From ddc817128e9faff0a122401c24d4eec2cc66701c Mon Sep 17 00:00:00 2001 From: n03an Date: Fri, 6 Sep 2024 18:19:22 +0800 Subject: [PATCH] add more final exam notes --- README.md | 2 + finals/notes.ipynb | 346 ++++++++++++++++++++++++++++++++++++++++++++- image.png | Bin 0 -> 110626 bytes 3 files changed, 346 insertions(+), 2 deletions(-) create mode 100644 image.png diff --git a/README.md b/README.md index 98a31dc..318e676 100644 --- a/README.md +++ b/README.md @@ -29,3 +29,5 @@ ### 📚 Jupiter Book Link All my notes in jupiter notebooks are published as a [digital book 📚](https://N0-man.github.io/MIT-MachineLearning-MicroMasters/) + +![alt text](image.png) diff --git a/finals/notes.ipynb b/finals/notes.ipynb index 4879dac..5fd34d0 100644 --- a/finals/notes.ipynb +++ b/finals/notes.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Problem 1\n", + "# Problem\n", "\n", "Consider a traning set of n samples and labels\n", "\n", @@ -59,7 +59,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Problem 2" + "# Problem" ] }, { @@ -132,6 +132,348 @@ "$$\n", "\n" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Question \n", + "Find $Q^*(x,a)$ in terms of $\\gamma$ and $p$\n", + "\n", + "$$\n", + "Q^*(x, a) = \\gamma V^*(y_1)\n", + "$$\n", + "\n", + "$$\n", + "Q^*(x, a) = \\frac{\\gamma}{1 - \\gamma p}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem" + ] + }, + { + "attachments": { + "image-2.png": { + "image/png": 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" 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" 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" 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+ } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "### 1. $ K_1(x, x') = \\left( 1 + \\frac{x \\cdot x'}{2} \\right) $\n", + "\n", + "This is a **polynomial kernel of degree 1** with a scaling factor $ \\frac{1}{2} $ for the dot product and a constant term $ 1 $. \n", + "\n", + "- A **polynomial kernel** is generally defined as:\n", + " $$\n", + " K(x, x') = \\left( \\alpha x \\cdot x' + c \\right)^d,\n", + " $$\n", + " where $ \\alpha $ is the scaling factor, $ c $ is the constant, and $ d $ is the degree.\n", + "\n", + "- In this case:\n", + " - $ \\alpha = \\frac{1}{2} $ (scaling factor),\n", + " - $ c = 1 $ (constant term),\n", + " - $ d = 1 $ (degree).\n", + " \n", + "Since the degree is 1, this is essentially a **linear kernel** with a constant term, but it still behaves linearly with respect to the input vectors.\n", + "\n", + "![image-2.png](attachment:image-2.png)\n", + "\n", + "### 2. $ K_2(x, x') = \\left( 1 + \\frac{x \\cdot x'}{2} \\right)^2 $\n", + "\n", + "This is a **polynomial kernel of degree 2**.\n", + "\n", + "- Here, the kernel corresponds to a quadratic polynomial in the input vectors.\n", + "- In this case:\n", + " - $ \\alpha = \\frac{1}{2} $,\n", + " - $ c = 1 $,\n", + " - $ d = 2 $ (degree).\n", + "\n", + "A degree-2 polynomial kernel can model quadratic interactions between features, meaning it allows for non-linear decision boundaries. This kernel is capable of capturing more complex patterns in the data compared to a linear kernel.\n", + "\n", + "![image-3.png](attachment:image-3.png)\n", + "\n", + "### 3. $ K_3(x, x') = \\left( 1 + \\frac{x \\cdot x'}{2} \\right)^3 $\n", + "\n", + "This is a **polynomial kernel of degree 3**.\n", + "\n", + "- This kernel represents a cubic polynomial in the input vectors.\n", + "- In this case:\n", + " - $ \\alpha = \\frac{1}{2} $,\n", + " - $ c = 1 $,\n", + " - $ d = 3 $ (degree).\n", + "\n", + "A degree-3 polynomial kernel can capture even more complex, higher-order interactions between the features. This type of kernel is more flexible and can model more complicated decision boundaries than lower-degree polynomial kernels.\n", + "\n", + "![image-4.png](attachment:image-4.png)\n", + "\n", + "### 4. $ K_ g(x,x')=\\exp \\left(\\left\\| x\\cdot x' \\right\\| ^2/2\\right) $\n", + "\n", + "This is a **non-linear RBF kernel**.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first explore a simple scenario where our vocabulary contains only 2 words, $V=\\{ A, B\\}$. Let $s_ t \\in \\mathbb {R}^2$ and we set the initial state $s _0$ and the weights before the last layer as follows:\n", + "\n", + "$$\n", + "s_0 = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} , \\quad W^{s,s} = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} , \\quad W^{s,x} = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given 3 training sentences\n", + "$$\n", + "AA, ABB, BAA\n", + "$$\n", + "\n", + "Encode each of them into a sequence of vectors. As an example, the sentence AA is encoded as $x^{(1)}=(x^{(1)}_1,x^{(1)}_2)$ where $x^{(1)}_1=x^{(1)}_2=[1,0]^ T$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To encode the sentences into vectors based on the provided vocabulary $ V = \\{ A, B \\} $ and the example encoding of the sentence $ AA $, we need to determine how each word in the vocabulary is represented as a vector. \n", + "\n", + "From the example given, we see that the word $ A $ is represented as:\n", + "\n", + "$$\n", + "x_A = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + "$$\n", + "\n", + "This indicates that the first component corresponds to the word $ A $, while the second component corresponds to the word $ B $ (which isn't present in the word $ A $). We can deduce that the word $ B $ would then be represented as:\n", + "\n", + "$$\n", + "x_B = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + "$$\n", + "\n", + "Now, let's encode the given sentences:\n", + "\n", + "1. **For the sentence $ ABB $**:\n", + " - The first word $ A $ is encoded as:\n", + " $$\n", + " x_1^{(2)} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " - The second word $ B $ is encoded as:\n", + " $$\n", + " x_2^{(2)} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + " - The third word $ B $ is encoded as:\n", + " $$\n", + " x_3^{(2)} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + "\n", + " Therefore, the encoding for the sentence $ ABB $ is:\n", + " $$\n", + " x^{(2)} = \\left( \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}, \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\right)\n", + " $$\n", + "\n", + "2. **For the sentence $ BAA $**:\n", + " - The first word $ B $ is encoded as:\n", + " $$\n", + " x_1^{(3)} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + " - The second word $ A $ is encoded as:\n", + " $$\n", + " x_2^{(3)} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " - The third word $ A $ is encoded as:\n", + " $$\n", + " x_3^{(3)} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + "\n", + " Therefore, the encoding for the sentence $ BAA $ is:\n", + " $$\n", + " x^{(3)} = \\left( \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}, \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\right)\n", + " $$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Question\n", + "Compute the final hidden statefor each of the three senteces $AAB, BAA, AA$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To compute the final hidden state for each of the sentences, we use the following steps. Given the initial state $ s_0 $ and the weights $ W^{s,s} $ and $ W^{s,x} $:\n", + "\n", + "- $ s_0 = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} $\n", + "- $ W^{s,s} = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} $\n", + "- $ W^{s,x} = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} $\n", + "\n", + "The update rule for the hidden state $ s_t $ is:\n", + "\n", + "$$\n", + "s_t = W^{s,s} s_{t-1} + W^{s,x} x_t\n", + "$$\n", + "\n", + "Let's compute the final hidden state for each sentence:\n", + "\n", + "#### 1. Sentence $ AAB $\n", + "\n", + "**Step 1: Encode the Sentence $ ABB $**\n", + "\n", + "The sentence $ ABB $ can be encoded as:\n", + "- $ x_1^{(4)} = x_A = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} $\n", + "- $ x_2^{(4)} = x_B = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} $\n", + "- $ x_3^{(4)} = x_B = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} $\n", + "\n", + "Thus, the sequence of vectors for the sentence $ ABB $ is:\n", + "$$\n", + "x^{(4)} = \\left( \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}, \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\right)\n", + "$$\n", + "\n", + "**Step 2: Compute the Hidden States**\n", + "\n", + "1. **At $ t = 1 $**:\n", + " $$\n", + " s_1 = W^{s,s} s_0 + W^{s,x} x_1^{(4)}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + "\n", + "2. **At $ t = 2 $**:\n", + " $$\n", + " s_2 = W^{s,s} s_1 + W^{s,x} x_2^{(4)}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} -1 + 0 \\\\ 0 + 1 \\end{bmatrix} = \\begin{bmatrix} -1 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + "\n", + "3. **At $ t = 3 $**:\n", + " $$\n", + " s_3 = W^{s,s} s_2 + W^{s,x} x_3^{(4)}\n", + " $$\n", + " $$\n", + " s_3 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} -1 \\\\ 1 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_3 = \\begin{bmatrix} 1 + 0 \\\\ -1 + 1 \\end{bmatrix} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + "\n", + "**Final hidden state for $ ABB $ is $ s_3 = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} $**\n", + "\n", + "#### 2. Sentence $ BAA $\n", + "\n", + "**Step 1: Encode the sentence:**\n", + "\n", + "$$\n", + "x^{(3)} = \\left( \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}, \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\right)\n", + "$$\n", + "\n", + "**Step 2: Compute the hidden states:**\n", + "\n", + "- **At $ t = 1 $:**\n", + " $$\n", + " s_1 = W^{s,s} s_0 + W^{s,x} x_1^{(3)}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", + " $$\n", + "\n", + "- **At $ t = 2 $:**\n", + " $$\n", + " s_2 = W^{s,s} s_1 + W^{s,x} x_2^{(3)}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} 1 - 0 \\\\ 0 - 1 \\end{bmatrix} = \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix}\n", + " $$\n", + "\n", + "- **At $ t = 3 $:**\n", + " $$\n", + " s_3 = W^{s,s} s_2 + W^{s,x} x_3^{(3)}\n", + " $$\n", + " $$\n", + " s_3 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_3 = \\begin{bmatrix} -1 + 1 \\\\ -1 + 0 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ -1 \\end{bmatrix}\n", + " $$\n", + "\n", + "**Final hidden state for $ BAA $ is $ s_3 = \\begin{bmatrix} 0 \\\\ -1 \\end{bmatrix} $.**\n", + "\n", + "#### 3. Sentence $ AA $\n", + "\n", + "**Step 1: Encode the sentence:**\n", + "\n", + "$$\n", + "x^{(1)} = \\left( \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\right)\n", + "$$\n", + "\n", + "**Step 2: Compute the hidden states:**\n", + "\n", + "- **At $ t = 1 $:**\n", + " $$\n", + " s_1 = W^{s,s} s_0 + W^{s,x} x_1^{(1)}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_1 = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + "\n", + "- **At $ t = 2 $:**\n", + " $$\n", + " s_2 = W^{s,s} s_1 + W^{s,x} x_2^{(1)}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} -1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + " $$\n", + " s_2 = \\begin{bmatrix} -1 + 1 \\\\ 0 + 0 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}\n", + " $$\n", + "\n", + "**Final hidden state for $ AA $ is $ s_2 = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} $.**" + ] } ], "metadata": { diff --git a/image.png b/image.png new file mode 100644 index 0000000000000000000000000000000000000000..025b1d35c7bae86a0d58274364de79fb2614b256 GIT binary patch literal 110626 zcmV*LKxDs(P)Px#L}ge>W=%~1DgXcg2mk?xX#fNO00031000^Q000001E2u_0{{R30RRC20H6W@ z1ONa40RR93?w|tz1ONa40RR938~^|S04AlYb^riC07*naRCodGy$N_6)s;4UBx~=M zTKj74vMk$@EibaX1K!vd!v`6YKr$J&5M~lEFaz04*fQ*yfrJ1*36Q~%4A>#@fbj-+ zw`?tzWy!*_WXW1u`_ir5(tqDuu2#3yl3LwW-PNr=&trG1y6V=wr>bt9d(L~_<3X<; zA10Z^YjBW$xoa<7S9;cP2Az)=-EjXsr1SMLY_r!FUymVL8Kb86HzrbyMoqb!}jU^MeR-WdTtnPjPp0B0=mli zM}y&SSN#&!t*2-9ouHd4YN4;^b!#4~06h@?9* zp`(r7e{UNF3|yiMA;I*(Kix_#0VHsgVNXGt9PwdtBRdiT`%{*DW^NJ7!Pf zBpXE=aC1f&Wd{sUdUPngRoYHJKYY>b94q&*mR{7-|M!1iQ7F4Un{Hc2d2x{z*^9DT 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