in Deep Neural Networks ■ Given the loss, let’s compute the parameter update rules: W4 ← W4 − η ∂L ∂ ˆy ∂ ˆy ∂W4 W3 ← W3 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂W3 W2 ← W2 − η ∂L ∂ ˆy ∂ ˆy...
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2) ∂h(1) |{z} ∼σ′ ∂h(1) ∂W1|{z} ∼σ′ ■ σ′ are ≤ 1 4 → product tends to become very small! 30/34 ˆy = σ \u0010 W4h(3) \u0011 ∂ ˆy ∂h(3) = σ′ \u0010 W4h(3) \u0011 · W4", "keywords": [ "neural" ], "retrievalText": "Neural Networks and Optimization. Chain Rule in Deep Neural Networks ■ Given the lo...
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"Unit 2: Model Optimization in Neural Networks page 64", "text": "Chain Rule in Deep Neural Networks ■ Given the loss, let’s compute the parameter update rules: W4 ← W4 − η ∂L ∂ ˆy ∂ ˆy ∂W4 W3 ← W3 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂W3 W2 ← W2 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂h(2) ∂h(2) ∂W2 W1 ← W1 − η ∂L ∂ ˆy ∂ ˆy ∂h(3)...
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"unit-02", "page": 66, "title": "Unit 2: Model Optimization in Neural Networks page 66", "text": "Chain Rule in Deep Neural Networks ■ Given the loss, let’s compute the parameter update rules: W4 ← W4 − η ∂L ∂ ˆy ∂ ˆy ∂W4 W3 ← W3 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂W3 W2 ← W2 − η ∂L ∂ ˆy ∂ ˆy ∂h(3) ∂h(3) ∂h...
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■ Additional layers would not be very useful (see p.7). 31/34" }, { "id": "unit-02-p068", "sourceId": "unit-02", "lectureId": "unit-02", "page": 68, "title": "Unit 2: Model Optimization in Neural Networks page 68", "text": "ReLU Function and Derivative 2.0 1.5 1.0 0.5 0.0 0.5...
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). ■ Layers in RNNs take their own output as input. ■ Method of choice for sequential data. ■ We will see that RNNs can be regarded as very deep feed-forward neural networks. ■ Therefore, also prone to vanishing gradients, which, in RNNs, corresponds to lack of long-term memory. ■ But instead of just using a different ...
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": "unit-03-p004", "sourceId": "unit-03", "lectureId": "unit-03", "page": 4, "title": "Unit 3: Recurrent Neural Networks page 4", "text": "Sequence Data ■ Assume a sample s is a sequence of length T with D features at each timestep t. □ T may vary between samples but D is constant □ s = (x...
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, e.g., h0 = 0 4/31 𝑥1 𝑥2 ℎ1 ℎ2 ℎ3 ො𝑦" }, { "id": "unit-03-p006", "sourceId": "unit-03", "lectureId": "unit-03", "page": 6, "title": "Unit 3: Recurrent Neural Networks page 6", "text": "Recurrent Neural Networks (RNNs) (1) ■ Solution: Recurrent Neural Networks (RNNs) □ Fee...
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, "retrievalText": "Reinforcement Learning and Q-Learning. Recurrent Neural Networks (RNNs) (1) ■ Solution: Recurrent Neural Networks (RNNs) □ Feed input sequence timestep by timestep into network, i.e., vector xt with D features at each timestep t □ Concatenate previous output ht−1 (=hidden state with H features...
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/31" }, { "id": "unit-03-p012", "sourceId": "unit-03", "lectureId": "unit-03", "page": 12, "title": "Unit 3: Recurrent Neural Networks page 12", "text": "Recurrent Neural Networks (RNNs) (3) ■ Graphical visualization is a simplification 𝒉𝑡−1 𝒉𝑡 RNN Layer 𝒙𝑡 RNN Layer … ...
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a feed-forward network with shared weights = unrolled over time RNN Layer 𝒙𝑡 𝒉𝑡 𝒉𝑡−1 10/31" }, { "id": "unit-03-p016", "sourceId": "unit-03", "lectureId": "unit-03", "page": 16, "title": "Unit 3: Recurrent Neural Networks page 16", "text": "Unrolling an RNN ■ An RNN can...
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unit-03", "lectureId": "unit-03", "page": 20, "title": "Unit 3: Recurrent Neural Networks page 20", "text": "Vanishing Gradients Problem ■ BPTT generates very deep networks ■ Depth scales with sequence length! → Vanishing or Exploding Gradients (Hochreiter, 1991) 𝒉0 𝒉1 RNN Layer 𝒙1 RNN Layer ...
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"bptt", "gradient" ], "retrievalText": "Sequence Models, RNNs, and LSTMs. Vanishing Gradients Problem ■ BPTT generates very deep networks ■ Depth scales with sequence length! → Vanishing or Exploding Gradients (Hochreiter, 1991) 𝒉0 𝒉1 RNN Layer 𝒙1 RNN Layer 𝒙2 RNN Layer 𝒙3 RNN Layer 𝒙𝑇 𝒉𝑇 …...
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selective about what to store and what to output ■ Memory: □ Should allow read and write operations □ Can store information indefinitely □ Proceeding in time involves identity function, alleviates vanishing gradients issue ■ Gates: □ Realized via hidden units □ States (open/closed) depend on current input and past □ Se...
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"Reinforcement Learning and Q-Learning. LSTM: Recurrent Hidden State ■ Input gate and cell input additionally receive old hidden state ht−1 as recurrent input (concatenated input) ■ Therefore, also gate states depend on the past 18/31 LSTM Layer + ⋅ 𝒄𝑡−1 𝒉𝑡−1 𝒄𝑡 𝒙𝑡 𝒊𝑡 ෤𝒄𝑡 𝒄𝑡 𝜎 tanh" }, { "i...
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-Term Memory: ht 22/31 LSTM Layer +⋅ ⋅ ⋅ 𝒄𝑡−1 𝒉𝑡−1 𝒄𝑡 𝒉𝑡 𝒙𝑡 𝒇𝑡 𝒊𝑡 ෤𝒄𝑡 𝒄𝑡 𝒐𝑡𝜎 𝜎 𝜎tanh tanh" }, { "id": "unit-03-p035", "sourceId": "unit-03", "lectureId": "unit-03", "page": 35, "title": "Unit 3: Recurrent Neural Networks page 35", "text": "LSTM Formulas...
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"retrievalText": "Sequence Models, RNNs, and LSTMs. RNN Types ■ There are 5 major RNN types □ Type depends on input format Tx and on output/prediction format Ty □ Different types for different scenarios/applications ■ For all types, the loss can be defined as the sum of the individual losses per timestamp: L(ˆy, y) = T...
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ෝ𝒚1 ෝ𝒚2 ෝ𝒚𝑇𝑦 … 30/31" }, { "id": "unit-03-p043", "sourceId": "unit-03", "lectureId": "unit-03", "page": 43, "title": "Unit 3: Recurrent Neural Networks page 43", "text": "What Y ou Should Remember ■ Why a feed-forward network has hard times with sequences ■ What the idea...
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we infer structure or meaning from observed sequences of symbols? ■ What is the structure of human thoughts? How to represent and model it? 2/49", "keywords": [ "hts", "language", "sequence" ], "retrievalText": "Language Models and Transformers. Introduction ■ Language is a com...
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": [], "retrievalText": "Language Models and Transformers. Early Attempts in AI - Connectionist Model 3 3McClelland, J. L., & Rumelhart, D. E. (2020). Distributed memory and the representation of general and specific information. In Connectionist Psychology (pp. 75-106). Psychology Press. 6/49" }, { ...
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04-p013", "sourceId": "unit-04", "lectureId": "unit-04", "page": 13, "title": "Unit 4: Language Modeling page 13", "text": "Word embedding process 10/49", "keywords": [ "embedding" ], "retrievalText": "Language Models and Transformers. Word embedding process 10/49...
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app\", \"iness\"] ■ Provides greater flexibility with regard to uncommon words/out-of-vocab words. ■ Subword tokenization trades off vocabulary size and sequence length: the vocabulary is smaller than a word-level vocabulary, while sequences are usually shorter than with character-level tokenization. ■ Popular approach...
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tokens, for simplicity we will stick with the term words 16/49" }, { "id": "unit-04-p020", "sourceId": "unit-04", "lectureId": "unit-04", "page": 20, "title": "Unit 4: Language Modeling page 20", "text": "RECURRENT LANGUAGE MODEL", "keywords": [ "language", ...
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, since the one-hot encoded vector just represents the index of the word in the vocabulary. ■ RNN: h(t) = RN N(h(t−1), e(t)) ■ Encoder/embedding matrix can be initialized randomly or with pre-trained embeddings (e.g. Word2Vec, GloVe). ■ If pre-trained embeddings are used, the encoder matrix may be frozen during trainin...
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"page": 29, "title": "Unit 4: Language Modeling page 29", "text": "How to train an RNN LM? ■ Start with a large text corpus: x(1), . . . , x(T ) ■ For every step t predict the output distribution ˆy(t) ■ Calculate the loss function: □ Negative Log-Likelihood of the predicted probability of each next word x(...
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", "page": 31, "title": "Unit 4: Language Modeling page 31", "text": "Training 27/49", "keywords": [], "retrievalText": "Language Models and Transformers. Training 27/49" }, { "id": "unit-04-p032", "sourceId": "unit-04", "lectureId": "unit-04", "page": 32, ...
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the same financial crisis that they can find reason to invest in the world. Thank you very much. God bless you. God bless you. Thank you. 9https://medium.com/@samim/obama-rnn-machine-generated-political-speeches-c8abd18a2ea0 34/49", "keywords": [ "state", "rnn" ], "retrievalText": "Lan...
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washington. the beauty of washington. not a good deal. we have to get to business. but i’ve always said qatar so what i do well. i think we’re going to get it back. no, it’s true. you know, it’s about time that on iraq. he couldn’t answer the question, is iraq. think of it. trillion. trillion dollars to the horrible th...
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capture long-term dependencies. ■ During training, transformer layers can process all positions in a sequence in parallel. During autoregressive generation, however, tokens are still generated one after another (inference time grows linearly with output length). ■ Google Gemini, Claude AI, and OpenAI’s GPT model famili...
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6) k(1), q(1), v(1) k(2), q(2), v(2) k(3), q(3), v(3) k(4), q(4), v(4) k(5), q(5), v(5) k(6), q(6), v(6) Wk, Wq, Wv k(2) · q(2) k(3) · q(3) k(4) · q(4) k(5) · q(5) k(6) · q(6) k(1) · q(2)k(1) · q(3)k(1) · q(4)k(1) · q(5)k(1) · q(6) k(2) · q(1) k(3) · q(1) k(4) · q(1) k(5) · q(1) k(6) · q(1) k(2) · q(3)k(2) · q(4)k(2) ·...
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3) · q(4)k(3) · q(5)k(3) · q(6) k(4) · q(2)k(4) · q(3) k(4) · q(5)k(4) · q(6) k(5) · q(2)k(5) · q(3)k(5) · q(4) k(5) · q(6) k(6) · q(2)k(6) · q(3)k(6) · q(4)k(6) · q(5) k(1), q(1) k(2), q(2) k(3), q(3) k(4), q(4) k(5), q(5) k(6), q(6) Tom works on tasksmath Ee(2) e(3) e(4) e(5) e(6)e(1) difficult Wk, Wq 41/49" }, ...
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) e(2) e(3) e(4) e(5) e(6) k(1), q(1), v(1) k(2), q(2), v(2) k(3), q(3), v(3) k(4), q(4), v(4) k(5), q(5), v(5) k(6), q(6), v(6) d(2,2) d(3,3) d(4,4) d(5,5) d(6,6) d(1,2) d(1,3) d(1,4) d(1,5) d(1,6) d(2,3) d(2,4) dot(2,5) d(2,6) d(3,4) d(3,5) d(3,6) d(4,5) d(4,6) d(5,6) -∞ d(3,2) d(4,1) d(4,2) d(4,3) d(5,4)d(5,3)d(5,2)...
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(2,6)) S(d(3,3)) S(d(3,4)) S(d(3,5)) S(d(3,6)) S(d(4,4)) S(d(4,5)) S(d(4,6)) S(d(5,5)) S(d(5,6)) S(d(6,6)) Tom works on tasksmathdifficult Tom works on difficult math tasks 43/49", "keywords": [ "softmax" ], "retrievalText": "Language Models and Transformers. Attention Step 2: Apply softmax Wk...
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), v(5) k(6), q(6), v(6) k(1), q(1) k(2), q(2) k(3), q(3) k(4), q(4) k(5), q(5) k(6), q(6) Wk, Wq, Wv Ee(2) e(3) e(4) e(5) e(6)e(1) 0.05 0.05 0.05 0.4 0.4 0.05 Tom works on tasksmathdifficult Tom works on difficult math tasks S(d) 0.017 0.011 0.045 0.0060.0160.027 0.2320.0160.0160.006 0.0050.0070.011 0.1040.088 0.9540....
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(2), q(2), v(2) k(3), q(3), v(3) k(4), q(4), v(4) k(5), q(5), v(5) k(6), q(6), v(6) k(1), q(1) k(2), q(2) k(3), q(3) k(4), q(4) k(5), q(5) k(6), q(6) Wk, Wq, Wv Ee(2) e(3) e(4) e(5) e(6)e(1) 0.05 0.05 0.05 0.4 0.4 0.05 Tom works on tasksmathdifficult Tom works on difficult math tasks = 1 S(d) 0.017 0.011 0.045 0.0060.0...
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0.006v(4)0.016v(4)0.027v(4) 0.232v(5)0.016v(5)0.016v(5)0.006v(5) 0.005v(6)0.007v(6)0.011v(6)0.104v(6)0.088v(6) k(1), q(1) k(2), q(2) k(3), q(3) k(4), q(4) k(5), q(5) k(6), q(6) Wk, Wq, Wv Ee(2) e(3) e(4) e(5) e(6)e(1) 0.954v(1)0.016v(1)0.010v(1)0.004v(1)0.004v(1)0.05v(1) 0.899v(2)0.044v(2)0.012v(2)0.012v(2)0.05v(2) 0.8...
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), and the proposed changes are concatenated, followed by a feed-forward layer. ■ These blocks of multi-headed attention/feed-forward are repeated, to refine the contextual token representations further (e.g. style and semantics of the text). ■ Finally, a linear layer then transforms the final embedding to the vocabula...
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Unit 5: Drug Discovery page 3", "text": "Introduction ■ Drug: A chemical substance of known structure, other than a nutrient or an essential dietary ingredient, which, when administered to a living organism, produces a biological effect. 2/35", "keywords": [ "drug" ], "retrievalText": "A...
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Discovery page 7", "text": "Needle in the Haystack ■ Given a target, find a suitable molecule that modulates its function. ■ How many possible candidates? ■ If max number of atoms is 13: 977 Million (109) ■ If max number of atoms is 17: 166 Billion (1011) ■ For drugs, max number of atoms is ∼ 40: 1060 6/35", ...
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molecule" ], "retrievalText": "AI for Drug Discovery. Excursion – Small Molecules: Periodic Table 10/35" }, { "id": "unit-05-p012", "sourceId": "unit-05", "lectureId": "unit-05", "page": 12, "title": "Unit 5: Drug Discovery page 12", "text": "Excursion – Small Mol...
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{ "id": "unit-05-p017", "sourceId": "unit-05", "lectureId": "unit-05", "page": 17, "title": "Unit 5: Drug Discovery page 17", "text": "Excursion – Small Molecules: MOL/SDF 16/35", "keywords": [ "molecule" ], "retrievalText": "AI for Drug Discovery. Excursion...
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. ■ Branches are indicated by parentheses. ■ Non-unique: one molecule has multiple SMILES strings. 21/35" }, { "id": "unit-05-p023", "sourceId": "unit-05", "lectureId": "unit-05", "page": 23, "title": "Unit 5: Drug Discovery page 23", "text": "Excursion – Small Molecules: RDK...
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. ■ “The innovation of neural network approaches lies in their ability to learn this representation automatically , mapping molecules into continuous vectors that are subsequently used to predict their properties.”2 2Cell, Volume 180, ISSUE 4, P688-702.e13, February 20, 2020 25/35", "keywords": [ "drug", ...
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": "Unit 5: Drug Discovery page 30", "text": "Generative Models for Molecules ■ Example: Inverse molecular design: 29/35", "keywords": [ "molecule", "molecular" ], "retrievalText": "AI for Drug Discovery. Generative Models for Molecules ■ Example: Inverse molecular design: 29/35"...
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. 32/35" }, { "id": "unit-05-p034", "sourceId": "unit-05", "lectureId": "unit-05", "page": 34, "title": "Unit 5: Drug Discovery page 34", "text": "AlphaFold ■ CASP challenge: Predict 3D structure from amino acid sequence3 ■ DeepMind’s AlphaFold achieved a major breakthrough u...
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electronic form, may be used for personal and non-commercial educational use only. Any reproduction of this material, no matter whether as a whole or in parts, no matter whether in printed or in electronic form, requires explicit prior acceptance of the authors. 1/34", "keywords": [ "state" ], ...
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Machine Learning 5/34", "keywords": [], "retrievalText": "Data and Supervised Learning Recap. Unsupervised Machine Learning 5/34" }, { "id": "unit-06-p007", "sourceId": "unit-06", "lectureId": "unit-06", "page": 7, "title": "Unit 6: Introduction to Reinforcement Learnin...
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": "unit-06-p010", "sourceId": "unit-06", "lectureId": "unit-06", "page": 10, "title": "Unit 6: Introduction to Reinforcement Learning page 10", "text": "The Goal of RL ■ The policy can be seen as the heart and the brain of the agent. The policy specifies the behavior of an agent for a spe...
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