text stringlengths 9 39.2M | dir stringlengths 25 226 | lang stringclasses 163 values | created_date timestamp[s] | updated_date timestamp[s] | repo_name stringclasses 751 values | repo_full_name stringclasses 752 values | star int64 1.01k 183k | len_tokens int64 1 18.5M |
|---|---|---|---|---|---|---|---|---|
```kotlin
package id.zelory.compressor.constraint
import android.graphics.Bitmap
import id.zelory.compressor.compressFormat
import id.zelory.compressor.loadBitmap
import id.zelory.compressor.overWrite
import java.io.File
/**
* Created on : January 24, 2020
* Author : zetbaitsu
* Name : Zetra
* GitHub : path_to_url
*/
class FormatConstraint(private val format: Bitmap.CompressFormat) : Constraint {
override fun isSatisfied(imageFile: File): Boolean {
return format == imageFile.compressFormat()
}
override fun satisfy(imageFile: File): File {
return overWrite(imageFile, loadBitmap(imageFile), format)
}
}
fun Compression.format(format: Bitmap.CompressFormat) {
constraint(FormatConstraint(format))
}
``` | /content/code_sandbox/compressor/src/main/java/id/zelory/compressor/constraint/FormatConstraint.kt | kotlin | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 175 |
```kotlin
package id.zelory.compressor.constraint
import java.io.File
/**
* Created on : January 25, 2020
* Author : zetbaitsu
* Name : Zetra
* GitHub : path_to_url
*/
class DestinationConstraint(private val destination: File) : Constraint {
override fun isSatisfied(imageFile: File): Boolean {
return imageFile.absolutePath == destination.absolutePath
}
override fun satisfy(imageFile: File): File {
return imageFile.copyTo(destination, true)
}
}
fun Compression.destination(destination: File) {
constraint(DestinationConstraint(destination))
}
``` | /content/code_sandbox/compressor/src/main/java/id/zelory/compressor/constraint/DestinationConstraint.kt | kotlin | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 132 |
```qmake
# Add project specific ProGuard rules here.
# By default, the flags in this file are appended to flags specified
# in /Users/macbookair/Library/Android/sdk/tools/proguard/proguard-android.txt
# You can edit the include path and order by changing the proguardFiles
# directive in build.gradle.
#
# For more details, see
# path_to_url
# Add any project specific keep options here:
# If your project uses WebView with JS, uncomment the following
# and specify the fully qualified class name to the JavaScript interface
# class:
#-keepclassmembers class fqcn.of.javascript.interface.for.webview {
# public *;
#}
``` | /content/code_sandbox/app/proguard-rules.pro | qmake | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 141 |
```kotlin
package id.zelory.compressor.constraint
import android.graphics.Bitmap
import id.zelory.compressor.decodeSampledBitmapFromFile
import id.zelory.compressor.determineImageRotation
import id.zelory.compressor.overWrite
import java.io.File
/**
* Created on : January 25, 2020
* Author : zetbaitsu
* Name : Zetra
* GitHub : path_to_url
*/
class DefaultConstraint(
private val width: Int = 612,
private val height: Int = 816,
private val format: Bitmap.CompressFormat = Bitmap.CompressFormat.JPEG,
private val quality: Int = 80
) : Constraint {
private var isResolved = false
override fun isSatisfied(imageFile: File): Boolean {
return isResolved
}
override fun satisfy(imageFile: File): File {
val result = decodeSampledBitmapFromFile(imageFile, width, height).run {
determineImageRotation(imageFile, this).run {
overWrite(imageFile, this, format, quality)
}
}
isResolved = true
return result
}
}
fun Compression.default(
width: Int = 612,
height: Int = 816,
format: Bitmap.CompressFormat = Bitmap.CompressFormat.JPEG,
quality: Int = 80
) {
constraint(DefaultConstraint(width, height, format, quality))
}
``` | /content/code_sandbox/compressor/src/main/java/id/zelory/compressor/constraint/DefaultConstraint.kt | kotlin | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 304 |
```xml
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="path_to_url"
xmlns:tools="path_to_url"
package="id.zelory.compressor.sample">
<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
<application
android:allowBackup="true"
android:icon="@mipmap/ic_launcher"
android:label="@string/app_name"
android:supportsRtl="true"
android:theme="@style/AppTheme"
tools:ignore="GoogleAppIndexingWarning">
<activity android:name=".MainActivity">
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.LAUNCHER" />
</intent-filter>
</activity>
</application>
</manifest>
``` | /content/code_sandbox/app/src/main/AndroidManifest.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 191 |
```xml
<resources>
<!-- Base application theme. -->
<style name="AppTheme" parent="Theme.AppCompat.Light.DarkActionBar">
<!-- Customize your theme here. -->
<item name="colorPrimary">@color/colorPrimary</item>
<item name="colorPrimaryDark">@color/colorPrimaryDark</item>
<item name="colorAccent">@color/colorAccent</item>
</style>
</resources>
``` | /content/code_sandbox/app/src/main/res/values/styles.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 87 |
```xml
<resources>
<string name="app_name">Compressor</string>
</resources>
``` | /content/code_sandbox/app/src/main/res/values/strings.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 20 |
```xml
<resources>
<!-- Default screen margins, per the Android Design guidelines. -->
<dimen name="activity_horizontal_margin">16dp</dimen>
<dimen name="activity_vertical_margin">16dp</dimen>
</resources>
``` | /content/code_sandbox/app/src/main/res/values/dimens.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 52 |
```xml
<?xml version="1.0" encoding="utf-8"?>
<resources>
<color name="colorPrimary">#3F51B5</color>
<color name="colorPrimaryDark">#303F9F</color>
<color name="colorAccent">#FF4081</color>
</resources>
``` | /content/code_sandbox/app/src/main/res/values/colors.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 67 |
```xml
<?xml version="1.0" encoding="utf-8"?>
<ScrollView
xmlns:android="path_to_url"
xmlns:tools="path_to_url"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:context=".MainActivity">
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:orientation="vertical"
android:paddingBottom="@dimen/activity_vertical_margin"
android:paddingLeft="@dimen/activity_horizontal_margin"
android:paddingRight="@dimen/activity_horizontal_margin"
android:paddingTop="@dimen/activity_vertical_margin">
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:orientation="horizontal">
<ImageView
android:id="@+id/actualImageView"
android:layout_width="0dp"
android:layout_height="240dp"
android:layout_marginEnd="4dp"
android:layout_marginRight="4dp"
android:layout_weight="1"
android:adjustViewBounds="true"/>
<ImageView
android:id="@+id/compressedImageView"
android:layout_width="0dp"
android:layout_height="240dp"
android:layout_marginLeft="4dp"
android:layout_marginStart="4dp"
android:layout_weight="1"
android:adjustViewBounds="true"/>
</LinearLayout>
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_marginTop="4dp"
android:orientation="horizontal">
<TextView
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_marginEnd="4dp"
android:layout_marginRight="4dp"
android:layout_weight="1"
android:gravity="center"
android:text="Actual Image"
android:textSize="12sp"/>
<TextView
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_marginLeft="4dp"
android:layout_marginStart="4dp"
android:layout_weight="1"
android:gravity="center"
android:text="Compressed Image"
android:textSize="12sp"/>
</LinearLayout>
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_marginTop="2dp"
android:orientation="horizontal">
<TextView
android:id="@+id/actualSizeTextView"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_marginEnd="4dp"
android:layout_marginRight="4dp"
android:layout_weight="1"
android:gravity="center"
android:text="Size : -"
android:textSize="12sp"/>
<TextView
android:id="@+id/compressedSizeTextView"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_marginLeft="4dp"
android:layout_marginStart="4dp"
android:layout_weight="1"
android:gravity="center"
android:text="Size : -"
android:textSize="12sp"/>
</LinearLayout>
<Button
android:id="@+id/chooseImageButton"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_marginTop="8dp"
android:text="Choose image"/>
<Button
android:id="@+id/compressImageButton"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_marginTop="8dp"
android:text="Compress image"/>
<Button
android:id="@+id/customCompressImageButton"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_marginTop="8dp"
android:text="Custom compress"/>
</LinearLayout>
</ScrollView>
``` | /content/code_sandbox/app/src/main/res/layout/activity_main.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 864 |
```xml
<resources>
<!-- Example customization of dimensions originally defined in res/values/dimens.xml
(such as screen margins) for screens with more than 820dp of available width. This
would include 7" and 10" devices in landscape (~960dp and ~1280dp respectively). -->
<dimen name="activity_horizontal_margin">64dp</dimen>
</resources>
``` | /content/code_sandbox/app/src/main/res/values-w820dp/dimens.xml | xml | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 83 |
```java
package id.zelory.compressor.sample;
import android.content.Context;
import android.database.Cursor;
import android.net.Uri;
import android.provider.OpenableColumns;
import android.util.Log;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
/**
* Created on : June 18, 2016
* Author : zetbaitsu
* Name : Zetra
* GitHub : path_to_url
*/
class FileUtil {
private static final int EOF = -1;
private static final int DEFAULT_BUFFER_SIZE = 1024 * 4;
private FileUtil() {
}
public static File from(Context context, Uri uri) throws IOException {
InputStream inputStream = context.getContentResolver().openInputStream(uri);
String fileName = getFileName(context, uri);
String[] splitName = splitFileName(fileName);
File tempFile = File.createTempFile(splitName[0], splitName[1]);
tempFile = rename(tempFile, fileName);
tempFile.deleteOnExit();
FileOutputStream out = null;
try {
out = new FileOutputStream(tempFile);
} catch (FileNotFoundException e) {
e.printStackTrace();
}
if (inputStream != null) {
copy(inputStream, out);
inputStream.close();
}
if (out != null) {
out.close();
}
return tempFile;
}
private static String[] splitFileName(String fileName) {
String name = fileName;
String extension = "";
int i = fileName.lastIndexOf(".");
if (i != -1) {
name = fileName.substring(0, i);
extension = fileName.substring(i);
}
return new String[]{name, extension};
}
private static String getFileName(Context context, Uri uri) {
String result = null;
if (uri.getScheme().equals("content")) {
Cursor cursor = context.getContentResolver().query(uri, null, null, null, null);
try {
if (cursor != null && cursor.moveToFirst()) {
result = cursor.getString(cursor.getColumnIndex(OpenableColumns.DISPLAY_NAME));
}
} catch (Exception e) {
e.printStackTrace();
} finally {
if (cursor != null) {
cursor.close();
}
}
}
if (result == null) {
result = uri.getPath();
int cut = result.lastIndexOf(File.separator);
if (cut != -1) {
result = result.substring(cut + 1);
}
}
return result;
}
private static File rename(File file, String newName) {
File newFile = new File(file.getParent(), newName);
if (!newFile.equals(file)) {
if (newFile.exists() && newFile.delete()) {
Log.d("FileUtil", "Delete old " + newName + " file");
}
if (file.renameTo(newFile)) {
Log.d("FileUtil", "Rename file to " + newName);
}
}
return newFile;
}
private static long copy(InputStream input, OutputStream output) throws IOException {
long count = 0;
int n;
byte[] buffer = new byte[DEFAULT_BUFFER_SIZE];
while (EOF != (n = input.read(buffer))) {
output.write(buffer, 0, n);
count += n;
}
return count;
}
}
``` | /content/code_sandbox/app/src/main/java/id/zelory/compressor/sample/FileUtil.java | java | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 710 |
```kotlin
package id.zelory.compressor.sample
import android.content.Intent
import android.graphics.Bitmap
import android.graphics.BitmapFactory
import android.graphics.Color
import android.os.Bundle
import android.os.Environment
import android.util.Log
import android.widget.Toast
import androidx.appcompat.app.AppCompatActivity
import androidx.lifecycle.lifecycleScope
import id.zelory.compressor.Compressor
import id.zelory.compressor.constraint.default
import id.zelory.compressor.constraint.destination
import id.zelory.compressor.constraint.format
import id.zelory.compressor.constraint.quality
import id.zelory.compressor.constraint.resolution
import id.zelory.compressor.constraint.size
import id.zelory.compressor.loadBitmap
import kotlinx.android.synthetic.main.activity_main.actualImageView
import kotlinx.android.synthetic.main.activity_main.actualSizeTextView
import kotlinx.android.synthetic.main.activity_main.chooseImageButton
import kotlinx.android.synthetic.main.activity_main.compressImageButton
import kotlinx.android.synthetic.main.activity_main.compressedImageView
import kotlinx.android.synthetic.main.activity_main.compressedSizeTextView
import kotlinx.android.synthetic.main.activity_main.customCompressImageButton
import kotlinx.coroutines.launch
import java.io.File
import java.io.IOException
import java.text.DecimalFormat
import java.util.*
import kotlin.math.log10
import kotlin.math.pow
/**
* Created on : January 25, 2020
* Author : zetbaitsu
* Name : Zetra
* GitHub : path_to_url
*/
class MainActivity : AppCompatActivity() {
companion object {
private const val PICK_IMAGE_REQUEST = 1
}
private var actualImage: File? = null
private var compressedImage: File? = null
override fun onCreate(savedInstanceState: Bundle?) {
super.onCreate(savedInstanceState)
setContentView(R.layout.activity_main)
actualImageView.setBackgroundColor(getRandomColor())
clearImage()
setupClickListener()
}
private fun setupClickListener() {
chooseImageButton.setOnClickListener { chooseImage() }
compressImageButton.setOnClickListener { compressImage() }
customCompressImageButton.setOnClickListener { customCompressImage() }
}
private fun chooseImage() {
val intent = Intent(Intent.ACTION_GET_CONTENT)
intent.type = "image/*"
startActivityForResult(intent, PICK_IMAGE_REQUEST)
}
private fun compressImage() {
actualImage?.let { imageFile ->
lifecycleScope.launch {
// Default compression
compressedImage = Compressor.compress(this@MainActivity, imageFile)
setCompressedImage()
}
} ?: showError("Please choose an image!")
}
private fun customCompressImage() {
actualImage?.let { imageFile ->
lifecycleScope.launch {
// Default compression with custom destination file
/*compressedImage = Compressor.compress(this@MainActivity, imageFile) {
default()
getExternalFilesDir(Environment.DIRECTORY_PICTURES)?.also {
val file = File("${it.absolutePath}${File.separator}my_image.${imageFile.extension}")
destination(file)
}
}*/
// Full custom
compressedImage = Compressor.compress(this@MainActivity, imageFile) {
resolution(1280, 720)
quality(80)
format(Bitmap.CompressFormat.WEBP)
size(2_097_152) // 2 MB
}
setCompressedImage()
}
} ?: showError("Please choose an image!")
}
private fun setCompressedImage() {
compressedImage?.let {
compressedImageView.setImageBitmap(BitmapFactory.decodeFile(it.absolutePath))
compressedSizeTextView.text = String.format("Size : %s", getReadableFileSize(it.length()))
Toast.makeText(this, "Compressed image save in " + it.path, Toast.LENGTH_LONG).show()
Log.d("Compressor", "Compressed image save in " + it.path)
}
}
private fun clearImage() {
actualImageView.setBackgroundColor(getRandomColor())
compressedImageView.setImageDrawable(null)
compressedImageView.setBackgroundColor(getRandomColor())
compressedSizeTextView.text = "Size : -"
}
override fun onActivityResult(requestCode: Int, resultCode: Int, data: Intent?) {
super.onActivityResult(requestCode, resultCode, data)
if (requestCode == PICK_IMAGE_REQUEST && resultCode == RESULT_OK) {
if (data == null) {
showError("Failed to open picture!")
return
}
try {
actualImage = FileUtil.from(this, data.data)?.also {
actualImageView.setImageBitmap(loadBitmap(it))
actualSizeTextView.text = String.format("Size : %s", getReadableFileSize(it.length()))
clearImage()
}
} catch (e: IOException) {
showError("Failed to read picture data!")
e.printStackTrace()
}
}
}
private fun showError(errorMessage: String) {
Toast.makeText(this, errorMessage, Toast.LENGTH_SHORT).show()
}
private fun getRandomColor() = Random().run {
Color.argb(100, nextInt(256), nextInt(256), nextInt(256))
}
private fun getReadableFileSize(size: Long): String {
if (size <= 0) {
return "0"
}
val units = arrayOf("B", "KB", "MB", "GB", "TB")
val digitGroups = (log10(size.toDouble()) / log10(1024.0)).toInt()
return DecimalFormat("#,##0.#").format(size / 1024.0.pow(digitGroups.toDouble())) + " " + units[digitGroups]
}
}
``` | /content/code_sandbox/app/src/main/java/id/zelory/compressor/sample/MainActivity.kt | kotlin | 2016-06-18T13:54:59 | 2024-08-16T08:02:02 | Compressor | zetbaitsu/Compressor | 7,034 | 1,126 |
```desktop
[Desktop Entry]
Type=Application
Name=Buckle
Comment=Bucklespring keyboard sound
Exec=buckle -f
Icon=input-keyboard
StartupNotify=false
Terminal=false
Hidden=false
``` | /content/code_sandbox/buckle.desktop | desktop | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 41 |
```c
#include <windows.h>
#include <winuser.h>
#include <stdio.h>
#include <io.h>
#include <fcntl.h>
#include "buckle.h"
void open_console();
LRESULT CALLBACK handle_kbh(int nCode, WPARAM wParam, LPARAM lParam);
static HHOOK kbh = NULL;
static int state[256] = { 0 };
int scan(int verbose)
{
HINSTANCE hInst = GetModuleHandle(NULL);
kbh = SetWindowsHookEx(WH_KEYBOARD_LL, handle_kbh, hInst, 0);
MSG msg;
while(GetMessage(&msg, (HWND) NULL, 0, 0) > 0) {
TranslateMessage(&msg);
DispatchMessage(&msg);
}
return 0;
}
LRESULT CALLBACK handle_kbh(int nCode, WPARAM wParam, LPARAM lParam)
{
KBDLLHOOKSTRUCT *ev = (KBDLLHOOKSTRUCT *)lParam;
printd("vkCode=%d scanCode=%d flags=%d time=%d",
(int)ev->vkCode, (int)ev->scanCode, (int)ev->flags, (int)ev->time);
int updown = (wParam == WM_KEYDOWN || wParam == WM_SYSKEYDOWN);
int code = ev->scanCode;
if(code < 256) {
if(state[code] != updown) {
play(code, updown);
state[code] = updown;
}
}
return CallNextHookEx(kbh, nCode, wParam, lParam);
}
void open_console()
{
int hConHandle;
INT_PTR lStdHandle;
CONSOLE_SCREEN_BUFFER_INFO coninfo;
FILE *fp;
AllocConsole();
GetConsoleScreenBufferInfo(GetStdHandle(STD_OUTPUT_HANDLE), &coninfo);
coninfo.dwSize.Y = 500;
SetConsoleScreenBufferSize(GetStdHandle(STD_OUTPUT_HANDLE), coninfo.dwSize);
lStdHandle = (INT_PTR)GetStdHandle(STD_OUTPUT_HANDLE);
hConHandle = _open_osfhandle(lStdHandle, _O_TEXT);
fp = _fdopen( hConHandle, "w" );
*stdout = *fp;
*stderr = *fp;
setvbuf(fp, NULL, _IONBF, 0 );
}
``` | /content/code_sandbox/scan-windows.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 471 |
```objective-c
#ifndef buckle_h
#define buckle_h
int play(int code, int press);
int scan(int verbose);
void printd(const char *fmt, ...);
void open_console(void);
#endif
``` | /content/code_sandbox/buckle.h | objective-c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 39 |
```c
#include <ApplicationServices/ApplicationServices.h>
#include "buckle.h"
/*
* From path_to_url
*/
static const int mactoset1[] =
{
/* set-1 SDL_QuartzKeys.h */
0x1e, /* QZ_a 0x00 */
0x1f, /* QZ_s 0x01 */
0x20, /* QZ_d 0x02 */
0x21, /* QZ_f 0x03 */
0x23, /* QZ_h 0x04 */
0x22, /* QZ_g 0x05 */
0x2c, /* QZ_z 0x06 */
0x2d, /* QZ_x 0x07 */
0x2e, /* QZ_c 0x08 */
0x2f, /* QZ_v 0x09 */
0x56, /* between lshift and z. 'INT 1'? */
0x30, /* QZ_b 0x0B */
0x10, /* QZ_q 0x0C */
0x11, /* QZ_w 0x0D */
0x12, /* QZ_e 0x0E */
0x13, /* QZ_r 0x0F */
0x15, /* QZ_y 0x10 */
0x14, /* QZ_t 0x11 */
0x02, /* QZ_1 0x12 */
0x03, /* QZ_2 0x13 */
0x04, /* QZ_3 0x14 */
0x05, /* QZ_4 0x15 */
0x07, /* QZ_6 0x16 */
0x06, /* QZ_5 0x17 */
0x0d, /* QZ_EQUALS 0x18 */
0x0a, /* QZ_9 0x19 */
0x08, /* QZ_7 0x1A */
0x0c, /* QZ_MINUS 0x1B */
0x09, /* QZ_8 0x1C */
0x0b, /* QZ_0 0x1D */
0x1b, /* QZ_RIGHTBRACKET 0x1E */
0x18, /* QZ_o 0x1F */
0x16, /* QZ_u 0x20 */
0x1a, /* QZ_LEFTBRACKET 0x21 */
0x17, /* QZ_i 0x22 */
0x19, /* QZ_p 0x23 */
0x1c, /* QZ_RETURN 0x24 */
0x26, /* QZ_l 0x25 */
0x24, /* QZ_j 0x26 */
0x28, /* QZ_QUOTE 0x27 */
0x25, /* QZ_k 0x28 */
0x27, /* QZ_SEMICOLON 0x29 */
0x2b, /* QZ_BACKSLASH 0x2A */
0x33, /* QZ_COMMA 0x2B */
0x35, /* QZ_SLASH 0x2C */
0x31, /* QZ_n 0x2D */
0x32, /* QZ_m 0x2E */
0x34, /* QZ_PERIOD 0x2F */
0x0f, /* QZ_TAB 0x30 */
0x39, /* QZ_SPACE 0x31 */
0x29, /* QZ_BACKQUOTE 0x32 */
0x0e, /* QZ_BACKSPACE 0x33 */
0x9c, /* QZ_IBOOK_ENTER 0x34 */
0x01, /* QZ_ESCAPE 0x35 */
0x5c, /* QZ_RMETA 0x36 */
0x5b, /* QZ_LMETA 0x37 */
0x2a, /* QZ_LSHIFT 0x38 */
0x3a, /* QZ_CAPSLOCK 0x39 */
0x38, /* QZ_LALT 0x3A */
0x1d, /* QZ_LCTRL 0x3B */
0x36, /* QZ_RSHIFT 0x3C */
0x38, /* QZ_RALT 0x3D */
0x1d, /* QZ_RCTRL 0x3E */
0, /* */
0, /* */
0x53, /* QZ_KP_PERIOD 0x41 */
0, /* */
0x37, /* QZ_KP_MULTIPLY 0x43 */
0, /* */
0x4e, /* QZ_KP_PLUS 0x45 */
0, /* */
0x45, /* QZ_NUMLOCK 0x47 */
0, /* */
0, /* */
0, /* */
0x35, /* QZ_KP_DIVIDE 0x4B */
0x1c, /* QZ_KP_ENTER 0x4C */
0, /* */
0x4a, /* QZ_KP_MINUS 0x4E */
0, /* */
0, /* */
0x0d/*?*/, /* QZ_KP_EQUALS 0x51 */
0x52, /* QZ_KP0 0x52 */
0x4f, /* QZ_KP1 0x53 */
0x50, /* QZ_KP2 0x54 */
0x51, /* QZ_KP3 0x55 */
0x4b, /* QZ_KP4 0x56 */
0x4c, /* QZ_KP5 0x57 */
0x4d, /* QZ_KP6 0x58 */
0x47, /* QZ_KP7 0x59 */
0, /* */
0x48, /* QZ_KP8 0x5B */
0x49, /* QZ_KP9 0x5C */
0x7d, /* yen, | (JIS) 0x5D */
0x73, /* _, ro (JIS) 0x5E */
0, /* */
0x3f, /* QZ_F5 0x60 */
0x40, /* QZ_F6 0x61 */
0x41, /* QZ_F7 0x62 */
0x3d, /* QZ_F3 0x63 */
0x42, /* QZ_F8 0x64 */
0x43, /* QZ_F9 0x65 */
0x29, /* Zen/Han (JIS) 0x66 */
0x57, /* QZ_F11 0x67 */
0x29, /* Zen/Han (JIS) 0x68 */
0x37, /* QZ_PRINT / F13 0x69 */
0x63, /* QZ_F16 0x6A */
0x46, /* QZ_SCROLLOCK 0x6B */
0, /* */
0x44, /* QZ_F10 0x6D */
0x5d, /* */
0x58, /* QZ_F12 0x6F */
0, /* */
0/* 0xe1,0x1d,0x45*/, /* QZ_PAUSE 0x71 */
0x52, /* QZ_INSERT / HELP 0x72 */
0x47, /* QZ_HOME 0x73 */
0x49, /* QZ_PAGEUP 0x74 */
0x53, /* QZ_DELETE 0x75 */
0x3e, /* QZ_F4 0x76 */
0x4f, /* QZ_END 0x77 */
0x3c, /* QZ_F2 0x78 */
0x51, /* QZ_PAGEDOWN 0x79 */
0x3b, /* QZ_F1 0x7A */
0x4b, /* QZ_LEFT 0x7B */
0x4d, /* QZ_RIGHT 0x7C */
0x50, /* QZ_DOWN 0x7D */
0x48, /* QZ_UP 0x7E */
0,/*0x5e|K_EX*/ /* QZ_POWER 0x7F */ /* have different break key! */
/* do NEVER deliver the Power
* scancode as e.g. Windows will
* handle it, @bugref{7692}. */
};
/*
* Adapted from path_to_url
*/
CGEventRef myCGEventCallback(CGEventTapProxy proxy, CGEventType type, CGEventRef event, void *refcon)
{
if ((type != kCGEventKeyDown) && (type != kCGEventKeyUp))
return event;
int mackeycode = (int)CGEventGetIntegerValueField(event, kCGKeyboardEventKeycode);
printd("Mac keycode: %d", mackeycode);
if (mackeycode >= sizeof(mactoset1)/sizeof(mactoset1[0]))
return event;
int key = mactoset1[mackeycode];
if (CGEventGetIntegerValueField(event, kCGKeyboardEventAutorepeat))
return event;
switch (type) {
case kCGEventKeyDown:
play(key, 1);
break;
case kCGEventKeyUp:
play(key, 0);
break;
default:
break;
}
return event;
}
int scan(int verbose)
{
CFMachPortRef eventTap;
CGEventMask eventMask;
CFRunLoopSourceRef runLoopSource;
/* Create an event tap. We are interested in key presses. */
eventMask = ((1 << kCGEventKeyDown) | (1 << kCGEventKeyUp));
eventTap = CGEventTapCreate(kCGSessionEventTap, kCGHeadInsertEventTap, 0, eventMask, myCGEventCallback, NULL);
if (!eventTap) {
fprintf(stderr, "failed to create event tap\n");
exit(1);
}
/* Create a run loop source. */
runLoopSource = CFMachPortCreateRunLoopSource( kCFAllocatorDefault, eventTap, 0);
/* Add to the current run loop. */
CFRunLoopAddSource(CFRunLoopGetCurrent(), runLoopSource, kCFRunLoopCommonModes);
/* Enable the event tap. */
CGEventTapEnable(eventTap, true);
/* Set it all running. */
CFRunLoopRun();
return 0;
}
void open_console(void)
{
}
``` | /content/code_sandbox/scan-mac.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 2,630 |
```c
#include <stdio.h>
#include <fcntl.h>
#include <unistd.h>
#include <sys/poll.h>
#include <string.h>
#include <errno.h>
#include <libinput.h>
#include "buckle.h"
static int open_restricted(const char *path, int flags, void *user_data)
{
int fd = open(path, flags);
if(fd < 0) {
fprintf(stderr, "Failed to open %s (%s)\n", path, strerror(errno));
}
return fd < 0 ? -errno : fd;
}
static void close_restricted(int fd, void *user_data)
{
close(fd);
}
static const struct libinput_interface interface = {
.open_restricted = open_restricted,
.close_restricted = close_restricted,
};
static void handle_key(struct libinput_event *ev)
{
struct libinput_event_keyboard *k = libinput_event_get_keyboard_event(ev);
enum libinput_key_state state = libinput_event_keyboard_get_key_state(k);
uint32_t key = libinput_event_keyboard_get_key(k);
play(key, state == LIBINPUT_KEY_STATE_PRESSED);
}
static void handle_events(struct libinput *li)
{
struct libinput_event *ev;
libinput_dispatch(li);
while((ev = libinput_get_event(li))) {
switch(libinput_event_get_type(ev)) {
case LIBINPUT_EVENT_KEYBOARD_KEY:
handle_key(ev);
break;
default:
break;
}
libinput_event_destroy(ev);
libinput_dispatch(li);
}
}
static void log_handler(struct libinput *li, enum libinput_log_priority priority,
const char *format, va_list args)
{
vprintf(format, args);
}
int scan(int verbose)
{
struct udev *udev;
struct libinput *li;
udev = udev_new();
if (!udev) {
fprintf(stderr, "Failed to initialize udev\n");
return -1;
}
li = libinput_udev_create_context(&interface, NULL, udev);
if(!li) {
fprintf(stderr, "Failed to initialize context\n");
return -1;
}
if(verbose) {
libinput_log_set_handler(li, log_handler);
libinput_log_set_priority(li, LIBINPUT_LOG_PRIORITY_DEBUG);
}
if (libinput_udev_assign_seat(li, "seat0")) {
fprintf(stderr, "Failed to set seat\n");
return -1;
}
libinput_dispatch(li);
struct pollfd fds;
fds.fd = libinput_get_fd(li);
fds.events = POLLIN;
fds.revents = 0;
while(poll(&fds, 1, -1) > -1) {
handle_events(li);
}
return 0;
}
void open_console(void)
{
}
``` | /content/code_sandbox/scan-libinput.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 576 |
```unknown
NAME := buckle
SRC := main.c
VERSION := 1.5.1
PATH_AUDIO ?= "./wav"
CFLAGS ?= -O3 -g
LDFLAGS ?= -g
CFLAGS += -Wall -Werror
CFLAGS += -DVERSION=\"$(VERSION)\"
CFLAGS += -DPATH_AUDIO=\"$(PATH_AUDIO)\"
ifdef mingw
BIN := $(NAME).exe
CROSS := i686-w64-mingw32-
CFLAGS += -Iwin32/include -Iwin32/include/AL
LDFLAGS += -mwindows -static-libgcc -static-libstdc++
LIBS += -Lwin32/lib -lALURE32 -lOpenAL32
SRC += scan-windows.c
else
OS := $(shell uname)
ifeq ($(OS), Darwin)
BIN := $(NAME)
PKG_CONFIG_PATH := "./mac/lib/pkgconfig"
LIBS += $(shell PKG_CONFIG_PATH=$(PKG_CONFIG_PATH) pkg-config --libs alure openal)
CFLAGS += $(shell PKG_CONFIG_PATH=$(PKG_CONFIG_PATH) pkg-config --cflags alure openal)
LDFLAGS += -framework ApplicationServices -framework OpenAL
SRC += scan-mac.c
else
BIN := $(NAME)
ifdef libinput
LIBS += $(shell pkg-config --libs openal alure libinput libudev)
CFLAGS += $(shell pkg-config --cflags openal alure libinput libudev)
SRC += scan-libinput.c
else
LIBS += $(shell pkg-config --libs openal alure xtst x11)
CFLAGS += $(shell pkg-config --cflags openal alure xtst x11)
SRC += scan-x11.c
endif
endif
endif
OBJS = $(subst .c,.o, $(SRC))
CC ?= $(CROSS)gcc
LD ?= $(CROSS)gcc
CCLD ?= $(CC)
STRIP = $(CROSS)strip
%.o: %.c
$(CC) $(CPPFLAGS) $(CFLAGS) -c $< -o $@
$(BIN): $(OBJS)
$(CCLD) $(LDFLAGS) -o $@ $(OBJS) $(LIBS)
dist:
mkdir -p $(NAME)-$(VERSION)
cp -a *.c *.h wav Makefile LICENSE $(NAME)-$(VERSION)
tar -zcf /tmp/$(NAME)-$(VERSION).tgz $(NAME)-$(VERSION)
rm -rf $(NAME)-$(VERSION)
rec: rec.c
gcc -Wall -Werror rec.c -o rec
clean:
$(RM) $(OBJS) $(BIN) core rec
strip: $(BIN)
$(STRIP) $(BIN)
``` | /content/code_sandbox/Makefile | unknown | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 625 |
```c
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <fcntl.h>
#include <sys/select.h>
#include <sys/time.h>
struct input_event {
struct timeval time;
unsigned short type;
unsigned short code;
unsigned int value;
};
#define HISTSIZE 60
int main(int argc, char **argv)
{
struct input_event event;
char cmd[256];
char fname[256];
FILE *f;
int fd_ev, fd_snd;
int samples = 0;
int triggered = 0;
FILE *fout = NULL;
int head = 0;
int16_t hist[HISTSIZE];
if(argc < 2) {
fprintf(stderr, "usage: %s </dev/input/event#>\n", argv[0]);
exit(1);
}
//f = popen("arecord -D plughw:1,0 -f cd -r 44100 -c 1", "r");
f = popen("parec --rate=44100 --format=s16le --channels=1", "r");
fd_snd = fileno(f);
fd_ev = open(argv[1], O_RDONLY);
if(fd_ev == -1) {
perror("Could not open event input");
exit(1);
}
fd_set fds;
while(1) {
FD_ZERO(&fds);
FD_SET(fd_ev, &fds);
FD_SET(fd_snd, &fds);
select(16, &fds, NULL, NULL, NULL);
if(FD_ISSET(fd_ev, &fds)) {
read(fd_ev, &event, sizeof event);
if(event.type != 1) continue;
if(event.value == 2) continue;
if(triggered == 0) {
snprintf(fname, sizeof fname, "wav-new/%02x-%d.wav", event.code, event.value);
snprintf(cmd, sizeof cmd, "sox -qq -r 44100 -e signed -b 16 -c 1 -t raw - %s", fname);
printf("%02x %d: ", event.code, event.value);
fflush(stdout);
fout = popen(cmd, "w");
samples = 0;
triggered = 1;
printf("%02x %d ", event.code, event.value);
fflush(stdout);
}
}
if(FD_ISSET(fd_snd, &fds)) {
int16_t buf;
read(fd_snd, &buf, sizeof buf);
if(triggered) {
if(samples == 0) {
if(buf < -2000 || buf > 2000) {
samples = 1;
printf(">");
fflush(stdout);
}
}
if(fout && samples) {
fwrite(&hist[head], 1, sizeof hist[head], fout);
if(samples > 44000/3) {
fclose(fout);
snprintf(cmd, sizeof(cmd), "paplay %s &", fname);
system(cmd);
printf(".\n");
fout = NULL;
triggered = 0;
}
}
if(samples) samples ++;
}
hist[head] = buf;
head = (head + 1) % HISTSIZE;
}
}
return 0;
}
``` | /content/code_sandbox/rec.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 704 |
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdarg.h>
#include <errno.h>
#include <stdint.h>
#include <inttypes.h>
#include <unistd.h>
#include <limits.h>
#include <stdbool.h>
#include <getopt.h>
#include <time.h>
#ifdef __APPLE__
#include <OpenAL/al.h>
#include <OpenAL/alure.h>
#else
#include <AL/al.h>
#include <AL/alure.h>
#endif
#include "buckle.h"
#define SRC_INVALID INT_MAX
#define DEFAULT_MUTE_KEYCODE 0x46 /* Scroll Lock */
#define TEST_ERROR(_msg) \
error = alGetError(); \
if (error != AL_NO_ERROR) { \
fprintf(stderr, _msg "\n"); \
exit(1); \
}
static void usage(char *exe);
static void list_devices(void);
static double find_key_loc(int code);
/*
* Horizontal position on keyboard for each key as they are located on my model-M
*/
static int keyloc[][32] = {
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x6e, 0x66, 0x68, 0x1c, 0x45, 0x62, 0x37, 0x4a, -1 },
{ 0x01, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x42, 0x43, 0x44, 0x57, 0x58, 0x6f, 0x6b, 0x6d, 0x47, 0x48, 0x49, 0x4e, -1 },
{ 0x29, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x4b, 0x4c, 0x4d, -1 },
{ 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x2b, 0x4f, 0x50, 0x51, 0x60, -1 },
{ 0x3a, 0x1e, 0x1f, 0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x1c, 0x52, 0x53, -1 },
{ 0x2a, 0x56, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, -1 },
{ 0x1d, 0x7d, 0x5b, 0x38, 0x39, 0x64, 0x61, 0x67, -1 },
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x69, 0x6c, 0x6a, -1 },
};
/*
* Horizontal position on keyboard of the pragmatic center of the row, since keys come in different sizes and shapes
*/
static double midloc[] = {
7.5,
7.5,
7.5,
6.5,
6.5,
6.5,
4.5,
};
static int opt_verbose = 0;
static int opt_no_click = 0;
static int opt_stereo_width = 50;
static int opt_gain = 100;
static int opt_fallback_sound = 0;
static int opt_mute_keycode = DEFAULT_MUTE_KEYCODE;
static const char *opt_device = NULL;
static const char *opt_path_audio = PATH_AUDIO;
static int muted = 0;
static const char short_opts[] = "d:fg:hlm:Mp:s:cv";
static const struct option long_opts[] = {
{ "device", required_argument, NULL, 'd' },
{ "fallback-sound", no_argument, NULL, 'f' },
{ "gain", required_argument, NULL, 'g' },
{ "help", no_argument, NULL, 'h' },
{ "list-devices", no_argument, NULL, 'l' },
{ "mute-keycode", required_argument, NULL, 'm' },
{ "mute", no_argument, NULL, 'M' },
{ "audio-path", required_argument, NULL, 'p' },
{ "stereo-width", required_argument, NULL, 's' },
{ "no-click", no_argument, NULL, 'c' },
{ "verbose", no_argument, NULL, 'v' },
{ 0, 0, 0, 0 }
};
int main(int argc, char **argv)
{
int c;
int rv = EXIT_SUCCESS;
int idx;
while( (c = getopt_long(argc, argv,
short_opts, long_opts, &idx)) != -1) {
switch(c) {
case 'd':
opt_device = optarg;
break;
case 'f':
opt_fallback_sound = 1;
break;
case 'g':
opt_gain = atoi(optarg);
break;
case 'h':
usage(argv[0]);
return 0;
case 'l':
list_devices();
return 0;
case 'm':
opt_mute_keycode = strtol(optarg, NULL, 0);
break;
case 'M':
muted = !muted;
break;
case 'p':
opt_path_audio = optarg;
break;
case 's':
opt_stereo_width = atoi(optarg);
break;
case 'c':
opt_no_click++;
break;
case 'v':
opt_verbose++;
break;
default:
usage(argv[0]);
return 1;
break;
}
}
if(opt_verbose) {
open_console();
}
/* Create openal context */
ALCdevice *device = NULL;
ALCcontext *context = NULL;
ALfloat listenerOri[] = { 0.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f };
ALCenum error;
if (!opt_device) {
opt_device = alcGetString(NULL, ALC_DEFAULT_DEVICE_SPECIFIER);
}
printd("Opening OpenAL audio device \"%s\"", opt_device);
device = alcOpenDevice(opt_device);
if (!device) {
fprintf(stderr, "unable to open default device\n");
rv = EXIT_FAILURE;
goto out;
}
context = alcCreateContext(device, NULL);
if (!alcMakeContextCurrent(context)) {
fprintf(stderr, "failed to make default context\n");
return -1;
}
TEST_ERROR("make default context");
alListener3f(AL_POSITION, 0, 0, 0);
alListener3f(AL_VELOCITY, 0, 0, 0);
alListenerfv(AL_ORIENTATION, listenerOri);
/* Path to data files can also be specified by environment, this is
* used by the snap package */
const char *env_path = getenv("BUCKLESPRING_WAV_DIR");
if (env_path) {
opt_path_audio = env_path;
}
printd("Using wav dir: \"%s\"\n", opt_path_audio);
scan(opt_verbose);
out:
device = alcGetContextsDevice(context);
alcMakeContextCurrent(NULL);
if(context) alcDestroyContext(context);
if(device) alcCloseDevice(device);
return rv;
}
static void usage(char *exe)
{
fprintf(stderr,
"bucklespring version " VERSION "\n"
"usage: %s [options]\n"
"\n"
"options:\n"
"\n"
" -d, --device=DEVICE use OpenAL audio device DEVICE\n"
" -f, --fallback-sound use a fallback sound for unknown keys\n"
" -g, --gain=GAIN set playback gain [0..100]\n"
" -m, --mute-keycode=CODE use CODE as mute key (default 0x46 for scroll lock)\n"
" -M, --mute start the program muted\n"
" -c, --no-click don't play a sound on mouse click\n"
" -h, --help show help\n"
" -l, --list-devices list available OpenAL audio devices\n"
" -p, --audio-path=PATH load .wav files from directory PATH\n"
" -s, --stereo-width=WIDTH set stereo width [0..100]\n"
" -v, --verbose increase verbosity / debugging\n",
exe
);
}
static void list_devices(void)
{
const ALCchar *devices = alcGetString(NULL, ALC_DEVICE_SPECIFIER);
const ALCchar *device = devices, *next = devices + 1;
size_t len = 0;
printf("Available audio devices:");
while (device && *device != '\0' && next && *next != '\0') {
fprintf(stdout, " \"%s\"", device);
len = strlen(device);
device += (len + 1);
next += (len + 2);
}
printf("\n");
}
void printd(const char *fmt, ...)
{
if(opt_verbose) {
char buf[256];
va_list va;
va_start(va, fmt);
vsnprintf(buf, sizeof(buf), fmt, va);
va_end(va);
fprintf(stderr, "%s\n", buf);
}
}
/*
* Find horizontal position of the given key on the keyboard. returns -1.0 for
* left to 1.0 for right
*/
static double find_key_loc(int code)
{
int row;
int col, keycol = 0;
for(row=0; row<8; row++) {
for(col=0; col<32; col++) {
if(keyloc[row][col] == code) keycol = col+1;
if(keyloc[row][col] == -1) break;
}
if(keycol) {
return ((double) keycol-midloc[row])/(col-midloc[row]);
}
}
return 0;
}
/*
* To silence play temporarily, press mute key (default ScrollLock) within 2
* seconds, same to unmute
*/
static void handle_mute_key(int mute_key)
{
static time_t t_prev;
static int count = 0;
if(mute_key) {
time_t t_now = time(NULL);
if(t_now - t_prev < 2) {
count ++;
if(count == 2) {
muted = !muted;
printd("Mute %s", muted ? "enabled" : "disabled");
count = 0;
}
} else {
count = 1;
}
t_prev = t_now;
} else {
count = 0;
}
}
/*
* Play audio file for given keycode. Wav files are loaded on demand
*/
int play(int code, int press)
{
ALCenum error;
printd("scancode %d/0x%x", code, code);
if (code == 0xff && opt_no_click) return 0;
/* Check for mute sequence: ScrollLock down+up+down */
if (press) {
handle_mute_key(code == opt_mute_keycode);
}
static ALuint buf[512] = { 0 };
static ALuint src[512] = { 0 };
int idx = code + press * 256;
if(src[idx] == 0) {
char fname[256];
snprintf(fname, sizeof(fname), "%s/%02x-%d.wav", opt_path_audio, code, press);
printd("Loading audio file \"%s\"", fname);
buf[idx] = alureCreateBufferFromFile(fname);
if(buf[idx] == 0) {
if(opt_fallback_sound) {
snprintf(fname, sizeof(fname), "%s/%02x-%d.wav", opt_path_audio, 0x31, press);
buf[idx] = alureCreateBufferFromFile(fname);
} else {
fprintf(stderr, "Error opening audio file \"%s\": %s\n", fname, alureGetErrorString());
}
if(buf[idx] == 0) {
src[idx] = SRC_INVALID;
return -1;
}
}
alGenSources((ALuint)1, &src[idx]);
TEST_ERROR("source generation");
double x = find_key_loc(code);
if (opt_stereo_width > 0) {
alSource3f(src[idx], AL_POSITION, -x, 0, (100 - opt_stereo_width) / 100.0);
}
alSourcef(src[idx], AL_GAIN, opt_gain / 100.0);
alSourcei(src[idx], AL_BUFFER, buf[idx]);
TEST_ERROR("buffer binding");
}
if(src[idx] != 0 && src[idx] != SRC_INVALID) {
if (!muted)
alSourcePlay(src[idx]);
TEST_ERROR("source playing");
}
return 0;
}
/*
* End
*/
``` | /content/code_sandbox/main.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 3,177 |
```c
#include <stdio.h>
#include <X11/XKBlib.h>
#include <X11/extensions/record.h>
#include "buckle.h"
void key_pressed_cb(XPointer arg, XRecordInterceptData *d);
int scan(int verbose)
{
/* Initialize and start Xrecord context */
XRecordRange* rr;
XRecordClientSpec rcs;
XRecordContext rc;
printd("Opening Xrecord context");
Display *dpy = XOpenDisplay(NULL);
if(dpy == NULL) {
fprintf(stderr, "Unable to open display\n");
return -1;
}
rr = XRecordAllocRange ();
if(rr == NULL) {
fprintf(stderr, "XRecordAllocRange error\n");
return -1;
}
rr->device_events.first = KeyPress;
rr->device_events.last = ButtonReleaseMask;
rcs = XRecordAllClients;
rc = XRecordCreateContext (dpy, 0, &rcs, 1, &rr, 1);
if(rc == 0) {
fprintf(stderr, "XRecordCreateContext error\n");
return -1;
}
XFree (rr);
if(XRecordEnableContext(dpy, rc, key_pressed_cb, NULL) == 0) {
fprintf(stderr, "XRecordEnableContext error\n");
return -1;
}
/* We never get here */
return 0;
}
/*
* Xrecord event callback
*/
void key_pressed_cb(XPointer arg, XRecordInterceptData *d)
{
if (d->category != XRecordFromServer)
return;
int key = ((unsigned char*) d->data)[1];
int type = ((unsigned char*) d->data)[0] & 0x7F;
int repeat = d->data[2] & 1;
key -= 8; /* X code to scan code? */
if(!repeat) {
switch (type) {
case KeyPress:
play(key, 1);
break;
case KeyRelease:
play(key, 0);
break;
case ButtonPress:
if(key == -5 || key == -7)
play(0xff, 1);
break;
case ButtonRelease:
if(key == -5 || key == -7)
play(0xff, 0);
break;
default:
break;
}
}
XRecordFreeData (d);
}
void open_console(void)
{
}
``` | /content/code_sandbox/scan-x11.c | c | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 521 |
```unknown
Name: OpenAL
Description: OpenAL is a cross-platform 3D audio API
Requires:
Version: 1.17.2
Libs:
Cflags:
``` | /content/code_sandbox/mac/lib/pkgconfig/openal.pc | unknown | 2016-02-03T12:20:04 | 2024-08-15T17:19:36 | bucklespring | zevv/bucklespring | 1,409 | 40 |
```unknown
#!/usr/bin/env lua
--require "format"
--[[
a file access mode
c process command name (all characters from proc or user structure)
C file structure share count
d file's device character code
D file's major/minor device number (0x<hexadecimal>)
f file descriptor (always selected)
F file structure address (0x<hexadecimal>)
G file flaGs (0x<hexadecimal>; names if +fg follows)
g process group ID
i file's inode number
K tasK ID
k link count
l file's lock status
L process login name
m marker between repeated output
n file name, comment, Internet address
N node identifier (ox<hexadecimal>
o file's offset (decimal)
p process ID (always selected)
P protocol name
r raw device number (0x<hexadecimal>)
R parent process ID
s file's size (decimal)
S file's stream identification
t file's type
T TCP/TPI information, identified by prefixes (the
`=' is part of the prefix):
QR=<read queue size>
QS=<send queue size>
SO=<socket options and values> (not all dialects)
SS=<socket states> (not all dialects)
ST=<connection state>
TF=<TCP flags and values> (not all dialects)
WR=<window read size> (not all dialects)
WW=<window write size> (not all dialects)
(TCP/TPI information isn't reported for all supported
UNIX dialects. The -h or -? help output for the
-T option will show what TCP/TPI reporting can be
requested.)
u process user ID
z Solaris 10 and higher zone name
Z SELinux security context (inhibited when SELinux is disabled)
0 use NUL field terminator character in place of NL
1-9 dialect-specific field identifiers (The output of -F? identifies the information to be found in dialect-specific fields.)
]]
local function printf(fmt, ...)
io.write(string.format(fmt, ...))
end
--
-- Parse lsof output into lua tables
--
local function parse_lsof()
local procs = {}
local cur, proc, file
for l in io.lines() do
if l:find("^COMMAND") then
io.stderr:write("Unexpected input, did you run lsof with the `-F` flag?\n")
os.exit(1)
end
local tag, val = l:sub(1, 1), l:sub(2)
if tag == 'p' then
if not procs[val] then
proc = { files = {} }
file = nil
cur = proc
procs[val] = proc
else
proc = nil
cur = nil
end
elseif tag == 'f' and proc then
file = { proc = proc }
cur = file
table.insert(proc.files, file)
end
if cur then
cur[tag] = val
end
-- skip kernel threads
if proc then
if file and file.f == "txt" and file.t == "unknown" then
procs[proc.p] = nil
proc = nil
file = nil
cur = nil
end
end
end
return procs
end
local function find_conns(procs)
local cs = {
fifo = {}, -- index by inode
unix = {}, -- index by inode
tcp = {}, -- index by sorted endpoints
udp = {}, -- index by sorted endpoints
pipe = {}, -- index by sorted endpoints
}
for pid, proc in pairs(procs) do
for _, file in ipairs(proc.files) do
if file.t == "unix" then
local us = cs.unix
local i = file.i or file.d
us[i] = us[i] or {}
table.insert(us[i], file)
end
if file.t == "FIFO" then
local fs = cs.fifo
fs[file.i] = fs[file.i] or {}
table.insert(fs[file.i], file)
end
if file.t == "PIPE" then -- BSD/MacOS
for n in file.n:gmatch("%->(.+)") do
local ps = { file.d, n }
table.sort(ps)
local id = table.concat(ps, "\\n")
local fs = cs.pipe
fs[id] = fs[id] or {}
table.insert(fs[id], file)
end
end
if file.t == "IPv4" or file.t == "IPv6" then
local a, b = file.n:match("(.-)%->(.+)")
local ps = { a, b }
table.sort(ps)
local id = table.concat(ps, "\\n")
local fs = (file.P == "TCP") and cs.tcp or cs.udp
fs[id] = fs[id] or {}
table.insert(fs[id], file)
end
end
end
return cs
end
local procs = parse_lsof()
local conns = find_conns(procs)
-- Generate graph
printf("digraph G {\n")
printf(" graph [ center=true, margin=0.2, nodesep=0.1, ranksep=0.3, rankdir=LR];\n")
printf(" node [ shape=box, style=\"rounded,filled\" width=0, height=0, fontname=Helvetica, fontsize=10];\n")
printf(" edge [ fontname=Helvetica, fontsize=10];\n")
-- Parent/child relationships
for pid, proc in pairs(procs) do
local color = (proc.R == "1") and "grey70" or "white"
printf(' p%d [ label = "%s\\n%d %s" fillcolor=%q ];\n', proc.p, proc.n or proc.c, proc.p, proc.L, color)
local proc_parent = procs[proc.R]
if proc_parent then
if proc_parent.p ~= "1" then
printf(' p%d -> p%d [ penwidth=2 weight=100 color=grey60 dir="none" ];\n', proc.R, proc.p)
end
end
end
-- Connections
local colors = {
fifo = "green",
unix = "purple",
tcp = "red",
udp = "orange",
pipe = "orange",
}
for type, conn in pairs(conns) do
for id, files in pairs(conn) do
-- one-on-one connections
if #files == 2 then
local f1, f2 = files[1], files[2]
local p1, p2 = f1.proc, f2.proc
if p1 ~= p2 then
local label = type .. ":\\n" .. id
local dir = "both"
if f1.a == "w" then
dir = "forward"
elseif f1.a == "r" then
dir = "backward"
end
printf(' p%d -> p%d [ color="%s" label="%s" dir="%s"];\n', p1.p, p2.p, colors[type] or "black", label, dir)
end
end
end
end
-- Done
printf("}\n")
-- vi: ft=lua ts=3 sw=3
``` | /content/code_sandbox/lsofgraph | unknown | 2016-02-08T13:04:38 | 2024-07-25T23:01:32 | lsofgraph | zevv/lsofgraph | 1,017 | 1,682 |
```tex
%% glossaries
%% Chapter 1
\newglossaryentry{perceptron}{
name={},
description={\emph{Perceptron}}
}
\newglossaryentry{sigmoid-neuron}{
name={S },
description={\emph{Sigmoid Neuron}}
}
\newglossaryentry{sigmoid-func}{
name={S },
description={\emph{Sigmoid Function}}
}
\newglossaryentry{sgd}{
name={},
description={\emph{Stochastic Gradient Descent}}
}
\newglossaryentry{weight}{
name={},
description={\emph{Weight}}
}
\newglossaryentry{bias}{
name={},
description={\emph{Bias}}
}
\newglossaryentry{threshold}{
name={},
description={\emph{Threshold}}
}
\newglossaryentry{epoch}{
name={},
description={\emph{Epoch}}
}
\newglossaryentry{mini-batch}{
name={},
description={\emph{Mini-batch}}
}
\newglossaryentry{hidden-layer}{
name={},
description={\emph{Hidden Layer}}
}
\newglossaryentry{mlp}{
name={},
description={\emph{Multilayer Perceptron}}
}
\newglossaryentry{rnn}{
name={},
description={\emph{Recurrent Neural Network(s)}}
}
\newglossaryentry{cost-func}{
name={},
description={\emph{Cost Function}}
}
\newglossaryentry{learning-rate}{
name={},
description={\emph{Learning Rate}}
}
\newglossaryentry{bp}{
name={},
description={\emph{Backpropagation}}
}
\newglossaryentry{svm}{
name={},
description={\emph{Support Vector Machine}}
}
\newglossaryentry{deep-neural-networks}{
name={},
description={\emph{Deep Neural Networks}}
}
\newglossaryentry{error}{
name={},
description={\emph{Error}}
}
\newglossaryentry{reln}{
name={},
description={\emph{Rectified Linear Neuron}}
}
\newglossaryentry{relu}{
name={},
description={\emph{Rectified Linear Unit}}
}
\newglossaryentry{softmax}{
name={},
description={\emph{Softmax}}
}
\newglossaryentry{softmax-func}{
name={},
description={\emph{Softmax Function}}
}
\newglossaryentry{log-likelihood}{
name={},
description={\emph{Log-likelihood}}
}
\newglossaryentry{regularization}{
name={},
description={\emph{Regularization}}
}
\newglossaryentry{weight-decay}{
name={},
description={\emph{Weight Decay}}
}
\newglossaryentry{regularization-term}{
name={},
description={\emph{Regularization Term}}
}
\newglossaryentry{lrf}{
name={},
description={\emph{Local Receptive Fields}}
}
\newglossaryentry{shared-weights}{
name={},
description={\emph{Shared Weights}}
}
\newglossaryentry{pooling}{
name={},
description={\emph{Pooling}}
}
\newglossaryentry{cnn}{
name={},
description={\emph{Convolutional Neural Networks}}
}
\newglossaryentry{idui}{
name={},
description={\emph{Intention-driven User Interface}}
}
\newglossaryentry{tanh}{
name={},
description={\emph{Tanh} tanch}
}
\newglossaryentry{tanh-func}{
name={},
description={\emph{Tanh Function}}
}
\newglossaryentry{tanh-neuron}{
name={},
description={\emph{Tanh Neuron}}
}
\newglossaryentry{hyperbolic-tangent}{
name={},
description={\emph{Hyperbolic Tangent}}
}
\newglossaryentry{hyper-params}{
name={},
description={\emph{Hyper-parameters}}
}
\newglossaryentry{lstm}{
name={},
description={\emph{Long Short-term Memory Units}}
}
\newglossaryentry{dbn}{
name={},
description={\emph{Deep Belief Network(s)}}
}
%% ------
\newglossaryentry{logistic-regression}{
name={Logistic },
description={\emph{Logistic Regression}}
}
\newglossaryentry{naive-bayes}{
name={},
description={\emph{naive Bayes}}
}
\newglossaryentry{representations}{
name={},
description={\emph{Representations}}
}
\newglossaryentry{rep-learning}{
name={},
description={\emph{Representation Learning}}
}
\newglossaryentry{autoencoder}{
name={},
description={\emph{Autoencoder (s)}}
}
\newglossaryentry{encoder}{
name={},
description={\emph{encoder}}
}
\newglossaryentry{decoder}{
name={},
description={\emph{decoder}}
}
\newglossaryentry{fov}{
name={},
description={\emph{factors of variation}}
}
%% Chapter 2
\newglossaryentry{scalar}{
name={},
description={scalar}
}
\newglossaryentry{scalars}{
name={},
description={Scalars}
}
\newglossaryentry{vec}{
name={},
description={vector}
}
\newglossaryentry{vecs}{
name={},
description={Vectors}
}
\newglossaryentry{matrix}{
name={},
description={matrix}
}
\newglossaryentry{matrices}{
name={},
description={Matrices}
}
\newglossaryentry{tensor}{
name={},
description={tensor}
}
\newglossaryentry{tensors}{
name={},
description={Tensors}
}
\newglossaryentry{transpose}{
name={},
description={transpose}
}
\newglossaryentry{main-diag}{
name={},
description={main diagonal}
}
\newglossaryentry{broadcasting}{
name={},
description={broadcasting}
}
\newglossaryentry{matrix-product}{
name={},
description={matrix product}
}
\newglossaryentry{element-product}{
name={},
description={element-wise product}
}
\newglossaryentry{hadamard-product}{
name={},
description={Hadamard product}
}
\newglossaryentry{dot-product}{
name={},
description={dot product}
}
\newglossaryentry{matrix-inversion}{
name={},
description={matrix inversion}
}
\newglossaryentry{identity-matrix}{
name={},
description={identity matrix}
}
\newglossaryentry{linear-comb}{
name={},
description={linear combination}
}
\newglossaryentry{span}{
name={},
description={span}
}
\newglossaryentry{column-space}{
name={},
description={column space}
}
\newglossaryentry{range}{
name={},
description={range}
}
\newglossaryentry{linear-dep}{
name={},
description={linear dependence}
}
\newglossaryentry{linearly-dep}{
name={},
description={linearly dependent}
}
\newglossaryentry{linearly-indep}{
name={},
description={linearly independent}
}
\newglossaryentry{linear-indep}{
name={},
description={linear independent}
}
\newglossaryentry{square}{
name={},
description={square}
}
\newglossaryentry{singular}{
name={},
description={singular}
}
\newglossaryentry{norm}{
name={},
description={norm}
}
\newglossaryentry{tri-inequal}{
name={},
description={triangle inequality}
}
\newglossaryentry{eu-norm}{
name={},
description={Euclidean norm}
}
\newglossaryentry{max-norm}{
name={},
description={max norm}
}
\newglossaryentry{fr-norm}{
name={},
description={Frobenius norm}
}
\newglossaryentry{diag}{
name={},
description={Diagonal}
}
\newglossaryentry{symmetric}{
name={},
description={symmetric}
}
\newglossaryentry{unit-vec}{
name={},
description={unit vector}
}
\newglossaryentry{unit-norm}{
name={},
description={unit norm}
}
\newglossaryentry{ortho}{
name={},
description={orthogonal}
}
\newglossaryentry{orthonormal}{
name={},
description={orthonormal}
}
\newglossaryentry{orthonormal-matrix}{
name={},
description={orthonormal matrix}
}
\newglossaryentry{eigen-decompos}{
name={},
description={eigendecomposition}
}
\newglossaryentry{eigen-vec}{
name={},
description={eigenvector}
}
\newglossaryentry{eigen-vecs}{
name={},
description={eigenvectors}
}
\newglossaryentry{eigen-val}{
name={},
description={eigenvalue}
}
\newglossaryentry{eigen-vals}{
name={},
description={eigenvalues}
}
\newglossaryentry{left-eigen-vec}{
name={},
description={left eigenvector}
}
\newglossaryentry{positive-definite}{
name={},
description={positive definite}
}
\newglossaryentry{positive-semidefinite}{
name={},
description={positive semidefinite}
}
\newglossaryentry{negative-definite}{
name={},
description={negative definite}
}
\newglossaryentry{negative-semidefinite}{
name={},
description={negative semidefinite}
}
\newglossaryentry{svd}{
name={},
description={singular value decomposition}
}
\newglossaryentry{singular-vecs}{
name={},
description={singular vectors}
}
\newglossaryentry{singular-vals}{
name={},
description={singular values}
}
\newglossaryentry{singular-val}{
name={},
description={singular value}
}
\newglossaryentry{left-singular-vecs}{
name={},
description={left-singular vectors}
}
\newglossaryentry{right-singular-vecs}{
name={},
description={right-singular vectors}
}
\newglossaryentry{moore-penrose-pseudoinverse}{
name={--},
description={Moore-Penrose pseudoinverse}
}
\newglossaryentry{pca}{
name={},
description={principal components analysis}
}
%% Chapter 4
\newglossaryentry{overflow}{
name={},
description={overflow}
}
\newglossaryentry{underflow}{
name={},
description={underflow}
}
\newglossaryentry{cond-num}{
name={},
description={condition number}
}
\newglossaryentry{obj-func}{
name={},
description={objective function}
}
\newglossaryentry{criterion}{
name={},
description={criterion, criterion funciton }
}
\newglossaryentry{loss-func}{
name={},
description={loss function}
}
\newglossaryentry{err-func}{
name={},
description={error function}
}
\newglossaryentry{gradient-descent}{
name={},
description={gradient descent}
}
\newglossaryentry{critical-points}{
name={},
description={critical points}
}
\newglossaryentry{stationary-points}{
name={},
description={stationary points}
}
\newglossaryentry{local-min}{
name={},
description={local minimum}
}
\newglossaryentry{local-max}{
name={},
description={local maximum}
}
\newglossaryentry{saddle-points}{
name={},
description={saddle points}
}
\newglossaryentry{global-min}{
name={},
description={global minimum}
}
\newglossaryentry{partial-derivatives}{
name={},
description={partial derivatives}
}
\newglossaryentry{gradient}{
name={},
description={gradient}
}
\newglossaryentry{directional-derivative}{
name={},
description={directional derivative}
}
\newglossaryentry{steepest-descent}{
name={},
description={method of steepest descent}
}
\newglossaryentry{line-search}{
name={},
description={line search}
}
\newglossaryentry{hill-climbing}{
name={},
description={hill climbing}
}
\newglossaryentry{jacobian-matrix}{
name={},
description={Jacobian matrix}
}
\newglossaryentry{second-derivative}{
name={},
description={second derivative}
}
\newglossaryentry{curvature}{
name={},
description={curvature}
}
\newglossaryentry{hessian-matrix}{
name={},
description={Hessian matrix}
}
\newglossaryentry{second-derivative-test}{
name={},
description={second derivative test}
}
%% Chapter 12
\newglossaryentry{warps}{
name={},
description={\emph{Warps}}
}
\newglossaryentry{overfitting}{
name={},
description={\emph{Overfitting}}
}
\newglossaryentry{overtraining}{
name={},
description={\emph{Overtraining}}
}
\newglossaryentry{generalization_error}{
name={},
description={\emph{Generalization error}}
}
\newglossaryentry{dropout}{
name={},
description={\emph{Dropout}, }
}
\newglossaryentry{bdt}{
name={},
description={\emph{Boosted decision trees}}
}
\newglossaryentry{gcn}{
name={},
description={\emph{Global contrast normalization}, }
}
\newglossaryentry{mode}{
name={},
description={\emph{mode}, }
}
``` | /content/code_sandbox/glossaries.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 3,279 |
```tex
% file: author.tex
\chapter{}
\label{ch:Author}
\begin{minipage}{0.7\linewidth}
\textbf{Michael Nielsen}
\href{path_to_url}{path_to_url}
\end{minipage}
\hfill
\begin{minipage}{0.25\linewidth}
\includegraphics[width=\textwidth]{mn.jpg}
\end{minipage}
``` | /content/code_sandbox/author.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```unknown
# Makefile
#
TEX = xelatex
MKIDX = makeindex
MKGLS = makeglossaries
RM = rm -rf
MAKE = make
TARGET = nndl-ebook.pdf
STYLES = $(wildcard *.sty)
SOURCES := $(wildcard *.tex)
IMAGEDEPS := $(wildcard images/*.tex)
IMAGEDEPS += $(wildcard images/*.png)
IMAGEDEPS += $(wildcard images/*.jpeg)
.PHONY: all graphics
all: graphics $(TARGET)
$(TARGET): $(SOURCES) $(STYLES) $(IMAGEDEPS)
$(TEX) $(basename $@)
# $(MKIDX) $(basename $@)
$(MKGLS) $(basename $@)
$(TEX) $(basename $@)
$(TEX) $(basename $@)
graphics:
$(MAKE) -C images
clean:
$(MAKE) -C images clean
$(RM) *.pdf
$(RM) *.aux
$(RM) *.log
$(RM) *.out
$(RM) *.toc
$(RM) *.idx
$(RM) *.ilg
$(RM) *.ind
``` | /content/code_sandbox/Makefile | unknown | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 253 |
```tex
% file: sai.tex
\chapter{\emph{}\,}
~~
~~
~~
~~
16
17
16
~~
~~
~~10001000 100
98\%
~~ 95\% 99\%
2007 (
) DNA 1.25 DNA
30 96\% ~~1.25 /30
0.04166666666
1.25 4 ~~
A adenine, C cytosine, G guanine, T thymine
2 4 1.25 2.5
2.5
1.25
1.25
~~ 26 ~~
1.25 2500
King James 30
1000 1000 100
~~10
~~ 70 X 1015
~~
1.25
1.25
1.25
1.25
9
2000 4
Mriganka Sur
orientation columns
orientation map
~~
1960
i.e.
Marvin Minsky
1970 1980 Minsky
agent society
Minsky
Minsky
Minsky
Minsky
~~~~
Python C Lisp
~~~~
1980 Jack Schwartz
Schwartz
Schwartz
ref
``` | /content/code_sandbox/sai.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 307 |
```tex
% file: translators.tex
\chapter{}
\label{ch:TranslationTeam}
\section*{}
\href{path_to_url}{Neural Networks and
Deep Learning} \LaTeX
\LaTeX
\href{path_to_url}{GitHub}
\href{path_to_url}{Xiaohu
Zhu }
\href{path_to_url}{}
\href{path_to_url}{}
\href{path_to_url}{issue}
\href{path_to_url}{GitHub}
\begin{flushright}
~Freeman Zhang
\end{flushright}
\section*{}
\label{sec:TranslationTeam}
\begin{itemize}
\item \textbf{\href{mailto:xhzhu.nju@gmail}{Xiaohu Zhu}}
\item \textbf{\href{mailto:zhanggyb@gmail.com}{Freeman Zhang}}
\item \\
\begin{tabular}{l l l l l l l}
\bfseries\href{path_to_url}{haria}
& \bfseries\href{path_to_url}{yaoqingyuan}
& \bfseries\href{path_to_url}{lzjqsdd}
& \bfseries\href{path_to_url}{allenwoods}
& \bfseries\href{path_to_url}{yangbenfa}
& \bfseries\href{path_to_url}{timqian}
& \bfseries\href{path_to_url}{jiefangxuanyan} \\
\end{tabular}
\end{itemize}
\section*{}
\label{sec:KnownIssues}
GitHub \href{path_to_url}{Issues}
``` | /content/code_sandbox/translation.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 362 |
```tex
% file: chap1.tex
\chapter{}
\label{ch:UsingNeuralNetsToRecognizeHandwrittenDigits}
\begin{center}
\includegraphics[width=64pt]{digits}\label{fig:digits}
\end{center}
504192
{\serif V1}14
{\serif V1}~~
{\serif V2}{\serif V3}{\serif V4} {\serif V5}~~
~~ 9
~~
\begin{center}
\includegraphics[width=.6\textwidth]{mnist_100_digits}
\end{center}
100
74
96\%
99\%
~~~~
\gls*{perceptron} \gls*{sigmoid-neuron}%
\gls*{sgd}
\section{}
\label{sec:Perceptrons}
\textbf{\gls{perceptron}}%
\gls*{perceptron}20
\href{path_to_url}{Frank Rosenblatt}
\href{path_to_url}{%
} \href{path_to_url}{Warren
McCulloch} \href{path_to_url}{Walter Pitts}
\href{path_to_url}{}
~~
\textbf{\gls{sigmoid-neuron}}
\gls*{sigmoid-neuron} \gls*{sigmoid-neuron}
\gls*{perceptron}
\gls*{perceptron}\gls*{perceptron}
$x_1,x_2,\ldots$
\begin{center}
\includegraphics{tikz0}
\end{center}
\gls*{perceptron}$x_1,x_2,x_3$
Rosenblatt \textbf{\gls{weight}}
$w_1,w_2,\ldots$$0$ $1$
\gls*{weight} $\sum_j w_j x_j$ %
\textbf{\gls{threshold}}\gls*{weight}\gls*{threshold}
\begin{equation}
\text{output} = \begin{cases}
0 & \quad \text{if } \sum_j w_j x_j \leq \text{ threshold} \\
1 & \quad \text{if } \sum_j w_j x_j > \text{ threshold} \\
\end{cases}
\tag{1}
\end{equation}
\gls*{perceptron}
\gls*{perceptron}\gls*{weight}
\gls*{weight}
\begin{enumerate}
\item
\item
\item
\end{enumerate}
$x_1,x_2$ $x_3$
$x_1 = 1$$x_1 = 0$$x_2
= 1$ $x_2 = 0$$x_3$
\gls*{perceptron}\gls*{weight}
$w_1 = 6$ $w_2 = 2$ $w_3 = 2$$w_1$
%
\gls*{perceptron}\gls*{threshold} $5$\gls*{perceptron}
$1$ $0$
\gls*{weight}\gls*{threshold}
\gls*{threshold} $3$ \gls*{perceptron}
\gls*{threshold}
\gls*{perceptron}%
\gls*{perceptron}%
\gls*{perceptron}
\begin{center}
\includegraphics{tikz1}
\end{center}
\gls*{perceptron}~~\gls*{perceptron}~~
\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}\gls*{perceptron}%
\gls*{perceptron}
\gls*{perceptron} $\sum_j w_j x_j$
$\sum_j w_j x_j$ $w
\cdot x \equiv \sum_j w_j x_j$ $w$ $x$ \gls*{weight}
\gls*{threshold}\gls*{perceptron}%
\textbf{\gls{bias}} $b \equiv -threshold$ \gls*{bias}%
\gls*{threshold}\gls*{perceptron}
\begin{equation}
\text{output} = \begin{cases}
0 & \quad \text{if } w\cdot x + b \leq 0 \\
1 & \quad \text{if } w\cdot x + b > 0
\end{cases}
\tag{2}
\end{equation}
\gls*{bias}\gls*{perceptron} $1$
\gls*{perceptron}\gls*{bias}%
\gls*{perceptron} $1$
$1$ \gls*{bias}\gls*{perceptron}
\gls*{threshold}\gls*{bias}
\gls*{perceptron}\gls*{perceptron}
\textbf{}\textbf{}\textbf{}
\gls*{weight} $-2$\gls*{bias} $3$
\gls*{perceptron}
\begin{center}
\includegraphics{tikz2}
\end{center}
$00$ $1$ $(-2)*0 + (-2)*0 + 3 = 3$
$*$ $11$ $0$ $(-2)*1 + (-2)*1 +
3 = -1$ \gls*{perceptron}
\gls*{perceptron}
$x_1$ $x_2$$x_1 \oplus x_2$ $x_1$ $x_2$
$1$ $1$ $x_1x_2$
\begin{center}
\includegraphics{tikz3}
\end{center}
\gls*{perceptron}\gls*{perceptron}
\gls*{weight} $-2$\gls*{bias} $3$
\begin{center}
\includegraphics{tikz4}
\end{center}
\gls*{perceptron}\gls*{perceptron}
\gls*{perceptron}\gls*{perceptron}
\gls*{weight} $-4$ \gls*{weight}
$-2$
\gls*{weight} $-2$\gls*{bias}
$3$\gls*{weight} $-4$
\begin{center}
\includegraphics{tikz5}
\end{center}
$x_1$ $x_2$ \gls*{perceptron}
\gls*{perceptron}~~~~
\begin{center}
\includegraphics{tikz6}
\end{center}
\gls*{perceptron}
\begin{center}
\includegraphics{tikz7}
\end{center}
\gls*{perceptron}
\gls*{perceptron} $\sum_j w_j x_j$
\gls*{perceptron} $b > 0$ $1$ $b \leq 0$ $0$%
\gls*{perceptron} $x_1$
\gls*{perceptron}\gls*{perceptron}
$x_1, x_2,\ldots$
\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}
\gls*{perceptron}
\textbf{}
\gls*{weight}\gls*{bias}
\textbf{}
\section{S }
\label{seq:sigmoid_neurons}
%
\gls*{perceptron}
\gls*{weight}\gls*{bias}
\gls*{weight}%
\gls*{bias}
\begin{center}
\includegraphics{tikz8}
\end{center}
\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}
98
\gls*{weight}\gls*{bias}
9\gls*{weight}\gls*{bias}
\gls*{perceptron}
\gls*{perceptron}\gls*{weight}\gls*{bias}
\gls*{perceptron} $0$ $1$
9
%
\gls*{weight}\gls*{bias}
\gls*{perceptron}
\gls*{sigmoid-neuron}%
\gls*{sigmoid-neuron}\gls*{perceptron}\gls*{weight}%
\gls*{bias}
, \gls*{sigmoid-neuron}\gls*{perceptron}
\gls*{sigmoid-neuron}
\begin{center}
\includegraphics{tikz9}
\end{center}
\gls*{perceptron}\gls*{sigmoid-neuron}$x_1,x_2,\ldots$
$0$ $1$ $0$ $1$
$0.638\ldots$ \gls*{sigmoid-neuron}
\gls*{sigmoid-neuron}\gls*{weight}$w_1,w_2,\ldots$%
\gls*{bias}$b$ $0$ $1$ $\sigma(w \cdot x+b)$
$\sigma$ S\footnote{$\sigma$ \textbf{
}\textbf{}
S }
\begin{equation}
\sigma(z) \equiv \frac{1}{1+e^{-z}}
\label{eq:3}\tag{3}
\end{equation}
$x_1,x_2,\ldots$\gls*{weight}
$w_1,w_2,\ldots$\gls*{bias} $b$ \gls*{sigmoid-neuron}
\begin{equation}
\frac{1}{1+\exp(-\sum_j w_j x_j-b)}
\label{eq:4}\tag{4}
\end{equation}
\gls*{sigmoid-neuron}\gls*{perceptron} S
\gls*{perceptron}
\gls*{sigmoid-neuron}\gls*{sigmoid-func}
\gls*{perceptron} $z \equiv w \cdot x + b$
$e^{-z} \approx 0$ $\sigma(z) \approx 1$ $z = w \cdot
x+b$ \gls*{sigmoid-neuron} $1$%
\gls*{perceptron} $z = w \cdot x+b$
$e^{-z} \rightarrow \infty$$\sigma(z) \approx 0$ $z = w \cdot x +b$
\gls*{sigmoid-neuron}\gls*{perceptron}
$w \cdot x+b$ \gls*{perceptron}
$\sigma$ $\sigma$
~~
\begin{center}
\includegraphics{sigmoid_function}
\label{fig:SigmoidFunction}
\end{center}
\begin{center}
\includegraphics{step_function}
\label{fig:StepFunction}
\end{center}
$\sigma$ $w\cdot x+b$
\footnote{ $w \cdot x +b = 0$ \gls*{perceptron} $0$
$1$
}S\gls*{perceptron} $\sigma$
\gls*{perceptron}$\sigma$
$\sigma$ \gls*{weight}%
\gls*{bias} $\Delta w_j$ $\Delta b$
$\Delta \mbox{output}$ $\Delta \mbox{output}$
\begin{equation}
\Delta \mbox{output} \approx \sum_j \frac{\partial \, \mbox{output}}{\partial w_j}
\Delta w_j + \frac{\partial \, \mbox{output}}{\partial b} \Delta b
\label{eq:5}\tag{5}
\end{equation}
\gls*{weight} $w_j$ $\partial \, \mbox{output} /
\partial w_j$ $\partial \, \mbox{output} /\partial b$ $output$
$w_j$ $b$
$\Delta
\mbox{output}$ \gls*{weight}\gls*{bias}~~ $\Delta w_j$
$\Delta b$~~\gls*{weight}
\gls*{bias}%
\gls*{sigmoid-neuron}\gls*{perceptron}%
\gls*{weight}\gls*{bias}
$\sigma$ ~\eqref{eq:3}
$\sigma$
$f(\cdot)$ $f(w \cdot x + b)$
~\eqref{eq:5}
$\sigma$
$\sigma$
\gls*{sigmoid-neuron}\gls*{perceptron}
\gls*{sigmoid-neuron} \gls*{sigmoid-neuron} $0$
$1$ $0$ $1$ $0.173\ldots$
$0.689\ldots$
99 $0$ $1$
\gls*{perceptron}
$0.5$ 9 $0.5$
9
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{sigmoid-neuron}\gls*{perceptron}}\\
\gls*{perceptron}\gls*{bias}$c>0$
\item \textbf{\gls*{sigmoid-neuron}\gls*{perceptron}}\\
~~\gls*{perceptron}
%
\gls*{perceptron} $x$ \gls*{weight}\gls*{bias} $w \cdot x + b
\neq 0$ \gls*{sigmoid-neuron}\gls*{perceptron}%
\gls*{weight}\gls*{bias} $c>0$ $c \rightarrow \infty$
\gls*{sigmoid-neuron}\gls*{perceptron}
\gls*{perceptron} $w \cdot x + b = 0$
\end{itemize}
\section{}
\begin{center}
\includegraphics{tikz10}
\end{center}
\textbf{}
\textbf{}\textbf{}
%
\textbf{\gls{hidden-layer}}~~
~~
\begin{center}
\includegraphics{tikz11}
\end{center}
\gls*{sigmoid-neuron}%
\gls*{perceptron}\textbf{\gls{mlp}}\textbf{MLP}
MLP
9
$64 \times 64$ $4096 = 64 \times
64$ $0$ $1$
$0.5$ $9$ $0.5$
$9$
%
\textbf{}~~
$\sigma$
%
\href{path_to_url}{\gls{rnn}}
\gls*{rnn}
\section{}
\begin{center}
\includegraphics[width=64pt]{digits}
\end{center}
\begin{center}
\includegraphics[height=32pt]{digits_separate}
\end{center}
\begin{center}
\includegraphics[height=24pt]{mnist_first_digit}
\end{center}
$5$
\begin{center}
\includegraphics{tikz12}
\end{center}
$28 \times 28$
$784 = 28 \times 28$ $784$
$0.0$ $1.0$
$n$ $n$
$n=15$
$10$ $\approx 1$
$0$ $1$
$0$ $9$
$6$
$6$
$10$
$0, 1, 2, \ldots, 9$
$4$ $0$
$1$~ $2^4 = 16$ $10$
$10$
$10$
4 $10$
10 $4$
$10$
0
\begin{center}
\includegraphics[height=32pt]{mnist_top_left_feature}
\end{center}
\gls*{weight}
\gls*{weight}
\begin{center}
\includegraphics[height=32pt]{mnist_other_features}
\end{center}
\hyperref[fig:digits]{}
$0$
\begin{center}
\includegraphics[height=32pt]{mnist_complete_zero}
\end{center}
$0$
$0$ ~~ $0$
$0$
$10$
$4$ $4$
\gls*{weight}4
\subsection*{}
\begin{itemize}
\item
%
\gls*{weight}\gls*{bias}3
$0.99$ $0.01$
\begin{center}
\includegraphics{tikz13}
\end{center}
\end{itemize}
\section{}
\label{sec:learning_with_gradient_descent}
~~
\href{path_to_url}{MNIST }
MNIST
\href{path_to_url}{NIST}
~~ MNIST
\begin{center}
\includegraphics[height=32pt]{digits_separate}
\end{center}
\hyperref[fig:digits]{}
MNIST 60,000
250
$28 \times 28$ 10,000
$28 \times 28$
\textbf{}
250
$x$ $x$ $28
\times 28 = 784$ $y
= y(x)$ $y$ $10$
$6$ $x$ $y(x) = (0, 0, 0, 0, 0, 0, 1, 0, 0, 0)^T$
$T$
\gls*{weight}\gls*{bias}
$y(x)$ $x$%
\textbf{\gls{cost-func}}\footnote{\textbf{}\textbf{}
}
\begin{equation}
C(w,b) \equiv \frac{1}{2n} \sum_x \| y(x) - a\|^2
\label{eq:6}\tag{6}
\end{equation}
$w$ \gls*{weight}$b$ \gls*{bias}$n$
$a$ $x$
$x$ $a$ $x$, $w$ $b$
$\|v\|$ $v$ $C$ %
\textbf{}\gls*{cost-func}\textbf{
}\textbf{MSE}
$C(w,b)$
$C(w,b)$ $C(w,b) \approx 0$ $x$
$y(x)$ $a$ \gls*{weight}%
\gls*{bias} $C(w,b) \approx 0$ $C(w,b)$
$y(x)$ $a$
\gls*{weight}\gls*{bias} $C(w,b)$
\gls*{weight}\gls*{bias}%
\textbf{}
\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}
\gls*{weight}%
\gls*{bias}
\gls*{weight}\gls*{bias}
~\eqref{eq:6} \textbf{}
\gls*{weight}\gls*{bias}
~\eqref{eq:6}
$C(w,b)$ %
\gls*{weight}\gls*{bias}
~~\gls*{weight} $w$ \gls*{bias} $b$ $\sigma$
MNIST
\textbf{
}
$C(v)$$v = v_1,
v_2, \ldots$ $v$ $w$ $b$ ~~
$C(v)$ $C$
$v1$ $v2$
\begin{center}
\includegraphics{valley}
\end{center}
$C$
\textbf{} $C$
$C$
$C$
\textbf{}%
\gls*{weight}\gls*{bias}
$C$
$C$
$C$
~~ $C$
$v1$ $v2$
$\Delta v1$ $\Delta v2$
$C$
\begin{equation}
\Delta C \approx \frac{\partial C}{\partial v_1} \Delta v_1 +
\frac{\partial C}{\partial v_2} \Delta v_2
\label{eq:7}\tag{7}
\end{equation}
$\Delta v_1$ $\Delta v_2$ $\Delta C$
$\Delta v$ $v$
$\Delta v \equiv (\Delta v_1, \Delta v_2)^T$$T$
$C$ $\left(\frac{\partial C}{\partial v_1},
\frac{\partial C}{\partial v_2}\right)^T$ $\nabla C$
\begin{equation}
\nabla C \equiv \left( \frac{\partial C}{\partial v_1}, \frac{\partial
C}{\partial v_2} \right)^T
\label{eq:8}\tag{8}
\end{equation}
$\Delta v$ $\nabla C$ $\Delta C$
$\nabla C$
$\nabla$ $\nabla$ $\nabla
C$ ~~~~
$\nabla$ $\nabla C$
$\nabla$
$\Delta C$ ~\eqref{eq:7}
\begin{equation}
\Delta C \approx \nabla C \cdot \Delta v
\label{eq:9}\tag{9}
\end{equation}
$\nabla C$ $\nabla C$ $v$
$C$
$\Delta v$ $\Delta C$
\begin{equation}
\Delta v = -\eta \nabla C
\label{eq:10}\tag{10}
\end{equation}
$\eta$ \textbf{\gls{learning-rate}}
~\eqref{eq:9} $\Delta C \approx -\eta \nabla C \cdot \nabla C = -\eta
\|\nabla C\|^2$ $\| \nabla C \|^2 \geq 0$$\Delta C \leq 0$
~\eqref{eq:10} $v$ $C$
~\eqref{eq:9}
~\eqref{eq:10}
~\eqref{eq:10} $\Delta v$ $v$
\begin{equation}
v \rightarrow v' = v -\eta \nabla C
\label{eq:11}\tag{11}
\end{equation}
$C$ ~~~~
$\nabla C$\textbf{
}
\begin{center}
\includegraphics{valley_with_ball}
\end{center}
$\Delta v$
\gls*{learning-rate} $\eta$
~\eqref{eq:9} $\Delta C > 0$
$\eta$ $\Delta v$
$\eta$
~\eqref{eq:9}
$C$ $C$
$C$ $m$ $v_1,\ldots,v_m$
$C$ $\Delta v = (\Delta v_1, \ldots, \Delta
v_m)^T$$\Delta C$
\begin{equation}
\Delta C \approx \nabla C \cdot \Delta v
\label{eq:12}\tag{12}
\end{equation}
$\nabla C$
\begin{equation}
\nabla C \equiv \left(\frac{\partial C}{\partial v_1}, \ldots,
\frac{\partial C}{\partial v_m}\right)^T
\label{eq:13}\tag{13}
\end{equation}
\begin{equation}
\Delta v = -\eta \nabla C
\label{eq:14}\tag{14}
\end{equation}
$\Delta C$ ~\eqref{eq:12}
$C$
\begin{equation}
v \rightarrow v' = v-\eta \nabla C
\label{eq:15}\tag{15}
\end{equation}
\textbf{}
$v$ $C$ ~~
$C$
$\Delta v$ $C$ $\Delta C \approx \nabla C
\cdot \Delta v$ $\| \Delta v \| = \epsilon$
$\epsilon > 0$ $C$
$\nabla C \cdot \Delta v$ $\Delta v$ $\Delta v = - \eta
\nabla C$ $\eta = \epsilon / \|\nabla C\|$ $\|\Delta v\| =
\epsilon$ $C$
\subsection*{}
\begin{itemize}
\item %
\href{path_to_urlSchwarz_inequality}{-
}
\item $C$ $C$
\end{itemize}
$C$
$\partial^2 C/ \partial v_j \partial v_k$
$v_j$\footnote{
$\partial^2 C/ \partial v_j \partial v_k = \partial^2
C/ \partial v_k \partial v_j$}
~\eqref{eq:6} \gls*{weight} $w_k$ \gls*{bias} $b_l$
\gls*{weight}\gls*{bias} $v_j$
$w_k$ $b_l$ $\nabla C$
$\partial C / \partial w_k$$\partial C / \partial b_l$
\begin{align}
\label{eq:16}w_k \rightarrow w_k' &= w_k-\eta \frac{\partial C}{\partial w_k}\tag{16}\\
\label{eq:17}b_l \rightarrow b_l' &= b_l-\eta \frac{\partial C}{\partial b_l}\tag{17}
\end{align}
\eqref{eq:6}
$C = \frac{1}{n} \sum_x C_x$ $C_x \equiv
\frac{\|y(x)-a\|^2}{2}$ $\nabla C$
$x$ $\nabla C_x$$\nabla C =
\frac{1}{n} \sum_x \nabla C_x$
\textbf{\gls{sgd}}
$\nabla C_x$ $\nabla C$
$\nabla C$
$m$
$X_1, X_2, \ldots, X_m$%
\textbf{\gls{mini-batch}} $m$ $\nabla C_{X_j}$
$\nabla C_x$
\begin{equation}
\frac{\sum_{j=1}^m \nabla C_{X_{j}}}{m} \approx \frac{\sum_x \nabla C_x}{n} = \nabla C
\label{eq:18}\tag{18}
\end{equation}
\begin{equation}
\nabla C \approx \frac{1}{m} \sum_{j=1}^m \nabla C_{X_{j}}
\label{eq:19}\tag{19}
\end{equation}
\gls*{mini-batch}
$w_k$ $b_l$
\gls*{bias}\gls*{mini-batch}
\begin{align}
\label{eq:20}w_k \rightarrow w_k' &= w_k-\frac{\eta}{m}
\sum_j \frac{\partial C_{X_j}}{\partial w_k}
\tag{20}\\
\label{eq:21}b_l \rightarrow b_l' &= b_l-\frac{\eta}{m}
\sum_j \frac{\partial C_{X_j}}{\partial b_l}
\tag{21}
\end{align}
\gls*{mini-batch} $X_j$
\gls*{mini-batch}
\textbf{\gls{epoch}}
\gls*{epoch}
\gls*{weight}\gls*{bias}
\gls*{mini-batch}~\eqref{eq:6}
$\frac{1}{n}$ \gls*{cost-func}
$\frac{1}{n}$
\gls*{mini-batch}~\eqref{eq:20}~\eqref{eq:21}
$\frac{1}{m}$%
\gls*{learning-rate} $\eta$
\gls*{mini-batch}
$n = 60,000$ MNIST
\gls*{mini-batch} $m = 10$ $6,000$
~~~~
$C$
\subsection*{}
\begin{itemize}
\item \gls*{mini-batch} $1$
$x$ $w_k \rightarrow w_k' = w_k - \eta \partial C_x /
\partial w_k$ $b_l \rightarrow b_l' = b_l - \eta \partial C_x / \partial
b_l$ \gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}\textbf{}%
\textbf{online}\textbf{on-line}\textbf{} online
$20$
\end{itemize}
$C$ \gls*{weight}\gls*{bias}
$\Delta C$
$C$
%
\href{path_to_url}{
}
\section{}
\label{sec:implementing_our_network_to_classify_digits}
MNIST
MNIST \lstinline!git!
\begin{lstlisting}[language=sh]
git clone path_to_url
\end{lstlisting}
\lstinline!git!%
\href{path_to_url}{
}
MNIST 60,000 10,000
MNIST
60,000 MNIST
50,000 10,000 %
\textbf{}
\textbf{\gls{hyper-params}}~~%
\gls*{learning-rate}
MNIST MNIST
MNIST 50,000
60,000\footnote{MNISTNIST
MNISTNIST
Yann LeCunCorinna CortesChristopher J. C. Burges
Python
MNISTLISA
\href{path_to_url}{}}
MNIST \href{path_to_url}{Numpy} Python
Numpy%
\href{path_to_url}{}
\lstinline!Network!
\lstinline!Network!
\begin{lstlisting}[language=Python]
class Network(object):
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
\end{lstlisting}
\lstinline!sizes!
2 3 1
\lstinline!Network!
\begin{lstlisting}[language=Python]
net = Network([2, 3, 1])
\end{lstlisting}
\lstinline!Network! \gls*{bias}\gls*{weight}
Numpy \lstinline!np.random.randn! 0 1
\gls*{weight}\gls*{bias}
\lstinline!Network!
\gls*{bias}\gls*{bias}
\gls*{bias}\gls*{weight} Numpy
\lstinline!net.weights[1]! \gls*{weight}
Numpy Python 0
\lstinline!net.weights[1]! $w$ $w_{jk}$
$k^{\rm th}$ $j^{\rm th}$ \gls*{weight}
$j$ $k$ ~~ $j$ $k$
\begin{equation}
a' = \sigma(w a + b)
\label{eq:22}\tag{22}
\end{equation}
$a$
$a'$\gls*{weight} $w$ $a$\gls*{bias} $b$
$w a +b$ $\sigma$ $\sigma$
\textbf{}~\eqref{eq:22} S
~\eqref{eq:4}
\subsection*{}
\begin{itemize}
\item ~\eqref{eq:22}\gls*{sigmoid-neuron}
~\eqref{eq:4}
\end{itemize}
\lstinline!Network! S
\begin{lstlisting}[language=Python]
def sigmoid(z):
return 1.0/(1.0+np.exp(-z))
\end{lstlisting}
$z$ Numpy Numpy
\lstinline!sigmoid!
\lstinline!Network! \lstinline!feedforward!
$a$\footnote{ $a$
\lstinline!(n,1)! Numpy ndarray \lstinline!(n,)!
\lstinline!n! \lstinline!(n,)!
\lstinline!(n,)!
\lstinline!(n,1)! ndarray
}
~\eqref{eq:22}
\begin{lstlisting}[language=Python]
def feedforward(self, a):
"""Return the output of the network if "a" is input."""
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a)+b)
return a
\end{lstlisting}
\lstinline!Network!
\lstinline!SGD!
\begin{lstlisting}[language=Python]
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
"""Train the neural network using mini-batch stochastic
gradient descent. The "training_data" is a list of tuples
"(x, y)" representing the training inputs and the desired
outputs. The other non-optional parameters are
self-explanatory. If "test_data" is provided then the
network will be evaluated against the test data after each
epoch, and partial progress printed out. This is useful for
tracking progress, but slows things down substantially."""
if test_data: n_test = len(test_data)
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k+mini_batch_size]
for k in xrange(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print "Epoch {0}: {1} / {2}".format(
j, self.evaluate(test_data), n_test)
else:
print "Epoch {0} complete".format(j)
\end{lstlisting}
\lstinline!training_data! \lstinline!(x, y)!
\lstinline!epochs! \lstinline!mini_batch_size!
~~\gls*{epoch}\gls*{mini-batch}{}\lstinline!eta! %
\gls*{learning-rate}$\eta$ \lstinline!test_data!
\gls*{epoch}
\gls*{mini-batch}{}
\lstinline!mini_batch!
\lstinline!self.update_mini_batch(mini_batch, eta)!
\lstinline!mini_batch! %
\gls*{weight}\gls*{bias} \lstinline!update_mini_batch!
\begin{lstlisting}[language=Python]
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The "mini_batch" is a list of tuples "(x, y)", and "eta"
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
\end{lstlisting}
\begin{lstlisting}[language=Python]
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
\end{lstlisting}
\textbf{\gls{bp}}
\lstinline!update_mini_batch! \lstinline!mini_batch!
\lstinline!self.weights!
\lstinline!self.biases!
\lstinline!self.backprop!
\lstinline!self.backprop!
$x$
\lstinline!self.backprop!
~~ \lstinline!self.SGD!
\lstinline!self.update_mini_batch!
\lstinline!self.backprop!
\lstinline!sigmoid_prime! $\sigma$
\lstinline!self.cost_derivative!
74
GitHub %
\href{path_to_url}{
}
\lstinputlisting[language=Python]{code_samples/src/network.py}
MNIST
\lstinline!mnist_loader.py! Python shell
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
\end{lstlisting}
Python
Python shell
MNIST 30
\lstinline!Network! \lstinline!network! Python
\begin{lstlisting}[language=Python]
>>> import network
>>> net = network.Network([784, 30, 10])
\end{lstlisting}
MNIST \lstinline!training_data! 30 %
\gls*{epoch}\gls*{mini-batch} 10\gls*{learning-rate} $\eta = 3.0$
\begin{lstlisting}[language=Python]
>>> net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
\end{lstlisting}
~~
2015
\gls*{epoch}
Python
\gls*{weight}\gls*{bias}
Javascript
\gls*{epoch} 10,000
9,129
\begin{lstlisting}[language=sh]
Epoch 0: 9129 / 10000
Epoch 1: 9295 / 10000
Epoch 2: 9348 / 10000
...
Epoch 27: 9528 / 10000
Epoch 28: 9542 / 10000
Epoch 29: 9534 / 10000
\end{lstlisting}
95\%~~ 95.42\%Epoch
28
\gls*{weight}
\gls*{bias}
100
\begin{lstlisting}[language=Python]
>>> net = network.Network([784, 100, 10])
>>> net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
\end{lstlisting}
96.59\%
\footnote{
}
\gls*{epoch}\gls*{mini-batch}
\gls*{learning-rate} $\eta$
\gls*{hyper-params}
\gls*{weight}\gls*{bias}\gls*{hyper-params}
\gls*{learning-rate} $\eta = 0.001$,
\begin{lstlisting}[language=Python]
>>> net = network.Network([784, 100, 10])
>>> net.SGD(training_data, 30, 10, 0.001, test_data=test_data)
\end{lstlisting}
\begin{lstlisting}[language=sh]
Epoch 0: 1139 / 10000
Epoch 1: 1136 / 10000
Epoch 2: 1135 / 10000
...
Epoch 27: 2101 / 10000
Epoch 28: 2123 / 10000
Epoch 29: 2142 / 10000
\end{lstlisting}
\gls*{learning-rate} $\eta = 0.01$
\gls*{learning-rate}
$\eta = 1.0$ %
\gls*{learning-rate}$3.0$
\gls*{hyper-params}\gls*{hyper-params}
\gls*{hyper-params}
30
$\eta = 100.0$
\begin{lstlisting}[language=Python]
>>> net = network.Network([784, 30, 10])
>>> net.SGD(training_data, 30, 10, 100.0, test_data=test_data)
\end{lstlisting}
\gls*{learning-rate}
\begin{lstlisting}[language=sh]
Epoch 0: 1009 / 10000
Epoch 1: 1009 / 10000
Epoch 2: 1009 / 10000
Epoch 3: 1009 / 10000
...
Epoch 27: 982 / 10000
Epoch 28: 982 / 10000
Epoch 29: 982 / 10000
\end{lstlisting}
\gls*{learning-rate}
\gls*{learning-rate}
%
\gls*{weight}\gls*{bias}
\gls*{epoch}
\gls*{learning-rate}\gls*{learning-rate}
\gls*{hyper-params}\gls*{hyper-params}
\subsection*{}
\begin{itemize}
\item ~~ 784 10
\end{itemize}
MNIST
MNIST ~~ Numpy
\lstinline!ndarry! \lstinline!ndarray!
\lstinputlisting[language=Python]{code_samples/src/mnist_loader.py}
10\%
$2$ $1$
\begin{center}
\includegraphics[height=32pt]{mnist_2_and_1}
\end{center}
$0, 1, 2,\ldots, 9$
~~
\href{path_to_url}{GitHub
} $10,000$
$2,225$ $22.25\%$
$20\%$ $50\%$
$50\%$
\textbf{\gls{svm}}\textbf{SVM} SVM
SVM
\href{path_to_url}{scikit-learn} Python
Python SVM
\href{path_to_url~cjlin/libsvm/}{LIBSVM} C
scikit-learn SVM $10,000$
$9,435$%
\href{path_to_url}{
}
SVM
SVM
$10,000$ $9,435$ scikit-learn SVM
SVM
\href{path_to_url}{Andreas Mueller} %
\href{path_to_url}{}
Mueller SVM 98.5\%
SVM70
MNIST
SVM2013 $10,000$ $9,979$
\href{path_to_url~wanli/}{Li Wan}
\href{path_to_url}{Matthew Zeiler}Sixin Zhang
\href{path_to_url}{Yann LeCun}
\href{path_to_url~fergus/pmwiki/pmwiki.php}{Rob Fergus}
MNIST
\begin{center}
\includegraphics[height=64pt]{mnist_really_bad_images}
\end{center}
MNIST
$10,000$ $21$
MNIST
Wan
\begin{center}
$\leq$ +
\end{center}
\section{}
\label{sec:toward_deep_learning}
\gls*{bias}
AI
\gls*{weight}%
\gls*{bias}
\footnote{
\href{path_to_url}{1}. \href{path_to_url}{Ester
Inbar}. \href{path_to_url}{2}. . \href{path_to_url}{3}. NASA,
ESA, G. Illingworth, D. Magee, and P. Oesch (University of California, Santa
Cruz), R. Bouwens (Leiden University), and the HUDF09 Team.
}
\begin{center}
\includegraphics[height=125pt]{images/Kangaroo_ST_03}
\includegraphics[height=125pt]{images/Albert_Einstein_at_the_age_of_three_(1882)}
\includegraphics[height=125pt]{images/The_Hubble_eXtreme_Deep_Field}
\end{center}
~~
\gls*{weight}\gls*{bias}
\begin{center}
\includegraphics{tikz14}
\end{center}
~~
~~
\begin{center}
\includegraphics{tikz15}
\end{center}
~~
~~
~~~~%
\textbf{\gls{deep-neural-networks}}
\gls*{weight}%
\gls*{bias}
\gls*{weight}\gls*{bias}~~80
90
2006
~~ 5 10
``` | /content/code_sandbox/chap1.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 10,454 |
```tex
% file: plots.tex
% The following 2 macros are used for plotting learning curve in chapter 3:
% learn cost curve of a single sigmoid neutron with quadratic cost function
\newcommand{\quadraticCostLearning}[4]{
\begin{tikzpicture}[
inner sep=0pt,
minimum size=10mm,
font=\footnotesize,
background rectangle/.style={
draw=gray!25,
fill=gray!10,
rounded corners
},
show background rectangle]
\coordinate (origin) at (0,0);
\coordinate(x) at (3.5,0);
\coordinate(y) at (0,2.5);
\node(i) [above=4 of origin,xshift=-5mm] {Input: $1.0$};
\node(n) [right=2 of i,circle,draw] {};
\node(epoch) [right=of x,xshift=-1cm] {Epoch};
\node(cost) [left=of y,xshift=1cm] {Cost};
\draw[->] (origin) to (x);
\draw[->] (origin) to (y);
%\draw[blue,thick,domain=0:2] plot (\x, {(\x*\x / 2)});
\tikzmath{ % Do not contain blank line
function sigmoid(\z) {
return 1/(1 + exp(- \z));
};
function sigmoid_neutron(\w,\b) {
return sigmoid(\w + \b);
};
function quad_cost(\a) { % the quadratic cost function
return (\a * \a)/2;
};
function quad_cost_derivative(\a) {
return \a * \a * (1-\a);
};
\w = #1; % start weight
\b = #2; % start bias
\e = #3; % eta, learning rate
\y = 0;
\a = sigmoid_neutron(\w,\b);
\dt = quad_cost_derivative(\a);
\xo = 0;
\yo = quad_cost(\a);
integer \x;
if #4 > 0 then {
for \x in {1,...,#4}{ % epoches
\a = sigmoid_neutron(\w,\b);
\dt = quad_cost_derivative(\a);
\w = \w - \e * \dt;
\b = \b - \e * \dt;
\y = quad_cost(\a);
{\draw[blue,thick] (\xo/100,\yo*5) -- (\x/100,\y*5);}; % scale y with 5 times
\xo = \xo + 1;
\yo = \y;
};
{\draw (\x/100,0) -- node[below] {$\x$} (\x/100,-0.1);};
};
{
\draw[->] (i) to node (w) [below] {
\scriptsize
\pgfkeys{/pgf/number format/.cd,showpos,fixed,fixed zerofill,precision=2,use period}
$w = \pgfmathprintnumber{\w}$
} (n);
\node(b) [below,xshift=5mm] at (n.south) {
\scriptsize
\pgfkeys{/pgf/number format/.cd,showpos,fixed,fixed zerofill,precision=2,use period}
$b = \pgfmathprintnumber{\b}$
};
\node(o) [right=of n] {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
Output: $\pgfmathprintnumber{\a}$
};
\draw[->] (n) to (o);
};
}
\end{tikzpicture}%
}
% learn cost curve of a single sigmoid neutron with cross entropy cost function
\newcommand{\crossEntropyCostLearning}[4]{
\begin{tikzpicture}[
inner sep=0pt,
minimum size=10mm,
font=\footnotesize,
background rectangle/.style={
draw=gray!25,
fill=gray!10,
rounded corners
},
show background rectangle]
\coordinate (origin) at (0,0);
\coordinate(x) at (3.5,0);
\coordinate(y) at (0,2.5);
\node(i) [above=4 of origin,xshift=-5mm] {Input: $1.0$};
\node(n) [right=2 of i,circle,draw] {};
\node(epoch) [right=of x,xshift=-1cm] {Epoch};
\node(cost) [left=of y,xshift=1cm] {Cost};
\draw[->] (origin) to (x);
\draw[->] (origin) to (y);
%\draw[blue,thick,domain=0:2] plot (\x, {(\x*\x / 2)});
\tikzmath{ % Do not contain blank line
function sigmoid(\z) {
return 1/(1 + exp(- \z));
};
function sigmoid_neutron(\w,\b) {
return sigmoid(\w + \b);
};
function cross_entropy_cost(\a) { % the quadratic cost function
return -ln(1 - \a);
};
function cross_entropy_cost_derivative(\a) {
return 1/(1 - \a);
};
\w = #1; % start weight
\b = #2; % start bias
\e = #3; % eta, learning rate
\y = 0;
\a = sigmoid_neutron(\w,\b);
\dt = cross_entropy_cost_derivative(\a);
\xo = 0;
\yo = cross_entropy_cost(\a);
integer \x;
if #4 > 0 then {
for \x in {1,...,#4}{ % epoches
\a = sigmoid_neutron(\w,\b);
\dt = cross_entropy_cost_derivative(\a);
\w = \w - \e * \dt;
\b = \b - \e * \dt;
\y = cross_entropy_cost(\a);
{\draw[blue,thick] (\xo/100,\yo/2) -- (\x/100,\y/2);}; % scale y to 1/2
\xo = \xo + 1;
\yo = \y;
};
{\draw (\x/100,0) -- node[below] {\footnotesize $\x$} (\x/100,-0.1);};
};
{
\draw[->] (i) to node (w) [below] {
\scriptsize
\pgfkeys{/pgf/number format/.cd,showpos,fixed,fixed zerofill,precision=2,use period}
$w = \pgfmathprintnumber{\w}$
} (n);
\node(b) [below,xshift=5mm] at (n.south) {
\scriptsize
\pgfkeys{/pgf/number format/.cd,showpos,fixed,fixed zerofill,precision=2,use period}
$b = \pgfmathprintnumber{\b}$
};
\node(o) [right=of n] {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
Output: $\pgfmathprintnumber{\a}$
};
\draw[->] (n) to (o);
};
}
\end{tikzpicture}%
}
% #1 - z1
% #2 - z2
% #3 - z3
% #4 - z4
\newcommand{\manipulateSoftmaxBars}[4]{
\begin{tikzpicture}[
font=\footnotesize,
base/.style={rectangle,draw,minimum width=100pt,minimum height=10pt},
slidebar/.style={base,rounded corners=2pt},
slidebarinner/.style={rectangle,fill=gray!50,rounded corners=2pt,minimum height=10pt},
colorbar/.style={base},
colorbarinner/.style={rectangle,minimum height=10pt,fill=blue!60!cyan}
]
\node(s1) [slidebar] {};
\node(z1) [below,anchor=north west] at (s1.south west) {$z^L_1 = #1$};
\node(b1) [colorbar,right=of s1] {};
%\node(a1) [below,anchor=north west] at (b1.south west) {$a^L_1 = 0.315$};
\node(s2) [slidebar,below=of s1] {};
\node(z2) [below,anchor=north west] at (s2.south west) {$z^L_2 = #2$};
\node(b2) [colorbar,right=of s2] {};
%\node(a2) [below,anchor=north west] at (b2.south west) {$a^L_2 = 0.009$};
\node(s3) [slidebar,below=of s2] {};
\node(z3) [below,anchor=north west] at (s3.south west) {$z^L_3 = #3$};
\node(b3) [colorbar,right=of s3] {};
%\node(a3) [below,anchor=north west] at (b3.south west) {$a^L_3 = 0.633$};
\node(s4) [slidebar,below=of s3] {};
\node(z4) [below,anchor=north west] at (s4.south west) {$z^L_4 = #4$};
\node(b4) [colorbar,right=of s4] {};
%\node(a4) [below,anchor=north west] at (b4.south west) {$a^L_4 = 0.043$};
\tikzmath{
function zsum(\za,\zb,\zc,\zd) {
return exp(\za) + exp(\zb) + exp(\zc) + exp(\zd);
};
function softmax(\n, \za, \zb, \zc, \zd) {
return exp(\n) / zsum (\za, \zb, \zc, \zd);
};
function getslidewidth(\x) {
return (\x + 5) * 10;
};
\a = softmax(#1, #1, #2, #3, #4);
\wa = \a * 100;
\wz = getslidewidth(#1);
{
\node(si1) [slidebarinner,minimum width=\wz pt,anchor=west] at (s1.west) {};
\node(bi1) [colorbarinner,right=of s1,minimum width=\wa pt] {};
\node(a1) [below,anchor=north west] at (b1.south west) {$a^L_1 = \a$};
};
\a = softmax(#2, #1, #2, #3, #4);
\wa = \a * 100;
\wz = getslidewidth(#2);
{
\node(si2) [slidebarinner,minimum width=\wz pt,anchor=west] at (s2.west) {};
\node(bi2) [colorbarinner,right=of s2,minimum width=\wa pt] {};
\node(a2) [below,anchor=north west] at (b2.south west) {$a^L_2 = \a$};
};
\a = softmax(#3, #1, #2, #3, #4);
\wa = \a * 100;
\wz = getslidewidth(#3);
{
\node(si3) [slidebarinner,minimum width=\wz pt,anchor=west] at (s3.west) {};
\node(bi3) [colorbarinner,right=of s3,minimum width=\wa pt] {};
\node(a3) [below,anchor=north west] at (b3.south west) {$a^L_3 = \a$};
};
\a = softmax(#4, #1, #2, #3, #4);
\wa = \a * 100;
\wz = getslidewidth(#4);
{
\node(si4) [slidebarinner,minimum width=\wz pt,anchor=west] at (s4.west) {};
\node(bi4) [colorbarinner,right=of s4,minimum width=\wa pt] {};
\node(a4) [below,anchor=north west] at (b4.south west) {$a^L_4 = \a$};
};
}
\end{tikzpicture}%
}
% draw neurons and plots in chapter 4.
% #1 - x weight
% #2 - bias
\newcommand{\manipulateTiGraph}[2]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node(n) [neuron] {};
\node(x) [neuron,left=1.25 of n,yshift=1.5cm] {$x$};
\node(y) [neuron,left=1.25 of n,yshift=-1.5cm] {$y$};
\draw[->] (x) -- node [blue,yshift=2mm,xshift=2mm] {$#1$} (n);
\draw[->] (y) -- node [yshift=-2mm,xshift=2mm] {$0$} (n);
\node [above,blue] at (n.north) {$#2$};
\draw[->] (n) -- ++(1cm, 0);
\end{scope}
\begin{scope}[xshift=2cm,yshift=-2.5cm]
\begin{axis}[
view={-30}{15},
axis background/.style={fill=blue!5},
xlabel=$x$,
ylabel=$y$,
xtick distance=1,
ytick distance=1,
ztick distance=1,
xtick={1},
ytick={1},
ztick={2},
title=Output,
colormap={simple}{rgb255=(235,95,95) rgb255=(255,155,145)}
]
\addplot3[surf,domain=0:1] {
1 / (1 + exp(-(#1) * x - (#2)))
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% #1 - x weight
% #2 - bias
\newcommand{\createTiGraphSurf}[2]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{axis}[
view={-30}{15},
axis background/.style={fill=blue!5},
xlabel=$x$,
ylabel=$y$,
xtick distance=1,
ytick distance=1,
ztick distance=1,
xtick={1},
ytick={1},
ztick={2},
title={Output ($w_1 = #1, b = #2$)},
colormap={simple}{rgb255=(235,95,95) rgb255=(255,155,145)}
]
\addplot3[surf,domain=0:1] {
1 / (1 + exp(-(#1) * x - (#2)))
};
\end{axis}
\end{tikzpicture}%
}
% #1 - weight
% #2 - bias
% #3 - title
\newcommand{\manipulateSingleHiddenNeuron}[3]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0) [neuron,right=of l0,yshift=-1.5cm] {};
\node (m1) [neuron,right=of l0,yshift=1.5cm] {};
\node (r0) [neuron,right=of m0,yshift=1.5cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0);
\draw[->] (l0) to node (w) [blue,above,xshift=-0.5cm] {$w = #1$} (m1);
\draw[->] (m0) to (r0);
\draw[->] (m1) to (r0);
\node(b) [blue,above] at (m1.north) {$b = #2$};
\end{scope}
\begin{scope}[xshift=6cm]
\begin{axis}[
width=5.6cm,
height=5.6cm,
xlabel={\normalsize $x$},
axis lines=left,
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymax=1.1,
title={#3}
]
\addplot[
orange,
thick,
domain=0:1,
samples=101
] {
1/(1 + exp(-(#1 * x + #2)))
};
\end{axis}
% \coordinate(o) at(0,0) node [left,xshift=1mm,yshift=-1mm] {\scriptsize $0$};
%
% \draw[->] (o) -- ++(3.75,0);
% \draw[->] (o) -- ++(0,3.75);
% \coordinate[right=3.5 of o] (cx);
% \coordinate[above=3.5 of o] (cy);
% \draw (cx) -- ++(0, -0.075) node[below,yshift=1mm] {\scriptsize 1};
% \draw (cy) -- ++(-0.075, 0) node[left,xshift=1mm] {\scriptsize 1};
%
% \node [below] at (1.75,0) {$x$};
% \node [above] at (1.75,3.5) {#3};
%
% \draw[orange,domain=0:1,samples=101,xscale=3.5,yscale=3.5]
% plot (\x, {(1/(1 + exp(-(#1 * \x + #2))))});
\end{scope}
\end{tikzpicture}%
}
% This macro generate images by two_hn_network.tex, bump_function.tex in images folder,
% to generate images used in chapter 4.
% #1 - s1
% #2 - w1
% #3 - s2
% #4 - w2
\newcommand{\manipulateTwoHNNetwork}[4]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0) [neuron,right=of l0,yshift=-1.5cm] {};
\node (m1) [neuron,right=of l0,yshift=1.5cm] {};
\node (r0) [neuron,right=of m0,yshift=1.5cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0);
\draw[->] (l0) to (m1);
\draw[->] (m0) to node [blue,xshift=5mm,yshift=-4mm] {$w_2 = #4$} (r0);
\draw[->] (m1) to node [blue,xshift=5mm,yshift=4mm] {$w_1 = #2$} (r0);
\node[blue,above] at (m1.north) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$s_1 = \pgfmathprintnumber{#1}$
};
\node[blue,above] at (m0.north) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$s_2 = \pgfmathprintnumber{#3}$
};
\end{scope}
\begin{scope}[xshift=6cm,yshift=-2.45cm]
\begin{axis}[
width=5.6cm,
height=7.6cm,
% xlabel={\normalsize $x$},
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
axis x line=middle,
axis y line=left,
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymin=-1.5,
ymax=2.1,
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\st,\wt,\sb,\wb) = \wt * sigma(\x * 1000 - 1000 * \st) + \wb * sigma(\x * 1000 - 1000 * \sb);
% f = w1 * a1 + w2 * a2
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=401
] {
f(x, #1, #2, #3, #4)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% This macro generate bump function by bump_fn.tex in images folder,
% to generate images used in chapter 4.
% #1 - s1
% #2 - s2
% #3 - h
\newcommand{\manipulateBumpFunction}[3]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0) [neuron,right=of l0,yshift=-1.5cm] {};
\node (m1) [neuron,right=of l0,yshift=1.5cm] {};
\node (r0) [neuron,right=of m0,yshift=1.5cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0);
\draw[->] (l0) to (m1);
\draw[->] (m0) to node [xshift=2mm,yshift=-2mm] {$-#3$} (r0);
\draw[->] (m1) to node [xshift=2mm,yshift=2mm] {$#3$} (r0);
\node[blue] at (m1.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#1}$
};
\node[blue] at (m0.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#2}$
};
\node [blue,right=0.6cm of m1, yshift=4mm] {$h = #3$};
\end{scope}
\begin{scope}[xshift=6cm,yshift=-2.45cm]
\begin{axis}[
width=5.6cm,
height=7.6cm,
% xlabel={\normalsize $x$},
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
axis x line=middle,
axis y line=left,
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymin=-1.5,
ymax=2.1,
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\st,\wt,\sb,\wb) = \wt * sigma(\x * 1000 - 1000 * \st) + \wb * sigma(\x * 1000 - 1000 * \sb);
% f = w1 * a1 + w2 * a2
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=401
] {
f(x, #1, #3, #2, -#3)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% This macro generate bump function by double_bump.tex in images folder,
% to generate images used in chapter 4.
% #1 - s1
% #2 - s2
% #3 - h1
% #4 - s3
% #5 - s4
% #6 - h2
\newcommand{\manipulateDoubleBump}[6]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (s2) [neuron,right=of l0,yshift=1.2cm] {};
\node (s3) [neuron,right=of l0,yshift=-1.2cm] {};
\node (s1) [neuron,above] at (s2.north) {};
\node (s4) [neuron,below] at (s3.south) {};
\node (r0) [neuron,right=of s2,yshift=-1.2cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (s1);
\draw[->] (l0) to (s2);
\draw[->] (l0) to (s3);
\draw[->] (l0) to (s4);
\draw[->] (s1) to node [blue,xshift=8mm,yshift=2mm] {$h = #3$} (r0);
\draw[->] (s2) to (r0);
\draw[->] (s3) to (r0);
\draw[->] (s4) to node [blue,xshift=8mm,yshift=-2mm] {$h = #6$} (r0);
\node[blue] at (s1.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#1}$
};
\node[blue] at (s2.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#2}$
};
\node[blue] at (s3.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#4}$
};
\node[blue] at (s4.center) {
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2,use period}
$\pgfmathprintnumber{#5}$
};
\end{scope}
\begin{scope}[xshift=6cm,yshift=-2.45cm]
\begin{axis}[
width=5.6cm,
height=7.6cm,
% xlabel={\normalsize $x$},
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
axis x line=middle,
axis y line=left,
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymin=-1.5,
ymax=2.1,
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\st,\wt,\sb,\wb) = \wt * sigma(\x * 1000 - 1000 * \st) + \wb * sigma(\x * 1000 - 1000 * \sb);
% f = w1 * a1 + w2 * a2
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=401
] {
f(x, #1, #3, #2, -#3) + f(x, #4, #6, #5, -#6)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
\newcommand{\manipulateFiveBumps}[5]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0g0) [neuron,right=1.5 of l0,yshift=-5.5mm] {$0.6$};
\node (m1g0) [neuron,right=1.5 of l0,yshift=5.5mm] {$0.4$};
\node (r0) [neuron,right=1.5 of m0g0,yshift=5.5mm] {};
\node (m0g1) [neuron,above=0.4 of m1g0] {$0.4$};
\node (m1g1) [neuron,above=1mm] at (m0g1.north) {$0.2$};
\node (m1g2) [neuron,below=0.4 of m0g0] {$0.6$};
\node (m0g2) [neuron,below=1mm] at (m1g2.south) {$0.8$};
\node (m0g3) [circle,inner sep=0pt,minimum size=10mm,above=0.4 of m1g1] {$0.2$};
\node (m1g3) [neuron,above=1mm] at (m0g3.north) {$0.0$};
\node (m1g4) [circle,inner sep=0pt,minimum size=10mm,below=0.4 of m0g2] {$0.8$};
\node (m0g4) [neuron,below=1mm] at (m1g4.south) {$1.0$};
\foreach \x in {0,1}
\foreach \y in {0,...,4} {
\draw[->] (l0) to (m\x g\y);
\draw[->] (m\x g\y) to (r0);
}
% cover the top and bottom neutrons for better look
\node (m0g3a) [neuron,fill=white] at (m0g3) {$0.2$};
\node (m1g4a) [neuron,fill=white] at (m1g4) {$0.8$};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0g0);
\draw[->] (l0) to (m1g0);
\draw[->] (m0g0) to (r0);
\draw[->] (m1g0) to (r0);
\node [blue,above=4.15cm of r0,xshift=-1cm] {$h = #1$};
\node [blue,above=1.7cm of r0,xshift=-3mm] {$h = #2$};
\node [blue,above,xshift=5mm] at (r0.north) {$h = #3$};
\node [blue,below=1.7cm of r0,xshift=-3mm] {$h = #4$};
\node [blue,below=4.15cm of r0,xshift=-1cm] {$h = #5$};
\end{scope}
\begin{scope}[xshift=7cm]
\begin{axis}[
width=5.6cm,
height=7.6cm,
% xlabel={\normalsize $x$},
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
axis x line=middle,
axis y line=left,
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymin=-1.95,
ymax=2.1,
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\st,\wt,\sb,\wb) = \wt * sigma(\x * 1000 - 1000 * \st) + \wb * sigma(\x * 1000 - 1000 * \sb);
% f = w1 * a1 + w2 * a2
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=401
] {
f(x, 0.0, #1, 0.2, -#1) +
f(x, 0.2, #2, 0.4, -#2) +
f(x, 0.2, #3, 0.6, -#3) +
f(x, 0.6, #4, 0.8, -#4) +
f(x, 0.8, #5, 1.0, -#5)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
\newcommand{\manipulateDesignFunction}[5]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0g0) [neuron,right=1.5 of l0,yshift=-5.5mm] {$0.6$};
\node (m1g0) [neuron,right=1.5 of l0,yshift=5.5mm] {$0.4$};
\node (r0) [neuron,right=1.5 of m0g0,yshift=5.5mm] {};
\node (m0g1) [neuron,above=0.4 of m1g0] {$0.4$};
\node (m1g1) [neuron,above=1mm] at (m0g1.north) {$0.2$};
\node (m1g2) [neuron,below=0.4 of m0g0] {$0.6$};
\node (m0g2) [neuron,below=1mm] at (m1g2.south) {$0.8$};
\node (m0g3) [circle,inner sep=0pt,minimum size=10mm,above=0.4 of m1g1] {$0.2$};
\node (m1g3) [neuron,above=1mm] at (m0g3.north) {$0.0$};
\node (m1g4) [circle,inner sep=0pt,minimum size=10mm,below=0.4 of m0g2] {$0.8$};
\node (m0g4) [neuron,below=1mm] at (m1g4.south) {$1.0$};
\foreach \x in {0,1}
\foreach \y in {0,...,4} {
\draw[->] (l0) to (m\x g\y);
\draw[->] (m\x g\y) to (r0);
}
% cover the top and bottom neutrons for better look
\node (m0g3a) [neuron,fill=white] at (m0g3) {$0.2$};
\node (m1g4a) [neuron,fill=white] at (m1g4) {$0.8$};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0g0);
\draw[->] (l0) to (m1g0);
\draw[->] (m0g0) to (r0);
\draw[->] (m1g0) to (r0);
\node [blue,above=4.15cm of r0,xshift=-1cm] {$h = #1$};
\node [blue,above=1.7cm of r0,xshift=-3mm] {$h = #2$};
\node [blue,above,xshift=5mm] at (r0.north) {$h = #3$};
\node [blue,below=1.7cm of r0,xshift=-3mm] {$h = #4$};
\node [blue,below=4.15cm of r0,xshift=-1cm] {$h = #5$};
\end{scope}
\begin{scope}[xshift=7cm]
\begin{axis}[
width=5.6cm,
height=7.6cm,
% xlabel={\normalsize $x$},
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
axis x line=middle,
axis y line=left,
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymin=-2.6,
ymax=3.1,
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\st,\wt,\sb,\wb) = \wt * sigma(\x * 1000 - 1000 * \st) + \wb * sigma(\x * 1000 - 1000 * \sb);
% f = w1 * a1 + w2 * a2
sigmaInverse(\z)=ln(\z/(1-\z));
g(\x)=0.2+0.4*\x*\x+0.3*\x*sin(15*deg(\x))+0.05*cos(50*deg(\x));
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=501
] {
f(x, 0.0, #1, 0.2, -#1) +
f(x, 0.2, #2, 0.4, -#2) +
f(x, 0.2, #3, 0.6, -#3) +
f(x, 0.6, #4, 0.8, -#4) +
f(x, 0.8, #5, 1.0, -#5)
};
\addplot[
blue!50,
domain=0:1,
samples=101
] {
sigmaInverse(g(x))
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% #1 - weight
% #2 - bias
\newcommand{\manipulateRamping}[2]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node(x) [neuron] {$x$};
\node(n) [neuron,right=2 of x] {};
\draw[->] (n) -- ++(1,0);
\draw[->] (x) to node (w) [blue,above] {$w = #1$} (n);
\node(b) [blue,above] at (n.north) {$b = #2$};
\end{scope}
\begin{scope}[xshift=5cm,yshift=-2cm]
\begin{axis}[
width=6.1cm,
height=6.1cm,
xlabel={\normalsize $x$},
axis lines=left,
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
xtick={0,1},
ytick={1},
xmax=1.1,
ymax=1.1,
% minor tick num=1,
title={},
declare function={
f(\x,\w,\b) = 1/(1 + exp(-(\w * \x + (\b)))) + 0.2 * sin(10 * deg(\w * \x + (\b))) * exp(-abs(\w * \x + (\b)));
}
]
\addplot[
orange,
thick,
domain=0:1,
samples=201
] {
f(x, #1, #2)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% #1 - h
% #2 - b
\newcommand{\manipulateTowerConstruction}[2]{
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node(n) [neuron] {};
\node(h0) [neuron,left=of n,yshift=1.2cm] {};
\node(h1) [neuron,above] at (h0.north) {};
\node(h2) [neuron,left=of n,yshift=-1.2cm] {};
\node(h3) [neuron,below] at (h2.south) {};
\node(x) [neuron,left=of h0,yshift=5mm] {$x$};
\node(y) [neuron,left=of h2,yshift=-5mm] {$y$};
\draw[->] (x) to (h0);
\draw[->] (x) to (h1);
\draw[->] (y) to (h2);
\draw[->] (y) to (h3);
\node (s0) at (h0.center) {$0.60$};
\node at (s0.north) {\tiny $x$};
\node (s1) at (h1.center) {$0.40$};
\node at (s1.north) {\tiny $x$};
\node (s2) at (h2.center) {$0.30$};
\node at (s2.north) {\tiny $y$};
\node (s3) at (h3.center) {$0.70$};
\node at (s3.north) {\tiny $y$};
\node [blue,right=4mm of h1] {$h = #1$};
\node [blue,above,yshift=2mm,xshift=2mm] at (n.north) {$b = #2$};
\draw[->] (h0) -- node [yshift=-2mm] {\scriptsize $-#1$} (n);
\draw[->] (h1) -- node [yshift=2mm] {\scriptsize $#1$} (n);
\draw[->] (h2) -- node [yshift=2mm] {\scriptsize $#1$} (n);
\draw[->] (h3) -- node [yshift=-2mm] {\scriptsize $-#1$} (n);
\draw[->] (n) -- ++(1cm, 0);
\end{scope}
\begin{scope}[xshift=2cm,yshift=-2.5cm]
% FIXME: rotate the zlabel, change plot color, and move z axis to right
\begin{axis}[
view={-30}{15},
axis background/.style={fill=blue!5},
xlabel=$x$,
ylabel=$y$,
xtick distance=1,
ytick distance=1,
ztick distance=1,
xtick={1},
ytick={1},
ztick={2},
zmin=0,
zmax=1,
title=Output,
colormap={simple}{rgb255=(235,95,95) rgb255=(255,155,145)},
declare function={
sigma(\z)=1/(1 + exp(-\z));
f(\x,\y,\h,\b)=sigma(\b + \h * (sigma(1000 * (\x - 0.4)) - sigma(1000 * (\x - 0.6))) + \h * (sigma(1000 * (\y - 0.3)) - sigma(1000 * (\y - 0.7))));
% f(x,y) = sigma(b + h * (sigma(1000*(x-0.4))-sigma(1000*(x-0.6))) + h*(sigma(1000*(y-0.3))-sigma(1000*(y-0.7))));
}]
\addplot3[surf,domain=0:1] {
f(x,y, #1, #2)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
% #1 - w1
% #2 - w2
\newcommand{\manipulateTwoTower}[2]{
\begin{tikzpicture}[
neuron/.style={circle,draw,fill=white,inner sep=0pt,minimum size=10mm},
invisible/.style={circle,inner sep=0pt,minimum size=10mm},
box/.style={rectangle,draw=gray,fill=gray!20,rounded corners=5pt,minimum width=3.5cm,minimum height=5.5cm}
]
\begin{scope}
\node(output) [neuron] {};
\node(box0) [box,left=of output,xshift=2.5mm,yshift=3cm] {};
\node(box1) [box,left=of output,xshift=2.5mm,yshift=-3cm] {};
\node(box0output) [neuron,left=of output,yshift=3cm] {};
\node(box0s1) [invisible,left=of box0output,yshift=1cm] {};
\node(box0s2) [neuron,left=of box0output,yshift=-1cm] {$0.8$};
\node(box0s0) [neuron,above] at (box0s1.north) {$0.1$};
\node(box0s3) [neuron,below] at (box0s2.south) {$0.9$};
\node(box1output) [neuron,left=of output,yshift=-3cm] {};
\node(box1s1) [neuron,left=of box1output,yshift=1cm] {$0.8$};
\node(box1s2) [invisible,left=of box1output,yshift=-1cm] {};
\node(box1s0) [neuron,above] at (box1s1.north) {$0.7$};
\node(box1s3) [neuron,below] at (box1s2.south) {$0.3$};
\node(x) [neuron,left=of box0s3] {$x$};
\node(y) [neuron,left=of box1s0] {$y$};
\foreach \x in {0,...,3} {
\draw[->] (box0s\x) to (box0output);
\draw[->] (box1s\x) to (box1output);
}
\draw[->] (x) to (box0s0);
\draw[->] (x) to (box0s1);
\draw[->] (x) to (box1s0);
\draw[->] (x) to (box1s1);
\draw[->] (y) to (box0s2);
\draw[->] (y) to (box0s3);
\draw[->] (y) to (box1s2);
\draw[->] (y) to (box1s3);
\node(box0s1a) [neuron] at (box0s1.center) {$0.2$};
\node(box1s2a) [neuron] at (box1s2.center) {$0.2$};
\draw[->] (box0output) -- node [blue,xshift=8mm] {$w = #1$} (output);
\draw[->] (box1output) -- node [blue,xshift=8mm] {$w = #2$} (output);
\draw[->] (output) -- ++(1cm, 0);
\end{scope}
\begin{scope}[xshift=2cm,yshift=-2.5cm]
\begin{axis}[
view={-30}{15},
axis background/.style={fill=blue!5},
xlabel=$x$,
ylabel=$y$,
xtick distance=1,
ytick distance=1,
xtick={1},
ytick={1},
ztick={2},
title=,
colormap={simple}{rgb255=(235,95,95) rgb255=(255,155,145)},
declare function={
sigma(\z)=1/(1 + exp(-\z));
f(\x,\y,\h,\b)= #1 * sigma(\b + \h * (sigma(1000 * (\x - 0.1)) - sigma(1000 * (\x - 0.2))) + \h * (sigma(1000 * (\y - 0.8)) - sigma(1000 * (\y - 0.9)))) + #2 * sigma(\b + \h * (sigma(1000 * (\x - 0.7)) - sigma(1000 * (\x - 0.8))) + \h * (sigma(1000 * (\y - 0.2)) - sigma(1000 * (\y - 0.3))));
}]
\addplot3[surf,domain=0:1] {
f(x,y,10,-16)
};
\end{axis}
\end{scope}
\end{tikzpicture}%
}
``` | /content/code_sandbox/plots.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 11,852 |
```tex
% file: title.tex
\begin{titlepage}
\begin{center}
\hfill\\
\vspace{1cm}
% title of this document
{\fontsize{36pt}{40pt}\NotoSansSCBold{} }\\
\vspace{1em}
{\LARGE\href{path_to_url}{Neural Networks and Deep Learning}}\\
\vspace{1cm}
\includegraphics{cayley}\\
\vspace{1cm}
{\LARGE \href{path_to_url}{Michael Nielsen} }\\
\vspace{1cm}
{\Large
\begin{tabular}{rl}
\href{mailto:xhzhu.nju@gmail}{Xiaohu Zhu} & \multirow{2}{*}{} \\
\href{mailto:zhanggyb@gmail.com}{Freeman Zhang} & \\
\end{tabular}
}\\
\vfill
{\large \today}\\
\vspace{1em}
{\large Version: \href{path_to_url}{0.5}}
\end{center}
\end{titlepage}
``` | /content/code_sandbox/title.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 256 |
```tex
% file: westernfonts.tex
\newfontfamily\SourceCodePro{SourceCodePro}[
UprightFont=*-Light,
BoldFont=*-Medium,
ItalicFont=*-LightIt,
BoldItalicFont=*-MediumIt]
\newfontfamily\SourceSerifPro{SourceSerifPro}[
UprightFont=*-Light,
BoldFont=*-Semibold]
\newcommand{\serif}[0]{\SourceSerifPro}
\setmonofont{SourceCodePro}[
UprightFont=*-Light,
BoldFont=*-Medium,
ItalicFont=*-LightIt,
BoldItalicFont=*-MediumIt]
``` | /content/code_sandbox/westernfonts.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 150 |
```tex
% file: history.tex
\chapter{}
\begin{table}[h]
\centering
\begin{tabularx}{0.9\textwidth}{ r X }
\toprule
\textbf{} & \textbf{}\\
\midrule
2017-04-09 & \vspace{-1.5ex}
\begin{compactitem}
\item Version 0.5
\item \href{path_to_url#serif-hans}{}
\item glossaries chapter, section gls
\item \href{mailto:gengchao@foxmail.com}{GC555}
\item \href{path_to_url}{1.6 }
\end{compactitem}\\
\midrule
2016-11-25 & Version 0.4: \\
\midrule
2016-08-08 & Version 0.3: Tex2016 \\
\midrule
2016-05-17 & Version 0.2: \\
\midrule
2016-04-16 & Version 0.1.1 \href{mailto:xhzhu.nju@gmail}{Xiaohu Zhu} \\
\midrule
2016-03-22 & Version 0.1\\
% \midrule
% \today & Version 1.0. Initial Release.\\
\bottomrule
\end{tabularx}
\caption{}
\label{table:DocumentChanges}
\end{table}
``` | /content/code_sandbox/history.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 358 |
```tex
% file: localization.tex
% load cjkfonts and set Source Han Sans SC as the default CJK fonts:
\usepackage[default]{cjkfonts}
\usepackage{titlesec}
\titleformat{\chapter}[display]
{\bfseries\huge}%
{\huge \thechapter{} }%
{10 pt}%
{\bfseries\huge}%
\renewcommand{\contentsname}{}
\renewcommand{\indexname}{}
% Redefine \emph to be both bold and italic, better in chinese document
% \let\emph\relax
%\DeclareTextFontCommand{\emph}{\bfseries\em} % bold and italic
% \DeclareTextFontCommand{\emph}{\bfseries} % just bold
\usepackage{indentfirst}
``` | /content/code_sandbox/localization.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 174 |
```tex
% file: about.tex
\chapter{}
\label{ch:About}
2006
2006``''
``''
Facebook
\section*{}
\label{sec:PrincipleOrientedApproach}
``''------
\section*{}
\label{sec:HandsOnApproach}
Python2.7Python
\href{path_to_url}{}
\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}
\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}
%
\href{path_to_url#the_backpropagation_algorithm}{
}
``` | /content/code_sandbox/about.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 125 |
```tex
% file: chap4.tex
\chapter{}
\label{ch:VisualProof}
$f(x)$
\begin{center}
\includegraphics{function}
\end{center}
\label{basic_network_precursor}
$x$ $f(x)$
\begin{center}
\includegraphics{basic_network}
\end{center}
$f = f(x_1, \ldots, x_m)$
$m = 3$ $n = 2$
\begin{center}
\includegraphics{vector_valued_network}
\end{center}
\textbf{}
\footnote{\href{path_to_url~gvc/Cybenko_MCSS.pdf}{Approximation
by superpositions of a sigmoidal function} George Cybenko (1989)
Cybenko
\href{path_to_url}{Multilayer
feedforward networks are universal approximators} Kurt Hornik
Maxwell Stinchcombe Halbert White (1989) Stone-Weierstrass
}\href{path_to_url
}{}\href{path_to_url}{
}
\footnote{}
mp4
\footnote{}
\section{}
\label{sec:two_caveats}
\textbf{}
\textbf{}
\hyperref[basic_network_precursor]{}
$f(x)$
\begin{center}
\includegraphics{bigger_network}
\end{center}
$\epsilon > 0$
$f(x)$ $g(x)$ $x$
$|g(x) - f(x)| < \epsilon$
\textbf{}
\section{}
\label{sec:universality_with_one_input_and_one_output}
\begin{center}
\includegraphics{function}
\end{center}
$f$
\begin{center}
\includegraphics{two_hidden_neurons}
\end{center}
$w$ $b$
\begin{center}
\includegraphics{basic_manipulation}
\end{center}
\hyperref[sec:sigmoid_neurons]{}
$\sigma(wx + b)$ $\sigma(z) \equiv 1/(1+e^{-z})$ S
S\footnote{
}
$b$
$2$ $3$
$w = 100$
$x = 0.3$
\begin{center}
\includegraphics{create_step_function}
\end{center}
$w = 999$
\begin{center}
\includegraphics{high_weight_function}
\end{center}
S
S
$w$
$x$
$w$ $b$
$b$ \textbf{} $w$ \textbf{}
$s = -b/w$
\begin{center}
\includegraphics{step}
\end{center}
$s$ $s =
-b/w$ $s$
\begin{center}
\includegraphics{step_parameterization}
\end{center}
$w$ ~~
$b = -ws$
$s_1$ $s_2$
$w_1$ $w_2$
\begin{center}
\includegraphics{two_hn_network}
\end{center}
\textbf{} $w_1 a_1 + w_2 a_2$ $a_1$ $a_2$
\footnote{ $\sigma(w_1
a_1+w_2 a_2 + b)$ $b$
} $a$
\textbf{}\textbf{activations}
$s_1$
$s_1$ $s_2$
$s_2$
0
$w_1$ $0.8$$w_2$ $-0.8$
$s_1$ $s_2$ $0.8$
\begin{center}
\includegraphics{bump_function}
\end{center}
$h$
$s_1 = \ldots$$w_1 = \ldots$
\begin{center}
\includegraphics{bump_fn}
\end{center}
$h$
{\serif if-then-else}
\begin{lstlisting}[language=Python]
if input >= step point:
add 1 to the weighted output
else:
add 0 to the weighted output
\end{lstlisting}
{\serif if-then-else}
\begin{center}
\includegraphics{double_bump}
\end{center}
$h$
$h$
$[0, 1]$ $N$ $N$
$N = 5$
\begin{center}
\includegraphics{five_bumps}
\end{center}
$0, 1/5$ $1/5, 2/5$
$4/5, 5/5$
$h$ $h$ $-h$
$h$
\textbf{}
$h$
$+h$ $-h$
$h$
\begin{center}
\includegraphics{function}
\end{center}
\begin{equation}
f(x) = 0.2+0.4 x^2+0.3x \sin(15 x) + 0.05 \cos(50 x)
\label{eq:113}\tag{113}
\end{equation}
$x$ $0$ $1$$y$ $0$ $1$
$\sum_j w_j a_j$
$\sigma(\sum_j w_j a_j + b)$ $b$
$\sigma^{-1} \circ f(x)$
$\sigma^{-1}$ $\sigma$
\begin{center}
\includegraphics{inverted_function}
\end{center}
$f(x)$ \footnote{
$0$}
%
\href{path_to_url#universality_with_one_input_and_one_output}{%
}
\textbf{}\textbf{}
$0.40$
$h$ $0.40$
\begin{center}
\href{path_to_url#universality_with_one_input_and_one_output}{\includegraphics{design_function}}
\end{center}
\begin{center}
\includegraphics{design_function_success}
\end{center}
$f(x)$
$w = 1000$
$b = -w s$ $s = 0.2$
$b = -1000 \times 0.2 = -200$
$h$ $h$$h = -0.5$
$-0.5$ $0.5$
$0$
$f(x) = 0.2+0.4 x^2+0.3 \sin(15 x) + 0.05
\cos(50 x)$ $[0, 1]$
$[0, 1]$
\section{}
\label{sec:many_input_variables}
\begin{center}
\includegraphics{two_inputs}
\end{center}
$x$ $y$ $w_1$ $w_2$
$b$ $w_2$ $0$ $w_1$ $b$
\begin{center}
\includegraphics{ti_graph}
\end{center}
$w_2 = 0$ $y$ $x$
$w_1$ $w_1 = 100$ $w_2$ $0$
\begin{center}
\begin{tabular}{c c}
\includegraphics{ti_graph-0} & \includegraphics{ti_graph-1}\\
\includegraphics{ti_graph-2} & \includegraphics{ti_graph-3}\\
\includegraphics{ti_graph-4} & \\
\end{tabular}
\end{center}
$s_x \equiv -b / w_1$
\begin{center}
\includegraphics{ti_graph_redux}
\end{center}
$x$ ~~ $w1 = 1000$~~
$w_2 = 0$ $x$ $x$
$y$ $w_2 = 1000$$x$
$0$ $w_1 = 0$ $y$
\begin{center}
\includegraphics{y_step}
\end{center}
$y$ $y$
$x$ $y$
$y$ $y$ $x$
$0$
$x$ $h$ $-h$
$h$
\begin{center}
\includegraphics{bump_3d}
\end{center}
$h$
$0.30$
$0.70$
$x$
$y$ $y$ $y$
$x$ $0$
\begin{center}
\includegraphics{bump_3d_y}
\end{center}
$y$ $y$ $x$ $y$
$x$ $0$
$x$ $y$
$h$
\begin{center}
\includegraphics{xy_bump}
\end{center}
$0$ $x$ $y$
$h$ $x$ $y$
\textbf{}
\begin{center}
\includegraphics{tower}
\end{center}
\begin{center}
\includegraphics{many_towers}
\end{center}
$2h$ $h$
{\serif
if-then-else}
\begin{lstlisting}[language=Python]
if input >= threshold:
output 1
else:
output 0
\end{lstlisting}
\begin{lstlisting}[language=Python]
if combined output from hidden neurons >= threshold:
output 1
else:
output 0
\end{lstlisting}
~~$3h/2$
S $h$ $b$
1{\serif
if-then-else} $h$ $-h$2$b$
{\serif if-then-else}
\begin{center}
\includegraphics{tower_construction}
\end{center}
$h$ {\serif if-then-else}
$b \approx -3h/2$
$h = 10$
\begin{center}
\includegraphics{tower_construction_2}
\end{center}
$h$
$h$ $b = -3h/2$
\textbf{}
\begin{center}
\includegraphics{the_two_towers}
\end{center}
\begin{center}
\includegraphics{many_towers_2}
\end{center}
$\sigma^{-1} \circ f$
$f$
$x_1, x_2, x_3$
\begin{center}
\includegraphics{tower_n_dim}
\end{center}
$x_1, x_2, x_3$ $s_1, t_1$ ~~
$s_1, t_1, s_2, \ldots$
$+h, -h$ $h$ $-5h/2$
$x_1$ $s_1$ $t_1$ $x_2$
$s_2$ $t_2$ $x_3$ $s_3$ $t_3$ $1$
$0$ $1$ $0$
$m$ $(-m+1/2)h$
%
$f(x_1,
\ldots, x_m) \in R^n$ $n$
$f^1(x_1, \ldots, x_m)$ $f^2(x_1, \ldots, x_m)$
$f^1$ $f^2$
\subsection*{}
\begin{itemize}
\item
a $x$ $y$
ba
c
c\hyperref[sec:fixing_up_the_step_functions]{}
\end{itemize}
\section{S }
\label{sec:extension_beyond_sigmoid_neurons}
S S
$x_1, x_2, \ldots$ $\sigma(\sum_j w_j x_j + b)$ $w_j$
$b$ $\sigma$ S
\begin{center}
\includegraphics{sigmoid}
\end{center}
$s(z)$
\begin{center}
\includegraphics{sigmoid_like}
\end{center}
$x_1, x_2, \ldots$ $w_1, w_2, \ldots$
$b$ $s(\sum_j w_j x_j + b)$
S
\begin{center}
\includegraphics{ramping}
\end{center}
$w = 100$
\begin{center}
\includegraphics{create_ramping}
\end{center}
S
$s(z)$ $s(z)$ $z
\rightarrow -\infty$ $z \rightarrow \infty$
$s(z)$
\subsection*{}
\begin{itemize}
\item
\hyperref[subsec:other_models_of_artificial_neuron]{}
\item $s(z) = z$
\end{itemize}
\section{}
\label{sec:fixing_up_the_step_functions}
\begin{center}
\includegraphics{failure}
\end{center}
~~
$f$
$\sigma^{-1} \circ f(x)$
\begin{center}
\includegraphics{inverted_function_2}
\end{center}
\begin{center}
\includegraphics{series_of_bumps}
\end{center}
$\sigma^{-1} \circ f(x)$
$\sigma^{-1}
\circ f(x) / 2$
\begin{center}
\includegraphics{half_bumps}
\end{center}
$\sigma^{-1} \circ f(x) / 2$
\begin{center}
\includegraphics{shifted_bumps}
\end{center}
$\sigma^{-1} \circ f(x) / 2$
$\sigma^{-1} \circ f(x)$
$2$
$M$ $\sigma^{-1} \circ f(x) / M$
$M$
\section{}
\label{sec:conclusion}
{\serif NAND}
\textbf{}
%
\hyperref[sec:toward_deep_learning]{}
\footnote{
\textbf{} Jen Dodd Chris Olah
Chris
Mike BostockAmit PatelBret Victor
Steven Wittens}
``` | /content/code_sandbox/chap4.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 3,186 |
```tex
% file: exercises_and_problems.tex
\chapter{}
\label{chap:ExercisesAndProblems}
``` | /content/code_sandbox/exercises_and_problems.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 26 |
```tex
% file: chap6.tex
\chapter{}
\label{ch:Deeplearning}
\hyperref[ch:WhyHardToTrain]{}
\hyperref[sec:convolutional_networks]{}
MNIST
\begin{center}
\includegraphics[width=64pt]{digits}
\end{center}
\gls*{pooling} GPU
\gls*{overfitting}\gls*{dropout}
\gls*{overfitting}
10,000 MNIST ~~
~~ 9,967 33
\begin{center}
\includegraphics[width=.75\textwidth]{ensemble_errors}
\end{center}
9 8 8
9
\gls*{rnn}\gls*{lstm}
\gls*{idui}
\gls*{bp}\gls*{regularization}\gls*{softmax-func}
MNIST
\section{}
\label{sec:convolutional_networks}
\begin{center}
\includegraphics[width=64pt]{digits}
\end{center}
\begin{center}
\includegraphics{tikz41}
\end{center}
$28 \times 28$ 784$= 28 \times 28$
\gls*{weight}\gls*{bias}~~~~
'0', '1', '2', $\ldots$, '8', '9'
\hyperref[98percent]{ 98\%
} \hyperref[sec:learning_with_gradient_descent]{MNIST
}
\textbf{}
\textbf{\gls{cnn}}\footnote{\gls*{cnn}
1970 1998
\href{path_to_url}{Gradient-based
learning applied to document recognition} Yann LeCun Lon
Bottou Yoshua Bengio Patrick HaffnerLeCun
\gls*{cnn}
\gls*{regularization}
\gls*{cnn}
}
\gls*{cnn}\textbf{\gls{lrf}}\textbf{\gls{shared-weights}}
\textbf{\gls{pooling}}\\
\textbf{\gls*{lrf}}
$28 \times 28$
$28 \times 28$
\begin{center}
\includegraphics{tikz42}
\end{center}
\gls*{hidden-layer}
$5 \times 5$ 25
\begin{center}
\includegraphics{tikz43}
\end{center}
\textbf{\gls*{lrf}}
\gls*{weight}\gls*{bias}
\gls*{lrf}
\gls*{lrf}\gls*{lrf}\gls*{hidden-layer}
\gls*{lrf}
\begin{center}
\includegraphics{tikz44}
\end{center}
\gls*{lrf}
\begin{center}
\includegraphics{tikz45}
\end{center}
\gls*{hidden-layer} $28 \times 28$ $5
\times 5$ \gls*{lrf}\gls*{hidden-layer} $24 \times 24$
\gls*{lrf} 23
23
\gls*{lrf}\textbf{}
$2$ \gls*{lrf} $2$
$1$
\footnote{
%
\hyperref[sec:how_to_choose_a_neural_network's_hyper-parameters]{}
\gls*{lrf}~~ $5 \times 5$ %
\gls*{lrf} $28 \times 28$ MNIST
\gls*{lrf}}\\
\textbf{\gls*{shared-weights}\gls*{bias}} \gls*{bias}
\gls*{lrf} $5 \times 5$ \gls*{weight} $24 \times 24$
\textbf{}\gls*{weight}\gls*{bias} $j, k$
\begin{equation}
\sigma\left(b + \sum_{l=0}^4 \sum_{m=0}^4 w_{l,m} a_{j+l, k+m} \right)
\label{eq:125}\tag{125}
\end{equation}
$\sigma$ ~~
\hyperref[sec:sigmoid_neurons]{\gls*{sigmoid-func}}$b$ \gls*{bias}
$w_{l,m}$ \gls*{weight} $5 \times 5$ $a_{x, y}$
$x, y$
\gls*{hidden-layer}\footnote{
}
\gls*{weight}\gls*{bias}
\gls*{lrf}
\footnote{
MNIST
MNIST
}
\gls*{hidden-layer}\textbf{}
\gls*{weight}\textbf{\gls*{shared-weights}}
\gls*{bias}\textbf{\gls*{bias}}\gls*{shared-weights}\gls*{bias}%
\textbf{}\textbf{}
\begin{center}
\includegraphics{tikz46}
\end{center}
3 $5 \times 5$
\gls*{shared-weights}\gls*{bias} 3
3
MNIST LeNet-5
6 $5 \times 5$ \gls*{lrf}
LeNet-5 20 40
\footnote{
\hyperref[final_conv]{}}
\begin{center}
\includegraphics[width=.65\textwidth]{net_full_layer_0}
\end{center}
20 20 $5 \times
5$ \gls*{lrf} $5 \times 5$ \gls*{weight}
\gls*{weight}
\gls*{weight}
\href{path_to_url}{Gabor }
Matthew Zeiler Rob Fergus 2013
\href{path_to_url}{Visualizing and Understanding
Convolutional Networks}
\gls*{shared-weights}\gls*{bias}
$25 = 5 \times 5$ \gls*{shared-weights}
\gls*{bias} $26$ $20$
$20 \times 26 = 520$
$784 = 28 \times 28$ $30$
$784 \times 30$ \gls*{weight} $30$
\gls*{bias} $23,550$ $40$
\textbf{}\textit{convolutional}~\eqref{eq:125}
\textbf{}\textit{convolution}
$a^1 = \sigma(b + w * a^0)$ $a^1$
$a^0$ $*$
\\
\textbf{\gls*{pooling}} \gls*{cnn}%
\textbf{\gls*{pooling}}\textit{pooling layers}\gls*{pooling}
\gls*{pooling}\footnote{
}
\gls*{pooling}
$2 \times 2$ \gls*{pooling}
\textbf{}\textit{max-pooling}\gls*{pooling}
\gls*{pooling} $2 \times 2$
\begin{center}
\includegraphics{tikz47}
\end{center}
$24 \times 24$ \gls*{pooling} $12
\times 12$
\gls*{pooling}
%
\gls*{pooling}
\begin{center}
\includegraphics{tikz48}
\end{center}
\gls*{pooling}
\gls*{pooling}
\gls*{pooling}\gls*{pooling}
\textbf{L2 \gls*{pooling}} $2 \times 2$
\gls*{pooling}L2
\gls*{pooling}
\gls*{pooling}
\gls*{pooling}
\\
\textbf{}
$10$ $10$
MNIST '0''1''2'
\begin{center}
\includegraphics{tikz49}
\end{center}
$28 \times 28$ MNIST
$5 \times 5$ \gls*{lrf} $3$
$3 \times 24 \times 24$ %
\gls*{pooling} $2 \times 2$ $3$ $3
\times 12 \times 12$
\gls*{pooling}%
\textbf{}
\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}
\gls*{sgd}\gls*{bp}
\gls*{bp}
\hyperref[ch:HowThebackpropagationalgorithmworks]{\gls*{bp}
}\gls*{pooling}
\hyperref[ch:HowThebackpropagationalgorithmworks]{
}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{bp}}\quad \gls*{bp}
\eqref{eq:bp1}--\eqref{eq:bp4}\hyperref[backpropsummary]{}
\gls*{pooling}
\gls*{bp}
\end{itemize}
\section{}
\label{seq:convolutional_neural_networks_in_practice}
\gls*{cnn}
MNIST
\lstinline!network3.py! \lstinline!network.py!
\lstinline!network2.py! \footnote{ \lstinline!network3.py!
Theano \gls*{cnn}
\href{path_to_url}{LeNet-5} Misha
Denil \href{path_to_url}{}
\href{path_to_url}{Chris Olah} }
\href{path_to_url}{GitHub}
\lstinline!network3.py!
\lstinline!network3.py!
\lstinline!network.py! \lstinline!network2.py! Python Numpy
\gls*{bp}\gls*{sgd}
\lstinline!network3.py!
\href{path_to_url}{Theano} \footnote{
\href{path_to_url~lisa/pointeurs/theano_scipy2010.pdf}{Theano:
A CPU and GPU Math Expression Compiler in Python} James Bergstra
Olivier Breuleux Frederic Bastien Pascal Lamblin Ravzan Pascanu
Guillaume Desjardins Joseph Turian David Warde-Farley Yoshua Bengio
2010 Theano
\href{path_to_url}{Pylearn2}
\href{path_to_url}{Keras}
\href{path_to_url}{Caffe}
\href{path_to_url}{Torch}} Theano \gls*{cnn}%
\gls*{bp}Theano
Theano CPU GPU GPU
Theano%
\href{path_to_url}{} Theano
Theano 0.6\footnote{Theano 0.7
Theano 0.7
} GPU Mac OS X Yosemite NVIDIA
GPU Ubuntu 14.04
\lstinline!networks3.py! \lstinline!networks3.py!
\lstinline!GPU! \lstinline!True! \lstinline!False!
Theano GPU %
\href{path_to_url}{
} Google Theano
GPU
\href{path_to_url}{Amazon Web Services} EC2 G2
GPU
CPU
CPU\\gls*{epoch}
\gls*{hidden-layer} $100$
60 \gls*{epoch}\gls*{learning-rate}$\eta =
0.1$\gls*{mini-batch} $10$\gls*{regularization}
\footnote{%
\href{path_to_url}{%
}}
\begin{lstlisting}[language=Python]
>>> import network3
>>> from network3 import Network
>>> from network3 import ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer
>>> training_data, validation_data, test_data = network3.load_data_shared()
>>> mini_batch_size = 10
>>> net = Network([
FullyConnectedLayer(n_in=784, n_out=100),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.1,
validation_data, test_data)
\end{lstlisting}
$97.80$\% \lstinline!test_data!
\gls*{epoch}\lstinline!validation_data!
\gls*{overfitting}\hyperref[validation_explanation]{
}\gls*{weight}\gls*{bias}
\footnote{
}
$97.80$\% \hyperref[chap3_98_04_percent]{}
$98.04$\%
$100$ \gls*{hidden-layer} $60$
\gls*{epoch}\gls*{mini-batch} $10$\gls*{learning-rate} $\eta = 0.1$
%
\hyperref[sec:overfitting_and_regularization]{\gls*{regularization}}
\gls*{overfitting}\gls*{regularization}
%
\gls*{regularization}S
\gls*{softmax}%
\hyperref[subsec:softmax]{}
~~\gls*{softmax}\gls*{log-likelihood}
$5 \times 5$
$1$$20$ \gls*{pooling}
$2 \times 2$ \gls*{pooling}
\begin{center}
\includegraphics{simple_conv}
\end{center}
\gls*{pooling}%
\gls*{lrf}
\footnote{ $10$
\gls*{mini-batch}\hyperref[mini_batch_size]{}
\gls*{mini-batch}\gls*{mini-batch}
}
\begin{lstlisting}[language=Python]
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2)),
FullyConnectedLayer(n_in=20*12*12, n_out=100),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.1,
validation_data, test_data)
\end{lstlisting}
$98.78$\%
\gls*{pooling}
\lstinline!network3.py! \lstinline!network3.py!
\lstinline!network3.py!
\subsection*{}
\begin{itemize}
\item --\gls*{pooling}\gls*{softmax}
\end{itemize}
$98.78$\%
--\gls*{pooling}--\gls*{pooling}
\gls*{hidden-layer} $5 \times 5$ \gls*{lrf}\gls*{pooling} $2
\times 2$ \gls*{hyper-params}
\begin{lstlisting}[language=Python]
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2)),
ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12),
filter_shape=(40, 20, 5, 5),
poolsize=(2, 2)),
FullyConnectedLayer(n_in=40*4*4, n_out=100),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.1,
validation_data, test_data)
\end{lstlisting}
$99.06$\%
--\gls*{pooling}
--\gls*{pooling} $12 \times 12$
--\gls*{pooling}
$20$
--\gls*{pooling} $20 \times 20 \times 12$
$20$ --\gls*{pooling}
--\gls*{pooling}--\gls*{pooling}
%
\gls*{lrf}\textbf{} $20 \times 5 \times 5$
--\gls*{pooling}\textbf{}
\gls*{lrf}\footnote{
3
%
\gls*{lrf}}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{tanh}}\quad %
\hyperref[subsec:other_models_of_artificial_neuron]{\gls*{tanh-func}}
\gls*{sigmoid-func}
S \gls*{tanh}
\gls*{tanh}\footnote{
\lstinline!activation_fn=tanh!
\lstinline!ConvPoolLayer! \lstinline!FullyConnectedLayer! }
S $20$ \gls*{epoch} $60$
$60$ \gls*{epoch}\gls*{tanh}
S \gls*{epoch} $60$ \gls*{epoch}
\gls*{tanh}
\gls*{tanh} S
\gls*{learning-rate}\footnote{
$\sigma(z) = (1+\tanh(z/2))/2$ }
\gls*{tanh} S \textbf{
\gls*{tanh}
\gls*{tanh}}
\end{itemize}
\textbf{\gls*{relu}} 1998
\footnote{\href{path_to_url}{"Gradient-based
learning applied to document recognition"} Yann LeCun Lon Bottou
Yoshua Bengio Patrick Haffner 1998
}
LeNet-5 MNIST
%
\hyperref[sec:other_models_of_artificial_neuron]{} S
$f(z) \equiv \max(0, z)$ $60$ %
\gls*{epoch}\gls*{learning-rate}$\eta = 0.03$
\hyperref[sec:overfitting_and_regularization]{L2 \gls*{regularization}}
\gls*{regularization} $\lambda = 0.1$
\begin{lstlisting}[language=Python]
>>> from network3 import ReLU
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12),
filter_shape=(40, 20, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4, n_out=100, activation_fn=ReLU),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.03,
validation_data, test_data, lmbda=0.1)
\end{lstlisting}
99.23\% S 99.06
S
S \gls*{tanh}
\footnote{ $\max(0, z)$ $z$ S
\hyperref[saturation]{}
}
\\
\textbf{}
shell
\lstinline!expand_mnist.py! \footnote{\lstinline!expand_mnist.py!
%
\href{path_to_url}{%
}}
\input{snippets/run_expand_mnist} % move to separate file to avoid syntax error caused by '$' in EMACS.
$50,000$ MNIST
$250,000$
\gls*{epoch}
~~ $5$
\gls*{overfitting}
$60$ \gls*{epoch}
\begin{lstlisting}[language=Python]
>>> expanded_training_data, _, _ = network3.load_data_shared(
"../data/mnist_expanded.pkl.gz")
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12),
filter_shape=(40, 20, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4, n_out=100, activation_fn=ReLU),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(expanded_training_data, 60, mini_batch_size, 0.03,
validation_data, test_data, lmbda=0.1)
\end{lstlisting}
99.37\% %
\hyperref[sec:other_techniques_for_regularization]{}
2003 SimardSteinkraus
Platt\footnote{\href{path_to_url}{Best
Practices for Convolutional Neural Networks Applied to Visual Document
Analysis} Patrice Simard Dave Steinkraus John
Platt 2003} MNIST
$99.6$\%--\gls*{pooling}
$100$ ~~
~~
MNIST
$99.6$\%
\subsection*{}
\begin{itemize}
\item
\end{itemize}
\textbf{}
$300$ $1,000$
$99.46$\% $99.43$\%99.37\%
$100$
\begin{lstlisting}[language=Python]
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12),
filter_shape=(40, 20, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4, n_out=100, activation_fn=ReLU),
FullyConnectedLayer(n_in=100, n_out=100, activation_fn=ReLU),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(expanded_training_data, 60, mini_batch_size, 0.03,
validation_data, test_data, lmbda=0.1)
\end{lstlisting}
99.43\%
$300$ $1,000$ $99.48$\%
$99.47$\%
\label{final_conv}
MNIST
\gls*{regularization}%
\gls*{overfitting}%
\hyperref[sec:other_techniques_for_regularization]{}
\begin{lstlisting}[language=Python]
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12),
filter_shape=(40, 20, 5, 5),
poolsize=(2, 2),
activation_fn=ReLU),
FullyConnectedLayer(
n_in=40*4*4, n_out=1000, activation_fn=ReLU, p_dropout=0.5),
FullyConnectedLayer(
n_in=1000, n_out=1000, activation_fn=ReLU, p_dropout=0.5),
SoftmaxLayer(n_in=1000, n_out=10, p_dropout=0.5)],
mini_batch_size)
>>> net.SGD(expanded_training_data, 40, mini_batch_size, 0.03,
validation_data, test_data)
\end{lstlisting}
$99.60$\%
$100$ $99.37$\%
\gls*{epoch} $40$\gls*{overfitting}
\gls*{hidden-layer} $1,000$ $100$
$300$ $1,000$ $1,000$
\\
\textbf{}
$5$
$99.6$\%
$5$
99.67\%
$33$ $10,000$
NMIST
\begin{center}
\includegraphics[width=.75\textwidth]{ensemble_errors}
\end{center}
6 5
6 0 5
3 8 9
6
9,967
\\
\textbf{}
\gls*{overfitting}
\gls*{shared-weights}
\gls*{regularization}\\
\textbf{} MNIST Rodrigo Benenson %
\href{path_to_url}{%
}
CireanMeier Gambardella Schmidhuber 2010
\footnote{\href{path_to_url}{Deep, Big, Simple Neural Nets
Excel on Handwritten Digit Recognition} Dan Claudiu Cirean Ueli
MeierLuca Maria Gambardella Jrgen Schmidhuber 2010}
$2,500$$2,000$$1,500$$1,000$ $500$ \gls*{hidden-layer} Simard
80
MNIST
99.65\%
GPU \gls*{epoch}
\gls*{learning-rate} $10^{-3}$ $10^{-6}$
\\
\textbf{} \hyperref[ch:WhyHardToTrain]{}
12
\gls*{regularization}\gls*{overfitting}
3 S ~~
$3$--$5$ 4 GPU
$40$ \gls*{epoch} $5$ MNIST
$30$ \gls*{epoch}3
4 $30$
\gls*{overfitting}
\hyperref[sec:the_cross-entropy_cost_function]{}
\hyperref[how_to_choose_a_neural_network's_hyper-parameters]{\gls*{weight}
}%
\hyperref[sec:other_techniques_for_regularization]{}
\\
\textbf{} --\gls*{pooling} $4$ \gls*{hidden-layer}
$4$ \gls*{hidden-layer}
\gls*{hidden-layer} $2$ \gls*{hidden-layer}2015
\gls*{hidden-layer}
$1$$2$ 00
~~
\\
\textbf{} \gls*{hidden-layer}
~~
\hyperref[sec:how_to_choose_a_neural_network's_hyper-parameters]{
}
\section{}
\label{sec:the_code_for_our_convolutional_networks}
\lstinline!network3.py!
\lstinline!network2.py! Theano
\lstinline!FullyConnectedLayer!
\begin{lstlisting}[language=Python]
class FullyConnectedLayer(object):
def __init__(self, n_in, n_out, activation_fn=sigmoid, p_dropout=0.0):
self.n_in = n_in
self.n_out = n_out
self.activation_fn = activation_fn
self.p_dropout = p_dropout
# Initialize weights and biases
self.w = theano.shared(
np.asarray(
np.random.normal(
loc=0.0, scale=np.sqrt(1.0/n_out), size=(n_in, n_out)),
dtype=theano.config.floatX),
name='w', borrow=True)
self.b = theano.shared(
np.asarray(np.random.normal(loc=0.0, scale=1.0, size=(n_out,)),
dtype=theano.config.floatX),
name='b', borrow=True)
self.params = [self.w, self.b]
def set_inpt(self, inpt, inpt_dropout, mini_batch_size):
self.inpt = inpt.reshape((mini_batch_size, self.n_in))
self.output = self.activation_fn(
(1-self.p_dropout)*T.dot(self.inpt, self.w) + self.b)
self.y_out = T.argmax(self.output, axis=1)
self.inpt_dropout = dropout_layer(
inpt_dropout.reshape((mini_batch_size, self.n_in)), self.p_dropout)
self.output_dropout = self.activation_fn(
T.dot(self.inpt_dropout, self.w) + self.b)
def accuracy(self, y):
"Return the accuracy for the mini-batch."
return T.mean(T.eq(y, self.y_out))
\end{lstlisting}
\lstinline!__init__!
\gls*{weight}
\gls*{weight} Theano
GPU
\href{path_to_url}{Theano }
sigmoid
\hyperref[sec:weight_initialization]{}\gls*{weight}
\gls*{tanh} Rectified Linear Function
\lstinline!__init__!
\lstinline!self.params = [self.W, self.b]!
\lstinline!Network.SGD! \lstinline!params!
\lstinline!set_inpt!
\lstinline!inpt! \lstinline!input! python \lstinline!input!
\lstinline!self.input! \lstinline!self.inpt_dropout!
dropout dropout
\lstinline!self.p_dropout! \lstinline!set_inpt!
\lstinline!dropout_layer!
\lstinline!self.inpt_dropout! \lstinline!self.output_dropout!
\lstinline!self.inpt! \lstinline!self.output!
\lstinline!ConvPoolLayer! \lstinline!SoftmaxLayer!
\lstinline!FullyConnectedLayer!
\lstinline!network3.py!
\lstinline!ConvPoolLayer! \lstinline!SoftmaxLayer!
Theano
max-pooling softmax
\hyperref[sec:softmax]{softmax layer}
\gls*{weight} sigmoid
\gls*{weight} sigmoid
\gls*{tanh} softmax
$0$ ad hoc
Network
\lstinline!__init__!
\begin{lstlisting}[language=Python]
class Network(object):
def __init__(self, layers, mini_batch_size):
"""Takes a list of `layers`, describing the network architecture, and
a value for the `mini_batch_size` to be used during training
by stochastic gradient descent.
"""
self.layers = layers
self.mini_batch_size = mini_batch_size
self.params = [param for layer in self.layers for param in layer.params]
self.x = T.matrix("x")
self.y = T.ivector("y")
init_layer = self.layers[0]
init_layer.set_inpt(self.x, self.x, self.mini_batch_size)
for j in xrange(1, len(self.layers)):
prev_layer, layer = self.layers[j-1], self.layers[j]
layer.set_inpt(
prev_layer.output, prev_layer.output_dropout, self.mini_batch_size)
self.output = self.layers[-1].output
self.output_dropout = self.layers[-1].output_dropout
\end{lstlisting}
\lstinline!self.params = [param for layer in ...]!
\lstinline!Network.SGD!
\lstinline!self.params! \lstinline!Network!
\lstinline!self.x = T.matrix("x")! \lstinline!self.y = T.ivector("y")!
Theano x y
Theano
Theano \gls*{pooling}
\begin{lstlisting}[language=Python]
init_layer.set_inpt(self.x, self.x, self.mini_batch_size)
\end{lstlisting}
mini-batch \gls*{mini-batch}
\lstinline!self.x!
dropoutdropout\lstinline!for!
\lstinline!self.x! \lstinline!Network!
\lstinline!output! \lstinline!output_dropout!
\lstinline!Network!
\lstinline!Network!
\lstinline!SGD!
\begin{lstlisting}[language=Python]
def SGD(self, training_data, epochs, mini_batch_size, eta,
validation_data, test_data, lmbda=0.0):
"""Train the network using mini-batch stochastic gradient descent."""
training_x, training_y = training_data
validation_x, validation_y = validation_data
test_x, test_y = test_data
# compute number of minibatches for training, validation and testing
num_training_batches = size(training_data)/mini_batch_size
num_validation_batches = size(validation_data)/mini_batch_size
num_test_batches = size(test_data)/mini_batch_size
# define the (regularized) cost function, symbolic gradients, and updates
l2_norm_squared = sum([(layer.w**2).sum() for layer in self.layers])
cost = self.layers[-1].cost(self)+\
0.5*lmbda*l2_norm_squared/num_training_batches
grads = T.grad(cost, self.params)
updates = [(param, param-eta*grad)
for param, grad in zip(self.params, grads)]
# define functions to train a mini-batch, and to compute the
# accuracy in validation and test mini-batches.
i = T.lscalar() # mini-batch index
train_mb = theano.function(
[i], cost, updates=updates,
givens={
self.x:
training_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size],
self.y:
training_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size]
})
validate_mb_accuracy = theano.function(
[i], self.layers[-1].accuracy(self.y),
givens={
self.x:
validation_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size],
self.y:
validation_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size]
})
test_mb_accuracy = theano.function(
[i], self.layers[-1].accuracy(self.y),
givens={
self.x:
test_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size],
self.y:
test_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size]
})
self.test_mb_predictions = theano.function(
[i], self.layers[-1].y_out,
givens={
self.x:
test_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size]
})
# Do the actual training
best_validation_accuracy = 0.0
for epoch in xrange(epochs):
for minibatch_index in xrange(num_training_batches):
iteration = num_training_batches*epoch+minibatch_index
if iteration
print("Training mini-batch number {0}".format(iteration))
cost_ij = train_mb(minibatch_index)
if (iteration+1)
validation_accuracy = np.mean(
[validate_mb_accuracy(j) for j in xrange(num_validation_batches)])
print("Epoch {0}: validation accuracy {1:.2
epoch, validation_accuracy))
if validation_accuracy >= best_validation_accuracy:
print("This is the best validation accuracy to date.")
best_validation_accuracy = validation_accuracy
best_iteration = iteration
if test_data:
test_accuracy = np.mean(
[test_mb_accuracy(j) for j in xrange(num_test_batches)])
print('The corresponding test accuracy is {0:.2
test_accuracy))
print("Finished training network.")
print("Best validation accuracy of {0:.2
best_validation_accuracy, best_iteration))
print("Corresponding test accuracy of {0:.2
\end{lstlisting}
x y \gls*{mini-batch}
Theano
\begin{lstlisting}[language=Python]
# define the (regularized) cost function, symbolic gradients, and updates
l2_norm_squared = sum([(layer.w**2).sum() for layer in self.layers])
cost = self.layers[-1].cost(self)+\
0.5*lmbda*l2_norm_squared/num_training_batches
grads = T.grad(cost, self.params)
updates = [(param, param-eta*grad)
for param, grad in zip(self.params, grads)]
\end{lstlisting}
\gls*{regularization}
Theano
\lstinline!cost! \lstinline!cost!
\lstinline!network3.py!
\lstinline!train_mini_batch! Theano
minibatch \lstinline!updates! \lstinline!Network!
\lstinline!validate_mb_accuracy! \lstinline!test_mb_accuracy!
minibatch \lstinline!Network!
\lstinline!SGD! ~~
\gls*{mini-batch}
\lstinline!network3.py!
\footnote{ GPU Theano GPU
mn@michaelnielsen.org}
\lstinputlisting[language=Python]{code_samples/src/network3.py}
\subsection*{}
\begin{itemize}
\item \lstinline!SGD! \gls*{epoch}
\hyperref[early_stopping]{}
\lstinline!network3.py!
\item \lstinline!Network!
\item \lstinline!SGD! $\eta$ \textbf{
\href{path_to_url#!topic/theano-users/NQ9NYLvleGc}{
}}
\item
\lstinline!network3.py! \textbf{
}
\item \lstinline!network3.py! \lstinline!load! \lstinline!save!
\item
\item \gls*{relu} S \gls*{tanh-func}
\hyperref[sec:weight_initialization]{}
\gls*{sigmoid-func} ReLU $c$
\gls*{weight} $c$ softmax
ReLU \gls*{sigmoid-func}
\textbf{
ReLU }
\item
%
\hyperref[sec:your_sha256_hashs_in_deep_neural_nets]{%
} sigmoid ReLU
\textbf{
}
\end{itemize}
\section{}
\label{sec:recent_progress_in_image_recognition}
1998 MNIST
GPU MNIST
~~
\gls*{regularization}
2100 2011 2015
\gls*{cnn}
2100
\\
\textbf{2012 LRMD } 2012
\footnote{\href{path_to_url}{Building
high-level features using large scale unsupervised learning} Quoc
LeMarc'Aurelio Ranzato Rajat Monga Matthieu Devin Kai Chen Greg
CorradoJeff Dean Andrew Ng 2012
LRMD
} LRMDLRMD
\href{path_to_url}{ImageNet}
2011 ImageNet 16,000,000 20,000
Mechanical Turk
ImageNet \footnote{ 2014 2011
ImageNet
ImageNet \href{path_to_url}{
ImageNet: a large-scale hierarchical image database} Jia
DengWei DongRichard Socher Li-Jia Li Kai Li Li
Fei-Fei 2009}
\begin{center}
\includegraphics[height=80pt]{imagenet1.jpg}%
\includegraphics[height=80pt]{imagenet2.jpg}%
\includegraphics[height=80pt]{imagenet3.jpg}%
\includegraphics[height=80pt]{imagenet4.jpg}
\end{center}
ImageNet \href{path_to_url}{}
MNIST
LRMD 15.8\% ImageNet
9.3\%
ImageNet\\
\textbf{2012 KSH } LRMD Krizhevsky,
Sutskever Hinton KSH
\footnote{\href{path_to_url~fritz/absps/imagenet.pdf}{ImageNet
classification with deep convolutional neural networks} Alex
KrizhevskyIlya Sutskever Geoffrey E. Hinton 2012} 2012
KSH \gls*{cnn} ImageNet
~~ImageNet Large-Scale Visual Recognition
ChallengeILSVRC
ILSVRC-2012 1,200,000 ImageNet 1,000
50,000 150,000 1,000
ILSVRC ImageNet
ImageNet
ImageNet $5$
$5$ KSH $84.7$\%
$73.8$\%
KSH $63.3$\%
KSH
KSH \gls*{cnn}
GPU GPU GPU NVIDIA
GeForce GTX 580 GPU
KSH $7$ $5$ \gls*{hidden-layer}\gls*{pooling}
$2$ $1,000$
$1,000$ KSH \footnote{ Ilya
Sutskever} $2$ $2$ GPU
\begin{center}
\includegraphics[width=.9\textwidth]{KSH}
\end{center}
$3 \times 224 \times 224$ $224 \times 224$
RBG ImageNet
KSH
$256$ $256 \times 256$
KSH $256 \times 256$ $224 \times 224$
\gls*{overfitting}
KSH $224 \times 224$
KSH
Alex
Krizhevsky \href{path_to_url}{cuda-convnet}
Theano
\footnote{\href{path_to_url}{Theano-based large-scale
visual recognition with multiple GPUs} Weiguang Ding Ruoyan
WangFei Mao Graham Taylor 2014}%
\href{path_to_url}{}
GPUCaffe
KSH
\href{path_to_url}{Model Zoo}\\
\textbf{2014 ILSVRC } 2012
2014 ILSVRC 2012 $120,000$
$1,000$ $5$
\footnote{\href{path_to_url}{Going deeper with
convolutions} Christian Szegedy Wei Liu Yangqing Jia Pierre
SermanetScott Reed Dragomir Anguelov Dumitru Erhan Vincent Vanhoucke
Andrew Rabinovich 2014} $22$
GoogLeNet LeNet-5 GoogLeNet 93.33\% $5$
2013 \href{path_to_url}{Clarifai}88.3\%2012
KSH84.7\%
GoogLeNet 93.33\% 2014
ILSVRC \footnote{\href{path_to_url}{ImageNet
large scale visual recognition challenge} Olga Russakovsky Jia
DengHao Su Jonathan Krause Sanjeev Satheesh Sean Ma Zhiheng
HuangAndrej Karpathy Aditya Khosla Michael Bernstein Alexander C.
Berg Li Fei-Fei2014}
ILSVRC Andrej
Karpathy %
\href{path_to_url}{%
} GoogLeNet
\begin{quote}
... 1000 5
ILSVRC
Amazon Mechanical Turk
GoogLeNet 1000
100~~
13--15\% GoogLeNet
... 1
...
... GoogLeNet 6.8\%...
5.1\% 1.7\%
\end{quote}
Karpathy
12.0\% top-5 GoogLeNet
top-5
\textbf{} 5.1\%
ILSVRC ~~
top-5
\\
\textbf{} ImageNet
Google
Google
\footnote{\href{path_to_url}{Multi-digit Number Recognition
from Street View Imagery using Deep Convolutional Neural Networks}
Ian J. Goodfellow Yaroslav Bulatov Julian Ibarz Sacha
Arnoud Vinay Shet2013} $100,000,000$
Google
Maps
OCR
2013
\footnote{\href{path_to_url}{Intriguing properties of
neural networks} Christian SzegedyWojciech Zaremba Ilya
Sutskever Joan Bruna Dumitru Erhan Ian Goodfellow Rob
Fergus 2013}
ImageNet
\begin{center}
\includegraphics[width=.75\textwidth]{adversarial.jpg}
\end{center}
KSH
\begin{quote}
\end{quote}
\footnote{\href{path_to_url}{Deep Neural Networks are
Easily Fooled: High Confidence Predictions for Unrecognizable Images}
Anh Nguyen Jason Yosinski Jeff Clune2014}
\section{}
\label{sec:other_approaches_to_deep_neural_nets}
MNIST
RNNBoltzmann Machine
\\
\textbf{\gls*{rnn}RNNs}
\textbf{\gls{rnn}} \textbf{RNN(s)}
RNN
\href{path_to_url}{ RNN
} RNN 13
RNN
RNN
RNN Turing %
\href{path_to_url}{ 2014 } RNN
python
python \href{path_to_url}{}
2014 RNN Turing
NTM
\lstinline!print(398345+42598)! Python
Web
RNN RNN
RNN RNN
RNN
to infinity and beyondtwo infinity and
beyondRNN
RNN
Google Android
\href{path_to_url}{Vincent Vanhoucke
2012-2015 }
RNN
RNN \gls*{bp}
RNN
RNN RNN \\
\textbf{\gls{lstm}LSTMs} RNNs
\hyperref[ch:WhyHardToTrain]{}
RNN
long short-term memory
RNN LSTM
\href{path_to_url}{Hochreiter Schmidhuber
1997 }LSTM RNN
LSTM \\
\textbf{} 2006
\textbf{\gls{dbn}}DBN\footnote{
Geoffrey Hinton, Simon Osindero Yee-Whye Teh 2006
\href{path_to_url~hinton/absps/fastnc.pdf}{A fast learning
algorithm for deep belief nets}, Geoffrey Hinton Ruslan Salakhutdinov
2006
\href{path_to_url}{Reducing the
dimensionality of data with neural networks}}DBN
RNN DBN DBN
DBN \textbf{}
DBN
DBN
DBN
Geoffrey Hinton
to recognize shapesfirst learn to generate images
DBN DBN
DBN
RNN
DBN
DBN
DBN
\href{path_to_url}{DBN }
\href{path_to_url~hinton/absps/guideTR.pdf}{}
DBN DBN Boltzmann
\\
\textbf{}
%
\href{path_to_url}{
}(see \href{path_to_url}{also this informative review
paper})%
\href{path_to_url}{
}%
\href{path_to_url}{}
%
\href{path_to_url~vmnih/docs/dqn.pdf}{}
\href{path_to_url}{
}
7 3
Playing Atari with
reinforcement learning
\section{}
\label{sec:on_the_future_of_neural_networks}
\textbf{}
\textbf{}
Google
[]?Google CEO Larry Page
\textbf{\gls{idui}}
SiriWolfram AlphaIBM Watson
2005
\textbf{}
\\
\textbf{}
1
1 10
\\
\textbf{}
1980
\gls*{bp} 1990
SVM
\gls*{overfitting}
ImageNet 10
\\
\textbf{}
AI
AI
\href{path_to_url}{Conway's law}
\begin{quote}
\end{quote}
Conway 747 747
dashboard dashboard
Conway
Conway
747
747
Conway
Conway Conway
~~
Conway
Conway
AI
Conway AI
AI 747
Werner
von Braun
Conway
Galen Hippocrates
deep\footnote{
deep
}
~~~~
\textbf{
} Conway
AI
AI
\footnote{
Yann LeCun
\href{path_to_url}{
}}Prolog
Prolog \href{path_to_url}{Eurisko}
Conway
SGD
AI
[]
AIConway
AI
AI
10
AI 60 10
``` | /content/code_sandbox/chap6.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 11,211 |
```tex
% file: chap2.tex
\chapter{}
\label{ch:HowTheBackpropagationAlgorithmWorks}
\hyperref[ch:UsingNeuralNetsToRecognizeHandwrittenDigits]{}
\gls*{weight}\gls*{bias}
\textbf{\gls{bp}}
\gls*{bp} 1970
\href{path_to_url}{David Rumelhart}
\href{path_to_url~hinton/}{Geoffrey Hinton}
\href{path_to_url}{Ronald Williams}
\href{path_to_url}{1986
}
\gls*{bp} $C$ \gls*{weight} $w$
\gls*{bias} $b$ $\partial C/\partial w$
\gls*{weight}\gls*{bias}
%
\gls*{bp}%
\gls*{weight}\gls*{bias}\gls*{bp}
\gls*{bp}
\section{}
\label{sec:warm_up}
\gls*{bp}%
\hyperref[sec:implementing_our_network_to_classify_digits]{}
\gls*{bp}
\gls*{weight} $w^l_{jk}$
$(l-1)^{\rm th}$ $k^{\rm th}$ $l^{\rm th}$ $j^{\rm th}$
\gls*{weight}
\gls*{weight}
\begin{center}
\includegraphics{tikz16}
\end{center}
$j$ $k$
\gls*{bias} $b^l_j$
$l^{\rm th}$ $j^{\rm th}$ \gls*{bias} $a^l_j$
$l^{\rm th}$ $j^{\rm th}$
\begin{center}
\includegraphics{tikz17}
\end{center}
$l^{\rm th}$ $j^{\rm th}$ $a^{l}_j$
$(l-1)^{\rm th}$ ~\eqref{eq:4}
\begin{equation}
a^{l}_j = \sigma\left( \sum_k w^{l}_{jk} a^{l-1}_k + b^l_j \right)
\label{eq:23}\tag{23}
\end{equation}
$(l-1)^{\rm th}$ $k$
$l$ \textbf{\gls*{weight}} $w^l$%
\gls*{weight} $w^l$ $l^{\rm th}$ \gls*{weight}
$j^{\rm th}$ $k^{\rm th}$ $w^l_{jk}$
$l$\textbf{\gls*{bias}}$b^l$
~~\gls*{bias} $b^l_j$
$l^{\rm th}$ $a^l$
$a^l_j$
$\sigma$~\eqref{eq:23}
$\sigma$ $v$
$\sigma(v)$
$\sigma(v)$ $\sigma(v)_j = \sigma(v_j)$
$f(x) = x^2$ $f$
\begin{equation}
f\left(\left[ \begin{array}{c} 2 \\ 3 \end{array} \right] \right)
= \left[ \begin{array}{c} f(2) \\ f(3) \end{array} \right]
= \left[ \begin{array}{c} 4 \\ 9 \end{array} \right]
\label{eq:24}\tag{24}
\end{equation}
$f$
~\eqref{eq:23}
\begin{equation}
a^{l} = \sigma(w^l a^{l-1}+b^l)
\label{eq:25}\tag{25}
\end{equation}
\gls*{weight}\gls*{bias}
$\sigma$
\footnote{ $w_{jk}^l$
$j$ $k$ ~\eqref{eq:25}
\gls*{weight}}
%
\hyperref[sec:implementing_our_network_to_classify_digits]{}
~\eqref{eq:25} $a^l$ $z^l \equiv w^l
a^{l-1}+b^l$ $z^l$ $l$ \textbf{
} $z^l$
~\eqref{eq:25} $a^l = \sigma(z^l)$
$z^l$ $z^l_j = \sum_k w^l_{jk} a^{l-1}_k+b^l_j$ $z^l_j$
$l$ $j$
\section{}
\label{sec:TwoAssumptionsWeNeedAboutTheCostFunction}
\gls*{bp} $C$ $w$ $b$ $\partial
C/\partial w$ $\partial C / \partial b$\gls*{bp}
~\eqref{eq:6}
\begin{equation}
C = \frac{1}{2n} \sum_x \|y(x)-a^L(x)\|^2
\label{eq:26}\tag{26}
\end{equation}
$n$ $x$$y = y(x)$
$L$ $a^L = a^L(x)$ $x$
\gls*{bp} $C$
$x$ $C_x$
$C=\frac{1}{n} \sum_x C_x$
$C_x = \frac{1}{2} ||y-a^L||^2$
\gls*{bp} $\partial
C_x/\partial w$ $\partial C_x/\partial b$
$\partial C/\partial w$ $\partial C/\partial b$
$x$ $C_x$
$C$
\begin{center}
\includegraphics{tikz18}
\end{center}
$x$
\begin{equation}
C = \frac{1}{2} \|y-a^L\|^2 = \frac{1}{2} \sum_j (y_j-a^L_j)^2
\label{eq:27}\tag{27}
\end{equation}
$y$
$y$ $x$
$y$ \gls*{weight}%
\gls*{bias} $C$
$a^L$ $y$
\section{Hadamard $s \odot t$}
\label{sec:the_hadamard_product}
\gls*{bp}~~
$s$ $t$ $s\odot
t$ \textbf{} $s\odot t$ $(s\odot t)_j = s_j
t_j$
\begin{equation}
\left[\begin{array}{c} 1 \\ 2 \end{array}\right]
\odot \left[\begin{array}{c} 3 \\ 4\end{array} \right]
= \left[ \begin{array}{c} 1 * 3 \\ 2 * 4 \end{array} \right]
= \left[ \begin{array}{c} 3 \\ 8 \end{array} \right]
\label{eq:28}\tag{28}
\end{equation}
\textbf{Hadamard }\textbf{Schur }
Hadamard \gls*{bp}
\section{}
\label{sec:the_four_fundamental_equations_behind_backpropagation}
\gls*{bp}\gls*{weight}\gls*{bias}
$\partial C/\partial w_{jk}^l$ $\partial C/\partial
b_j^l$$\delta_j^l$
$l^{th}$ $j^{th}$ \textbf{\gls{error}}
\gls*{bp} $\delta_j^l$ $\partial
C/\partial w_{jk}^l$ $\partial C/\partial b_j^l$
\begin{center}
\includegraphics{tikz19}
\end{center}
$l$ $j^{th}$
$\Delta z_j^l$
$\sigma(z_j^l)$ $\sigma(z_j^l + \Delta z_j^l)$
$\frac{\partial C}{\partial z_j^l} \Delta z_j^l$
$\Delta
z_j^l$ $\frac{\partial C}{\partial z_j^l}$
$\frac{\partial C}{\partial z_j^l}$ $\Delta
z_j^l$ $\frac{\partial C}{\partial z_j^l}$$0$
$z_j^l$
\footnote{ $\Delta z_j^l$
}
$\frac{\partial C}{\partial z_j^l}$
$l$ $j^{th}$ $\delta_j^l$
\begin{equation}
\delta^l_j \equiv \frac{\partial C}{\partial z^l_j}
\label{eq:29}\tag{29}
\end{equation}
$\delta^l$ $l$ \gls*{bp}
$\delta^l$
$\partial C/\partial w_{jk}^l$ $\partial C/\partial b_j^l$
$z_j^l$
$a_j^l$ $\frac{\partial C}{\partial a_j^l}$
\gls*{bp} $\delta_j^l =
\partial C / \partial z_j^l$ \footnote{
96.0\% 4.0\%
}\\
\textbf{} \gls*{bp}
$\delta^l$
\gls*{bp}
%
\hyperref[sec:proof_of_the_four_fundamental_equations]{}
%
\hyperref[sec:the_backpropagation_algorithm]{}%
\hyperref[sec:the_code_for_backpropagation]{}
Python \hyperref[sec:backpropagation_the_big_picture]{}
\gls*{bp}
\\
\textbf{$\delta^L$}
\begin{equation}
\delta^L_j = \frac{\partial C}{\partial a^L_j} \sigma'(z^L_j)
\label{eq:bp1}\tag{BP1}
\end{equation}
$\partial C/\partial a_j^L$
$j^{th}$ $C$ $j$
$\delta_j^L$ $\sigma'(z_j^L)$
$z_j^L$ $\sigma$
\eqref{eq:bp1}
$z_j^L$ $\sigma'(z_j^L)$
$\partial C/\partial a_j^L$
$\partial C/\partial a_j^L$
$C = \frac{1}{2} \sum_j(y_j-a_j)^2$ $\partial C/\partial a_j^L = (a_j -
y_j)$
~\eqref{eq:bp1} $\delta^L$
\begin{equation}
\delta^L = \nabla_a C \odot \sigma'(z^L)
\label{eq:bp1a}\tag{BP1a}
\end{equation}
$\nabla_a C$ $\partial C/\partial a_j^L$
$\nabla_a C$ $C$ ~\eqref{eq:bp1}
~\eqref{eq:bp1a} \eqref{eq:bp1}
$\nabla_a C = (a^L - y)$
\eqref{eq:bp1}
\begin{equation}
\delta^L = (a^L-y) \odot \sigma'(z^L)
\label{eq:30}\tag{30}
\end{equation}
Numpy \\
\textbf{ $\delta^{l+1}$ $\delta^l$}
\begin{equation}
\delta^l = ((w^{l+1})^T \delta^{l+1}) \odot \sigma'(z^l)
\label{eq:bp2}\tag{BP2}
\end{equation}
$(w^{l+1})^T$ $(l+1)^{\rm th}$ \gls*{weight} $w^{l+1}$
$l+1^{\rm th}$
$\delta^{l+1}$\gls*{weight} $(w^{l+1})^T$
\textbf{} $l^{\rm th}$
Hadamard $\odot \sigma'(z^l)$
$l$ $l$ $\delta$
~\eqref{eq:bp1} ~\eqref{eq:bp2} $\delta^l$
~\eqref{eq:bp1} $\delta^L$~\eqref{eq:bp2}
$\delta^{L-1}$~\eqref{eq:bp2} $\delta^{L-2}$
\gls*{bp}\\
\textbf{\gls*{bias}}
\begin{equation}
\frac{\partial C}{\partial b^l_j} = \delta^l_j
\label{eq:bp3}\tag{BP3}
\end{equation}
$\delta^l_j$ $\partial C / \partial b^l_j$ \textbf{
} \eqref{eq:bp1} \eqref{eq:bp2}
$\delta^l_j$ \eqref{eq:bp3}
\begin{equation}
\frac{\partial C}{\partial b} = \delta
\label{eq:31}\tag{31}
\end{equation}
$\delta$ \gls*{bias} $b$ \\
\textbf{\gls*{weight}}
\begin{equation}
\frac{\partial C}{\partial w^l_{jk}} = a^{l-1}_k \delta^l_j
\label{eq:bp4}\tag{BP4}
\end{equation}
$\partial C/\partial w_{jk}^l$ $\delta^l$
$a^{l-1}$
\begin{equation}
\frac{\partial
C}{\partial w} = a_{\rm in} \delta_{\rm out}
\label{eq:32}\tag{32}
\end{equation}
$a_{\rm in}$ \gls*{weight} $w$ $\delta_{\rm out}$
\gls*{weight} $w$ \gls*{weight} $w$
\gls*{weight}
\begin{center}
\includegraphics{tikz20}
\end{center}
~\eqref{eq:32} $a_{\rm in}$ $a_{\rm in}
\approx 0$ $\partial C/\partial w$ %
\gls*{weight}\textbf{}\gls*{weight}
\eqref{eq:bp4} \gls*{weight}
\eqref{eq:bp1}--\eqref{eq:bp4}
~\eqref{eq:bp1} $\sigma'(z_k^l)$%
\hyperref[fig:StepFunction]{S} $\sigma(z^L_j)$ $0$
$1$ $\sigma$ $\sigma'(z^L_j) \approx 0$
$\approx 0$$\approx 1$
\gls*{weight}\textbf{}\gls*{weight}
\gls*{bias}
~\eqref{eq:bp2}
$\sigma'(z^l)$$\delta_j^l$
\gls*{weight}\footnote{ ${w^{l+1}}^T
\delta^{l+1}$ $\sigma'(z_k^l)$
}
\gls*{weight}
\textbf{}
S $\sigma$ $\sigma'$
$0$S
\eqref{eq:bp1}--\eqref{eq:bp4}
\begin{center}
\begin{minipage}{0.7\textwidth}
\begin{framed}
\centering
\textbf{\gls*{bp}}\label{backpropsummary}\\
\vspace{1.5ex}
\begin{tabular}{ll}
$\delta^L = \nabla_a C \odot \sigma'(z^L)$ & \hspace{2cm}\eqref{eq:bp1} \\[1.5ex]
$\delta^l = ((w^{l+1})^T \delta^{l+1}) \odot \sigma'(z^l)$ & \hspace{2cm}\eqref{eq:bp2} \\[1.5ex]
$\frac{\partial C}{\partial b^l_j} = \delta^l_j$ & \hspace{2cm}\eqref{eq:bp3} \\[1.5ex]
$\frac{\partial C}{\partial w^l_{jk}} = a^{l-1}_k \delta^l_j$ & \hspace{2cm}\eqref{eq:bp4}
\end{tabular}
\end{framed}
\end{minipage}
\end{center}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{bp}} Hadamard
\gls*{bp}~\eqref{eq:bp1} ~\eqref{eq:bp2}
1~\eqref{eq:bp1}
\begin{equation}
\delta^L = \Sigma'(z^L) \nabla_a C
\label{eq:33}\tag{33}
\end{equation}
$\Sigma'(z^L)$ $\sigma'(z_j^L)$
$0$ $\nabla_a C$ 2
~\eqref{eq:bp2}
\begin{equation}
\delta^l = \Sigma'(z^l) (w^{l+1})^T \delta^{l+1}
\label{eq:34}\tag{34}
\end{equation}
312
\begin{equation}
\delta^l = \Sigma'(z^l) (w^{l+1})^T \ldots \Sigma'(z^{L-1}) (w^L)^T
\Sigma'(z^L) \nabla_a C
\label{eq:35}\tag{35}
\end{equation}
\eqref{eq:bp1} \eqref{eq:bp2}
Hadamard
\end{itemize}
\section{}
\label{sec:proof_of_the_four_fundamental_equations}
\eqref{eq:bp1}--\eqref{eq:bp4}
\href{path_to_url}{}%
~\eqref{eq:bp1} $\delta^L$
\begin{equation}
\delta^L_j = \frac{\partial C}{\partial z^L_j}
\label{eq:36}\tag{36}
\end{equation}
\begin{equation}
\delta^L_j = \sum_k \frac{\partial C}{\partial a^L_k} \frac{\partial a^L_k}{\partial z^L_j}
\label{eq:37}\tag{37}
\end{equation}
$k$ $k^{\rm th}$
$a^L_k$ $k=j$ $j^{\rm th}$ \gls*{weight}
$z^L_j$ $k \neq j$ $\partial a^L_k / \partial z^L_j$
\begin{equation}
\delta^L_j = \frac{\partial C}{\partial a^L_j} \frac{\partial a^L_j}{\partial z^L_j}
\label{eq:38}\tag{38}
\end{equation}
$a^L_j = \sigma(z^L_j)$ $\sigma'(z^L_j)$
\begin{equation}
\delta^L_j = \frac{\partial C}{\partial a^L_j} \sigma'(z^L_j)
\label{eq:39}\tag{39}
\end{equation}
~\eqref{eq:bp1}
~\eqref{eq:bp2} $\delta^{l+1}$
$\delta^l$ $\delta^{l+1}_k = \partial C / \partial
z^{l+1}_k$ $\delta^l_j = \partial C / \partial z^l_j$
\begin{align}
\delta^l_j &= \frac{\partial C}{\partial z^l_j} \label{eq:40}\tag{40}\\
&= \sum_k \frac{\partial C}{\partial z^{l+1}_k} \frac{\partial z^{l+1}_k}{\partial z^l_j} \label{eq:41}\tag{41}\\
&= \sum_k \frac{\partial z^{l+1}_k}{\partial z^l_j} \delta^{l+1}_k \label{eq:42}\tag{42}
\end{align}
$\delta^{l+1}_k$
\begin{equation}
z^{l+1}_k = \sum_j w^{l+1}_{kj} a^l_j +b^{l+1}_k = \sum_j w^{l+1}_{kj} \sigma(z^l_j) +b^{l+1}_k
\label{eq:43}\tag{43}
\end{equation}
\begin{equation}
\frac{\partial z^{l+1}_k}{\partial z^l_j} = w^{l+1}_{kj} \sigma'(z^l_j)
\label{eq:44}\tag{44}
\end{equation}
~\eqref{eq:42}
\begin{equation}
\delta^l_j = \sum_k w^{l+1}_{kj} \delta^{l+1}_k \sigma'(z^l_j)
\label{eq:45}\tag{45}
\end{equation}
~\eqref{eq:bp2}
~\eqref{eq:bp3} ~\eqref{eq:bp4}
\subsection*{}
\begin{itemize}
\item ~\eqref{eq:bp3} ~\eqref{eq:bp4}
\end{itemize}
\gls*{bp}
\gls*{bp}
\gls*{bp}~~
\section{}
\label{sec:the_backpropagation_algorithm}
\gls*{bp}
\begin{enumerate}
\item \textbf{ $x$} $a^{1}$
\item \textbf{} $l=2,3,...,L$ $z^l = w^la^{l-1} +
b^l$ $a^l = \sigma(z^l)$
\item \textbf{ $\delta^L$} $\delta^L = \nabla_a C \odot
\sigma'(z^L)$
\item \textbf{} $l=L-1, L-2,...,2$
$\delta^l = ((w^{l+1})^T\delta^{l+1})\odot \sigma'(z^l)$
\item \textbf{} $\frac{\partial C}{\partial w^l_{jk}} =
a^{l-1}_k \delta^l_j$ $\frac{\partial C}{\partial b_j^l} = \delta_j^l$
\end{enumerate}
\textbf{}
$\delta^l$
\gls*{weight}\gls*{bias}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{bp}}\quad
$f(\sum_j w_jx_j + b)$ $f$ S
\gls*{bp}
\item \textbf{\gls*{bp}}\quad $\sigma$
$\sigma(z) = z$\gls*{bp}
\end{itemize}
\gls*{bp}$C=C_x$
\gls*{bp}
$m$ \gls*{mini-batch}
\gls*{mini-batch}
\begin{enumerate}
\item \textbf{}
\item \textbf{ $x$} $a^{x,1}$
\begin{itemize}
\item \textbf{} $l=2,3,...,L$ $z^{x,l} = w^la^{x,l-1} +
b^l$ $a^{x,l} = \sigma(z^{x,l})$
\item \textbf{ $\delta^{x,L}$}
$\delta^{x,L} = \nabla_a C_x \odot \sigma'(z^{x,L})$
\item \textbf{\gls*{bp}} $l=L-1, L-2, ..., 2$
$\delta^{x,l} = ((w^{l+1})^T\delta^{x,l+1})\odot \sigma'(z^{x,l})$
\end{itemize}
\item \textbf{} $l=L-1, L-2, ..., 2$ $w^l \rightarrow w^l
- \frac{\eta}{m}\sum_x \delta^{x,l}(a^{x,l-1})^T$ $b^l \rightarrow b^l -
\frac{\eta}{m}\sum_x \delta^{x,l}$ \gls*{weight}\gls*{bias}
\end{enumerate}
\gls*{mini-batch}
\gls*{epoch}
\section{}
\label{sec:the_code_for_backpropagation}
\gls*{bp}\gls*{bp}
\hyperref[sec:implementing_our_network_to_classify_digits]{}
\lstinline!Network! \lstinline!update_mini_batch!
\lstinline!backprop!
\lstinline!update_mini_batch! \lstinline!mini_batch!
\lstinline!Network! \gls*{weight}\gls*{bias}
\begin{lstlisting}[language=Python]
class Network(object):
...
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The "mini_batch" is a list of tuples "(x, y)", and "eta"
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
\end{lstlisting}
\lstinline!delta_nabla_b!%
\lstinline!delta_nabla_w = self.backprop(x, y)!
\lstinline!backprop!
$\partial C_x/\partial b_j^l$ $\partial C_x/\partial w_{jk}^l$
\lstinline!backprop! ~~
Python ~~
\lstinline!l[-3]!
\lstinline!backprop!
$\sigma$ $\sigma'$
%
\hyperref[sec:implementing_our_network_to_classify_digits]{
}
\begin{lstlisting}[language=Python]
class Network(object):
...
def backprop(self, x, y):
"""Return a tuple "(nabla_b, nabla_w)" representing the
gradient for the cost function C_x. "nabla_b" and
"nabla_w" are layer-by-layer lists of numpy arrays, similar
to "self.biases" and "self.weights"."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
...
def cost_derivative(self, output_activations, y):
"""Return the vector of partial derivatives \partial C_x /
\partial a for the output activations."""
return (output_activations-y)
def sigmoid(z):
"""The sigmoid function."""
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z):
"""Derivative of the sigmoid function."""
return sigmoid(z)*(1-sigmoid(z))
\end{lstlisting}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{mini-batch}\gls*{bp}}\quad
\gls*{mini-batch}%
\gls*{bp}\gls*{mini-batch}
$X=[x_1, x_2, ..., x_m]$%
\gls*{mini-batch}$x$\gls*{weight}
\gls*{bias}S
\gls*{bp} \lstinline!network.py!
%
\gls*{mini-batch}MNIST
2 %
\gls*{bp}
\end{itemize}
\section{}
\gls*{bp}
5060
%
\gls*{weight} $C = C(w)$\gls*{bias}%
\gls*{weight} $w_1, w_2, \ldots$ \gls*{weight} $w_j$
$\partial C / \partial w_j$
\begin{equation}
\frac{\partial
C}{\partial w_{j}} \approx \frac{C(w+\epsilon
e_j)-C(w)}{\epsilon}
\label{eq:46}\tag{46}
\end{equation}
$\epsilon > 0$ $e_j$ $j$
$w_j$ $C$ $\partial
C/\partial w_j$~\eqref{eq:46} $\partial
C/\partial b$
$1,000,000$ \gls*{weight}\gls*{weight} $w_j$
$C(w+\epsilon e_j)$ $\partial C/\partial w_j$
$1, 000, 000 $ $1, 000, 000$
$C(w)$ $1,000,001$
\gls*{bp}\textbf{} $\partial
C/\partial w_j$
\footnote{
\gls*{weight}\gls*{bp}
\gls*{weight}}%
\gls*{bp}\gls*{bp}
\gls*{bp}~\eqref{eq:46}
1986
\gls*{bp} 1980
\gls*{bp}
\gls*{bp}
\section{}
\label{sec:backpropagation_the_big_picture}
\gls*{bp}
\gls*{bp}
$w_{jk}^l$
$\Delta w_{jk}^l$
\begin{center}
\includegraphics{tikz22}
\end{center}
\begin{center}
\includegraphics{tikz23}
\end{center}
\textbf{}
\begin{center}
\includegraphics{tikz24}
\end{center}
\begin{center}
\includegraphics{tikz25}
\end{center}
$\Delta C$ $\Delta w_{jk}^l$
\begin{equation}
\Delta C \approx \frac{\partial C}{\partial w^l_{jk}} \Delta w^l_{jk}
\label{eq:47}\tag{47}
\end{equation}
$\frac{\partial C}{\partial w_{jk}^l}$
$w_{jk}^l$ $C$
$\partial C /
\partial w^l_{jk}$
$\Delta w_{jk}^l$ $l^{th}$ $j^{th}$
$\Delta a_j^l$
\begin{equation}
\Delta a^l_j \approx \frac{\partial a^l_j}{\partial w^l_{jk}} \Delta w^l_{jk}
\label{eq:48}\tag{48}
\end{equation}
$\Delta a_j^l$ $(l+1)^{\rm th}$ \textbf{}
$a_q^{l+1}$
\begin{center}
\includegraphics{tikz26}
\end{center}
\begin{equation}
\Delta a^{l+1}_q \approx \frac{\partial a^{l+1}_q}{\partial a^l_j} \Delta
a^l_j
\label{eq:49}\tag{49}
\end{equation}
~\eqref{eq:48}
\begin{equation}
\Delta a^{l+1}_q \approx \frac{\partial a^{l+1}_q}{\partial a^l_j}
\frac{\partial a^l_j}{\partial w^l_{jk}} \Delta w^l_{jk}
\label{eq:50}\tag{50}
\end{equation}
$\Delta a^{l+1}_q$
$w_{jk}^l$ $C$
$a_j^l, a_q^{l+1},
...,a_n^{L-1},a_m^{L}$
\begin{equation}
\Delta C \approx \frac{\partial C}{\partial a^L_m}
\frac{\partial a^L_m}{\partial a^{L-1}_n}
\frac{\partial a^{L-1}_n}{\partial a^{L-2}_p} \ldots
\frac{\partial a^{l+1}_q}{\partial a^l_j}
\frac{\partial a^l_j}{\partial w^l_{jk}} \Delta w^l_{jk}
\label{eq:51}\tag{51}
\end{equation}
$\partial a/\partial a$
$\partial C/\partial a_m^L$ $C$
$w_{jk}^l$
$C$
\begin{equation}
\Delta C \approx \sum_{mnp\ldots q} \frac{\partial C}{\partial a^L_m}
\frac{\partial a^L_m}{\partial a^{L-1}_n} \frac{\partial a^{L-1}_n}{\partial
a^{L-2}_p} \ldots \frac{\partial a^{l+1}_q}{\partial a^l_j} \frac{\partial
a^l_j}{\partial w^l_{jk}} \Delta w^l_{jk}
\label{eq:52}\tag{52}
\end{equation}
~\eqref{eq:47}
\begin{equation}
\frac{\partial C}{\partial w^l_{jk}} = \sum_{mnp\ldots q} \frac{\partial
C}{\partial a^L_m} \frac{\partial a^L_m}{\partial a^{L-1}_n} \frac{\partial
a^{L-1}_n}{\partial a^{L-2}_p} \ldots \frac{\partial a^{l+1}_q}{\partial
a^l_j} \frac{\partial a^l_j}{\partial w^l_{jk}}
\label{eq:53}\tag{53}
\end{equation}
~\eqref{eq:53}
$C$ \gls*{weight}
\gls*{weight}
$\partial a_j^l/\partial w_{jk}^l$
$\partial C/\partial w_{jk}^l$
\gls*{weight}
\begin{center}
\includegraphics{tikz27}
\end{center}
\gls*{weight}
~\eqref{eq:53}
\gls*{bp}\gls*{bp}
\gls*{bp}\gls*{weight}\gls*{bias}
\gls*{bp}
~~\gls*{bp}
\gls*{bp}
\footnote{
~\eqref{eq:53} $a_q^{l+1}$
$z^{l+1}_q$
$a_q^{l+1}$
}
``` | /content/code_sandbox/chap2.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 8,685 |
```tex
% cjkfonts.sty
%
% A XeLaTeX package for typesetting CJK documents.
%
% Options:
% default: boolean option, cjkfonts is set as the default font family and as the sans serif family for CJK text.
% Identification
% ==============
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{cjkfonts}[2015/12/12 A simple XeLaTeX package to set CJK fonts]
% Required Packages
% =================
\RequirePackage{ifthen}
\RequirePackage{xeCJK}
% Set key-value options
\RequirePackage{kvoptions}
\DeclareBoolOption[false]{default}
\ProcessKeyvalOptions*
%% Configuration for parindent
%% ===========================
\def\elegant@CJKChar@size{\hskip \f@size \p@}
\newdimen\elegant@CJKChar@size@dimen
\settowidth\elegant@CJKChar@size@dimen{\elegant@CJKChar@size\CJKglue}
\setlength{\parindent}{2\elegant@CJKChar@size@dimen}
%% Configuration for fonts
%% =======================
\newCJKfontfamily[NotoSansSC]\NotoSansSC[
UprightFont=NotoSansCJKsc-Light,
BoldFont=NotoSansCJKsc-Bold,
ItalicFont=NotoSansCJKsc-Light,
BoldItalicFont=NotoSansCJKsc-Bold,
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSansSC}
\newCJKfontfamily[NotoSansMonoSC]\NotoSansMonoSC[
UprightFont=NotoSansMonoCJKsc-Regular,
BoldFont=NotoSansMonoCJKsc-Bold,
ItalicFont=NotoSansMonoCJKsc-Regular,
BoldItalicFont=NotoSansMonoCJKsc-Bold,
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSansMonoSC}
\newCJKfontfamily[NotoSansSCThin]\NotoSansSCThin[
UprightFont=NotoSansCJKsc-Thin,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCLight]\NotoSansSCLight[
UprightFont=NotoSansCJKsc-Light,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCDemiLight]\NotoSansSCDemiLight[
UprightFont=NotoSansCJKsc-DemiLight,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCRegular]\NotoSansSCRegular[
UprightFont=NotoSansCJKsc-Regular,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCMedium]\NotoSansSCMedium[
UprightFont=NotoSansCJKsc-Medium,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCBold]\NotoSansSCBold[
UprightFont=NotoSansCJKsc-Bold,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansSCBlack]\NotoSansSCBlack[
UprightFont=NotoSansCJKsc-Black,
AutoFakeSlant=true]{NotoSansSC}
\newCJKfontfamily[NotoSansMonoSCRegular]\NotoSansMonoSCRegular[
UprightFont=NotoSansMonoCJKsc-Regular,
AutoFakeSlant=true]{NotoSansMonoSCRegular}
\newCJKfontfamily[NotoSansMonoSCBold]\NotoSansMonoSCBold[
UprightFont=NotoSansMonoCJKsc-Bold,
AutoFakeSlant=true]{NotoSansMonoSCBold}
\newCJKfontfamily[NotoSerifSC]\NotoSerifSC[
UprightFont=NotoSerifCJKsc-Light,
BoldFont=NotoSerifCJKsc-Bold,
ItalicFont=NotoSerifCJKsc-Light,
BoldItalicFont=NotoSerifCJKsc-Bold,
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCThin]\NotoSerifSCThin[
UprightFont=NotoSerifCJKsc-Thin,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCLight]\NotoSerifSCLight[
UprightFont=NotoSerifCJKsc-Light,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCDemiLight]\NotoSerifSCDemiLight[
UprightFont=NotoSerifCJKsc-DemiLight,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCRegular]\NotoSerifSCRegular[
UprightFont=NotoSerifCJKsc-Regular,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCMedium]\NotoSerifSCMedium[
UprightFont=NotoSerifCJKsc-Medium,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCBold]\NotoSerifSCBold[
UprightFont=NotoSerifCJKsc-Bold,
AutoFakeSlant=true]{NotoSerifSC}
\newCJKfontfamily[NotoSerifSCBlack]\NotoSerifSCBlack[
UprightFont=NotoSerifCJKsc-Black,
AutoFakeSlant=true]{NotoSerifSC}
\ifthenelse{\boolean{cjkfonts@default}}{
\setCJKmainfont[
UprightFont={NotoSerifCJKsc-Light},
BoldFont={NotoSerifCJKsc-Bold},
ItalicFont={NotoSerifCJKsc-Light},
BoldItalicFont={NotoSerifCJKsc-Bold},
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSerifSC}
\setCJKsansfont[
UprightFont={NotoSansCJKsc-Light},
BoldFont={NotoSansCJKsc-Bold},
ItalicFont={NotoSansCJKsc-Light},
BoldItalicFont={NotoSansCJKsc-Bold},
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSansSC}
\setCJKmonofont[
UprightFont={NotoSansCJKsc-Light},
BoldFont={NotoSansCJKsc-Bold},
ItalicFont={NotoSansCJKsc-Light},
BoldItalicFont={NotoSansCJKsc-Bold},
ItalicFeatures=FakeSlant,
BoldItalicFeatures=FakeSlant]{NotoSansMonoSC}
}{}
%% This must be the last command
\endinput
``` | /content/code_sandbox/cjkfonts.sty | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 1,527 |
```tex
% file: preface.tex
\chapter{}
\label{chap:Introduction}
\begin{itemize}
\item
\item
\end{itemize}
\hyperref[ch:About]{}
\hyperref[ch:UsingNeuralNetsToRecognizeHandwrittenDigits]{}
``` | /content/code_sandbox/preface.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 62 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,a4paper,oneside]{book}
\usepackage[margin=2.5cm]{geometry}
\input{main}
``` | /content/code_sandbox/nndl-ebook.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 53 |
```tex
% file: acknowledgements.tex
\chapter{}
\label{ch:acknowledgements}
Paul BlooreChris DawsonAndrew DohertyIlya GrigorikAlex
KosorukoffChris Olah Rob Spekkens
Rob Chris
Yoshua Bengio
``` | /content/code_sandbox/acknowledgements.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 58 |
```tex
% file: faq.tex
\chapter{Frequently Asked Questions}
\begin{center}
\begin{tikzpicture}[
inner sep=0pt,
minimum size=10mm,
background rectangle/.style={
draw=gray!25,
fill=gray!10,
rounded corners
},
show background rectangle]
%\pgfkeys{/pgf/number format/showpos,precision=2,use period}
\node(o) {\footnotesize Number: $\pgfmathprintnumber{0.012345}$};
\end{tikzpicture}
\end{center}
``` | /content/code_sandbox/faq.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 137 |
```tex
% file: chap5.tex
\chapter{}
\label{ch:WhyHardToTrain}
{\serif AND}{\serif OR}
\begin{center}
\includegraphics{shallow_circuit}
\end{center}
{\serif AND}{\serif NAND}~~
{\serif AND}
\begin{center}
\includegraphics{circuit_multiplication}
\end{center}
1980\footnote{
Johan
Hstad 2012 \href{path_to_url}{On the
correlation of parity and small-depth circuits} }
\begin{center}
\includegraphics{tikz35}
\end{center}
98\%
\begin{center}
\includegraphics{tikz36}
\end{center}
\footnote{Razvan Pascanu,
Guido Montfar, and Yoshua Bengio 2014
\href{path_to_url}{On the number of response regions of
deep feed forward networks with piece-wise linear activations}
Yoshua Bengio 2009
\href{path_to_url~bengioy/papers/ftml_book.pdf}{Learning deep
architectures for AI} }
~~\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}%
\hyperref[sec:learning_with_gradient_descent]{}~~
\section{}
\label{sec:the_vanishing_gradient_problem}
MNIST \footnote{ MNIST %
\hyperref[sec:learning_with_gradient_descent]{}%
\hyperref[sec:implementing_our_network_to_classify_digits]{}}
Python 2.7Numpy
\begin{lstlisting}[language=sh]
git clone path_to_url
\end{lstlisting}
\lstinline!git!%
\href{path_to_url}{
} \lstinline!src!
Python MNIST
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
\end{lstlisting}
\begin{lstlisting}[language=Python]
>>> import network2
>>> net = network2.Network([784, 30, 10])
\end{lstlisting}
784 $28 \times 28 = 784$
30 10 10 MNIST
('0', '1', '2', ..., 9)
30 \gls*{epoch}\gls*{mini-batch} 10 $\eta = 0.1$
\gls*{regularization} $\lambda = 5.0$ \lstinline!validation_data!
\footnote{
}
\begin{lstlisting}[language=Python]
>>> net.SGD(training_data, 30, 10, 0.1, lmbda=5.0,
... evaluation_data=validation_data, monitor_evaluation_accuracy=True)
\end{lstlisting}
96.48\%
30
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 30, 30, 10])
>>> net.SGD(training_data, 30, 10, 0.1, lmbda=5.0,
... evaluation_data=validation_data, monitor_evaluation_accuracy=True)
\end{lstlisting}
96.90\%
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 30, 30, 30, 10])
>>> net.SGD(training_data, 30, 10, 0.1, lmbda=5.0,
... evaluation_data=validation_data, monitor_evaluation_accuracy=True)
\end{lstlisting}
96.57\%
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 30, 30, 30, 30, 10])
>>> net.SGD(training_data, 30, 10, 0.1, lmbda=5.0,
... evaluation_data=validation_data, monitor_evaluation_accuracy=True)
\end{lstlisting}
96.53\%
\footnote{%
\hyperref[identity_neuron]{}}
$[784, 30, 30, 10]$ $30$
$\frac{\partial C}{\partial b}$
%
\hyperref[sec:the_four_fundamental_equations_behind_backpropagation]{}
$6$
\footnote{
\href{path_to_url}{\lstinline!generate_gradient.py!}
}
\begin{center}
\includegraphics{initial_gradient}
\end{center}
$\delta_j^l = \partial C/\partial b_j^l$
$l$ $j$ $\delta^1$
$\delta^2$
$||\delta^1||$
$||\delta^2||$
$||\delta^1|| = 0.07$
$||\delta^2|| = 0.31$
$[784, 30, 30,
10]$ $0.012, 0.060, 0.283$
30
$0.003, 0.017, 0.070, 0.285$
\begin{center}
\includegraphics[width=.6\textwidth]{training_speed_2_layers}
\end{center}
$1000$ $500$ batch
~~ minibatch $1000$
$50,000$
minibatch
$[784, 30, 30, 30, 10]$
\begin{center}
\includegraphics[width=.6\textwidth]{training_speed_3_layers}
\end{center}
$[784, 30, 30, 30, 30, 10]$
\begin{center}
\includegraphics[width=.6\textwidth]{training_speed_4_layers}
\end{center}
$100$
%
\gls*{bp}
\textbf{
}\footnote{
\href{path_to_url}{Gradient
flow in recurrent nets: the difficulty of learning long-term dependencies}
Sepp HochreiterYoshua Bengio Paolo Frasconi Jrgen
Schmidhuber 2001\gls*{rnn}
Sepp Hochreiter
\href{path_to_url~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf}{Untersuchungen
zu dynamischen neuronalen Netzen} 1991}
~~\textbf{}
%
\textbf{}
$f(x)$ $f'(x)$
MNIST
\section{}
\label{sec:your_sha256_hashs_in_deep_neural_nets}
\begin{center}
\includegraphics{tikz37}
\end{center}
$w_1, w_2, \ldots$ $b_1, b_2, \ldots$ $C$
$j$ $a_j = \sigma(z_j)$ $\sigma$
\hyperref[sigmoid_neurons]{S } $z_j = w_j * a_{j-1} + b_j$
$C$ $a_4$
$\partial C/\partial b_1$
$\partial C/\partial b_1$
$\partial C/\partial b_1$
\begin{center}
\includegraphics{tikz38}
\end{center}
$\sigma'(z_j)$ $w_j$
$\partial C/\partial a_4$
$b_1$ $\Delta b_1$
$\Delta a_1$
$\Delta z_2$ $\Delta
a_2$ $\Delta C$
\begin{equation}
\frac{\partial C}{\partial b_1} \approx \frac{\Delta C}{\Delta b_1}
\label{eq:114}\tag{114}
\end{equation}
$\partial C/\partial b_1$
$\Delta b_1$ $a_1$ $a_1 =
\sigma(z_1) = \sigma(w_1 a_0 + b_1)$
\begin{align}
\Delta a_1 & \approx
\frac{\partial \sigma(w_1 a_0+b_1)}{\partial b_1} \Delta b_1 \label{eq:115}\tag{115}\\
& = \sigma'(z_1) \Delta b_1 \label{eq:116}\tag{116}
\end{align}
$\sigma'(z_1)$ $\partial C/\partial b_1$
$\Delta b_1$
$\Delta a_1$$\Delta a_1$ $z_2 = w_2 * a_1 +
b_2$:
\begin{align}
\Delta z_2 & \approx
\frac{\partial z_2}{\partial a_1} \Delta a_1 \label{eq:117}\tag{117}\\
& = w_2 \Delta a_1 \label{eq:118}\tag{118}
\end{align}
$\Delta z_2$ $\Delta a_1$ $b_1$
$z_2$
\begin{equation}
\Delta z_2 \approx \sigma'(z_1) w_2 \Delta b_1
\label{eq:119}\tag{119}
\end{equation}
$\partial C/\partial b_1$
$\sigma'(z_j)$ $w_j$
$\Delta C$ $\Delta b_1$
\begin{equation}
\Delta C \approx \sigma'(z_1) w_2 \sigma'(z_2) \ldots \sigma'(z_4)
\frac{\partial C}{\partial a_4} \Delta b_1
\label{eq:120}\tag{120}
\end{equation}
$\Delta b_1$
\begin{equation}
\frac{\partial C}{\partial b_1} = \sigma'(z_1) w_2 \sigma'(z_2) \ldots
\sigma'(z_4) \frac{\partial C}{\partial a_4}
\label{eq:121}\tag{121}
\end{equation}
\textbf{}
\begin{equation}
\frac{\partial C}{\partial b_1} = \sigma'(z_1) \, w_2 \sigma'(z_2) \, w_3
\sigma'(z_3) \, w_4 \sigma'(z_4) \, \frac{\partial C}{\partial a_4}
\label{eq:122}\tag{122}
\end{equation}
$w_j \sigma'(z_j)$
sigmoid
\begin{center}
\includegraphics{sigmoid_prime_graph}
\end{center}
$\sigma'(0)=1/4$
$0$ $1$
$|w_j| < 1$ $w_j \sigma'(z_j) < 1/4$
**
$\partial C/\partial b_1$
$\partial C/\partial b_3$
\begin{center}
\includegraphics{tikz39}
\end{center}
$\partial C/\partial b_1$
$< 1/4$ $\partial C/\partial b_1$ $\partial C/\partial
b_3$ 1/16
$w_j$ $w_j
\sigma'(z_j)$ $w_j \sigma'(z_j) < 1/4$
1%
\gls*{bp} \\
\textbf{}
$w_1 = w_2 = w_3 = w_4 = 100$
$\sigma'(z_j)$
$z_j = 0$ $sigma'(z_j) = 1/4$
$z_1 = w_1 * a_0 + b_1$ $b_1 = -100 * a_0$
$w_j * \sigma'(z_j)$
$100*1/4 = 25$\\
\textbf{}
\textbf{}
\subsection*{}
\begin{itemize}
\item $|\sigma'(z)| < 1/4$
\end{itemize}
\textbf{}
sigmoid
$|w\sigma'(z)|$ $|w\sigma'(z)| >= 1$
$w$
$\sigma'(z)$ $w$$\sigma'(z) = \sigma'(w*a+b)$ $a$
$w$ $\sigma'(wa+b)$
$w$ $wa + b$
$\sigma'$ $\sigma'$
\subsection*{}
\begin{itemize}
\item $|w\sigma'(wa+b)|$ $|w\sigma'(wa+b)| >= 1$1
$|w| >= 4$ 2 $|w| >= 4$
$|w\sigma'(wa+b)| >= 1$ $a$
$\frac{2}{|w|}\ln(\frac{|w|(1+\sqrt{1-4/|w|})}{2}-1)$
3 $|w| ~= 6.9$
$0.45$
\item \textbf{}\label{identity_neuron} $x$
$w_1$ $b$ $w_2$
$w_2 \sigma(w_1*x +b)~=x$
$x \in [0, 1]$
\textbf{ $x = 1/2 + \Delta$ $w_1$ $w_1 *
\Delta$ }
\end{itemize}
\section{}
\begin{center}
\includegraphics{tikz40}
\end{center}
$L$ $l$
\begin{equation}
\delta^l = \Sigma'(z^l) (w^{l+1})^T \Sigma'(z^{l+1}) (w^{l+2})^T \ldots
\Sigma'(z^L) \nabla_a C
\label{eq:124}\tag{124}
\end{equation}
$\Sigma'(z^l)$ $l$ $\sigma'(z)$
$w^l$ $\nabla_{a} C$
$(w^j)^T \Sigma' (z^j)$ (pair) $\Sigma'(z^j)$
$1/4$ $w^j$ $(w^j)^T
\sigma' (z^l)$
sigmoid
\section{}
~~
2010 Glorot
Bengio\footnote{\href{path_to_url}{Understanding
the difficulty of training deep feedforward neural networks} Xavier
Glorot Yoshua Bengio2010
\href{path_to_url}{Efficient
BackProp} S Yann LeCun Lon
Bottou Genevieve Orr Klaus-Robert Mller1998} sigmoid
sigmoid
$0$
sigmoid
2013 Sutskever, Martens, Dahl
Hinton\footnote{\href{path_to_url~hinton/absps/momentum.pdf}{On
the importance of initialization and momentum in deep learning} Ilya
SutskeverJames Martens George Dahl Geoffrey Hinton 2013}
momentum $SGD$
``` | /content/code_sandbox/chap5.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 3,454 |
```tex
% file: copyright.tex
\chapter{}
\href{path_to_url}{path_to_url}
Michael A. Nielsen, ``Neural Networks and Deep
Learning'', Determination Press, 2015
\href{path_to_url}{Creative
\href{mailto:mn@michaelnielsen.org}{}
\hyperref[sec:TranslationTeam]{}
``` | /content/code_sandbox/copyright.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 76 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
% your_sha256_hash--------------
% customize the headers with fancyhdr package
% your_sha256_hash--------------
\usepackage{fancyhdr}
\fancyhf{}
\fancyhead[LE]{\leftmark}
\fancyhead[RO]{\nouppercase{\rightmark}}
\fancyfoot[LE,RO]{\thepage}
\pagestyle{fancy}
% your_sha256_hash--------------
% Index package
% your_sha256_hash--------------
% \usepackage{makeidx}
% \makeindex
% your_sha256_hash--------------
% load hyperref to use hyperlinks
% your_sha256_hash--------------
\usepackage[colorlinks=true,linkcolor=blue]{hyperref}
\usepackage[all]{hypcap} % Be sure to call this package after loading hyperref.
% your_sha256_hash--------------
% Glossaries, must be after hyperref
% your_sha256_hash--------------
\usepackage[xindy,toc]{glossaries}
\makeglossaries{}
% your_sha256_hash--------------
% load tocbibind to add contents,list of figures, list of tables and
% bibliography into the toc
% your_sha256_hash--------------
\usepackage{tocbibind}
% your_sha256_hash--------------
% Needed to load images
% your_sha256_hash--------------
\usepackage{graphicx}
\graphicspath{ {images/} } % where to look for images
\usepackage{color}
\usepackage{tabularx}
\usepackage{multirow}
\usepackage{framed}
% your_sha256_hash--------------
% for code example
% your_sha256_hash--------------
\usepackage{listings}
\definecolor{syntax_comment}{rgb}{0.72,0.14,0.15} % red
\definecolor{syntax_key}{rgb}{0.05,0.5,0.07}
\definecolor{syntax_gray}{rgb}{0.5,0.5,0.5}
\definecolor{syntax_string}{rgb}{0.58,0,0.82} % mauve
\definecolor{background}{rgb}{0.975,0.975,0.975}
\lstset{ %
backgroundcolor=\color{background}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}
basicstyle=\scriptsize\ttfamily, % the size of the fonts that are used for the code
breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
breaklines=true, % sets automatic line breaking
captionpos=b, % sets the caption-position to bottom
commentstyle=\itshape\color{syntax_comment}, % comment style
% deletekeywords={...}, % if you want to delete keywords from the given language
% escapeinside={\%*}{*)}, % if you want to add LaTeX within your code
extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
% frame=single, % adds a frame around the code
keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
keywordstyle=\color{syntax_key}, % keyword style
% language=Octave, % the language of the code
% otherkeywords={*,...}, % if you want to add more keywords to the set
numbers=none, % where to put the line-numbers; possible values are (none, left, right)
numbersep=5pt, % how far the line-numbers are from the code
numberstyle=\tiny\color{syntax_gray}, % the style that is used for the line-numbers
rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
showstringspaces=false, % underline spaces within strings only
showtabs=false, % show tabs within strings adding particular underscores
stepnumber=1, % the step between two line-numbers. If it's 1, each line will be numbered
stringstyle=\color{syntax_string}, % string literal style
tabsize=2 % sets default tabsize to 2 spaces
% title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title
}
% your_sha256_hash--------------
% for long and nice table
% your_sha256_hash--------------
\usepackage{longtable}
\usepackage{booktabs}
\usepackage{ltxtable}
% your_sha256_hash--------------
% for compact item list
% your_sha256_hash--------------
\usepackage{paralist}
% your_sha256_hash--------------
% Math - Warning: before cjkfonts (xeCJK) and other package loads fontspec
% your_sha256_hash--------------
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
% font selection for mathematics with XeLaTeX, MUST after amsfonts
\usepackage{mathspec}
% \setmathsfont(Digits,Latin,Greek)[Numbers={Lining,Proportional}]{Minion Pro}
% There's no italic sans-serif math font by default, but it's needed in this book
% follow: path_to_url
% to define a \mathsfit{} macro
\DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl}
\SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{sl}
% your_sha256_hash--------------
% Localization setting
% your_sha256_hash--------------
\input{localization.tex}
% Set Roboto and Source Code Pro, which are installed with TexLive, for western
% fonts:
\input{westernfonts.tex}
\usepackage{setspace}
\onehalfspacing{}
%\usepackage{tikz} % load TikZ/PGF
%\usetikzlibrary{circuits.logic.US,positioning,decorations.pathreplacing,mindmap,backgrounds,math}
\usepackage{pgfplots} % load PDFPlots
%\pgfplotsset{compat=yourversion}
% your_sha256_hash--------------
% Load glossaries
% your_sha256_hash--------------
\input{glossaries}
\input{plots}
% your_sha256_hash--------------
% The document body
% your_sha256_hash--------------
\begin{document}
\input{title}
\frontmatter
%\maketitle
\input{copyright}
\tableofcontents
%\listoffigures
%\listoftables
\pagebreak
\input{author}
\input{translation}
\input{preface}
\input{about}
\input{exercises_and_problems}
\mainmatter{}
\input{chap1}
\input{chap2}
\input{chap3}
\input{chap4}
\input{chap5}
\input{chap6}
\appendix
\input{sai}
\input{acknowledgements}
%\input{faq}
\input{history}
\backmatter{}
% \printindex
\printglossary[title={}]
\end{document}
``` | /content/code_sandbox/main.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 1,600 |
```tex
\begin{lstlisting}[language=Python]
$ python expand_mnist.py
\end{lstlisting}
``` | /content/code_sandbox/snippets/run_expand_mnist.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 24 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\crossEntropyCostLearning{2.0}{2.0}{0.005}{0}
\end{document}
``` | /content/code_sandbox/images/saturation4-0.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\quadraticCostLearning{0.6}{0.9}{0.15}{300}
\end{document}
``` | /content/code_sandbox/images/saturation1-300.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{math}
\begin{document}
% borrow the code from path_to_url
\begin{tikzpicture}[scale=.06pt]
\tikzmath{
% --------------------------
% the parameters of the tree
% --------------------------
\power=2.5; % the scale base factor
\deviation=44.5; % the angle between the 3 child edges
\numsteps=5; % number of levels
let \startcolor=magenta; % the start color
let \endcolor=black; % the end color
% your_sha256_hash---------
% the function that draw one edge and call itself to draw the 3 child edges
% your_sha256_hash---------
function Branch(\x,\y,\rotate,\step){
\step=\step-1; % stops drawing if step < 0
if (\step >= 0) then {
\mix = int(100*\step/(\numsteps-1)); % the color mix parameter is in [0,100]
\scale = \power^\step; % the scale factor
{ % "print" the tikz command that draw the edge
\draw[shift={(\x pt,\y pt)}, rotate=\rotate, scale=\scale,
color=\startcolor!\mix!\endcolor, line width=\scale*.1 pt,
line cap=round]
(0,0)--(1,0) coordinate(newbase);
};
coordinate \b; \b1 = (newbase); % the new base point
for \a in {-\deviation,0,\deviation}{
Branch(\bx1,\by1,mod(\rotate+\a,360),\step); % draw one child edge
};
};
};
% ----------------------
% draw the four branches
% ----------------------
for \angle in {0,45,...,360}{
Branch(0,0,\angle,\numsteps);
};
}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/cayley.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 481 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\quadraticCostLearning{2.0}{2.0}{0.15}{200}
\end{document}
``` | /content/code_sandbox/images/saturation2-200.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
% file: chap3.tex
\chapter{}
\label{ch:ImprovingTheWayNeuralNetworksLearn}
%
\gls*{bp}
\gls*{cost-func}~~%
\hyperref[sec:the_cross-entropy_cost_function]{}\gls*{cost-func}%
\hyperref[sec:overfitting_and_regularization]{\gls*{regularization}}L1 L2 \gls*{regularization}
\gls*{dropout}%
\hyperref[sec:weight_initialization]{\gls*{weight}}%
\hyperref[sec:how_to_choose_a_neural_network's_hyper-parameters]{
}%
\hyperref[sec:other_techniques]{}
%
\hyperref[sec:handwriting_recognition_revisited_the_code]{}
\hyperref[ch:UsingNeuralNetsToRecognizeHandwrittenDigits]{}
\section{}
\label{sec:the_cross-entropy_cost_function}
\begin{center}
\includegraphics{tikz28}
\end{center}
$1$ $0$
\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias} $0.6$ $0.9$
$0.82$ $0.0$
$0.0$ %
\gls*{weight}\gls*{bias}\gls*{learning-rate}
$\eta=0.15$
\gls*{cost-func}$C$
\begin{center}
\includegraphics{saturation1-0}
\end{center}
\gls*{epoch}\gls*{weight}\gls*{bias}
\begin{center}
\includegraphics{saturation1-50}\includegraphics{saturation1-100}\\
\includegraphics{saturation1-150}\includegraphics{saturation1-200}\\
\includegraphics{saturation1-250}\includegraphics{saturation1-300}
\end{center}
\gls*{cost-func}\gls*{weight}\gls*{bias}
$0.09$ $0.0$
\gls*{weight}\gls*{bias} $2.0$ $0.98$
\begin{center}
\includegraphics{saturation2-0}
\end{center}
\label{saturation2_anchor}
\begin{center}
\includegraphics{saturation2-50}\includegraphics{saturation2-100}\\
\includegraphics{saturation2-150}\includegraphics{saturation2-200}\\
\includegraphics{saturation2-250}\includegraphics{saturation2-300}
\end{center}
\gls*{learning-rate}$\eta=0.15$
$150$ \gls*{weight}\gls*{bias}
$0.0$
\gls*{weight}\gls*{bias}
\gls*{cost-func}$\partial C/\partial w$ $\partial C/\partial b$
~\eqref{eq:6}\gls*{cost-func}
\begin{equation}
C = \frac{(y-a)^2}{2}
\label{eq:54}\tag{54}
\end{equation}
$a$ $x=1$$y=0$ %
\gls*{weight} $a = \sigma(z)$ $z = wx+b$
\gls*{weight}\gls*{bias}
\begin{align}
\frac{\partial C}{\partial w} &= (a-y)\sigma'(z) x = a \sigma'(z)\label{eq:55}\tag{55}\\
\frac{\partial C}{\partial b} &= (a-y)\sigma'(z) = a \sigma'(z)\label{eq:56}\tag{56}
\end{align}
$x = 1$ $y = 0$
$\sigma'(z)$ $\sigma$
\begin{center}
\includegraphics{sigmoid_function}
\end{center}
$1$
$\sigma'(z)$ ~\eqref{eq:55} ~\eqref{eq:56} $\partial
C/\partial w$ $\partial C/\partial b$
\subsection{}
\label{sec:introducing_the_cross-entropy_cost_function}
\gls*{cost-func}
$x_1, x_2, \ldots$ \gls*{weight} $w_1,
w_2, \ldots$ \gls*{bias} $b$
\begin{center}
\includegraphics{tikz29}
\end{center}
$a = \sigma(z)$ $z = \sum_j w_j x_j+b$
\gls*{cost-func}
\begin{equation}
C = -\frac{1}{n} \sum_x \left[y \ln a + (1-y ) \ln (1-a) \right]
\label{eq:57}\tag{57}
\end{equation}
$n$ $x$ $y$
~\eqref{eq:57}
\gls*{cost-func}
\gls*{cost-func}
\gls*{cost-func}$C > 0$a
\eqref{eq:57} $(0,1)$
b
$x$
$0$\footnote{ $y$ $0$$1$
}$y=0$ $a\approx 0$
\eqref{eq:57} $y=0$
$-\ln (1-a)\approx 0$$y=1$ $a\approx 1$
$0$
\gls*{cost-func}\gls*{cost-func}
\gls*{cost-func}\gls*{cost-func}
\gls*{weight}
$a=\sigma(z)$ \eqref{eq:57}
\begin{align}
\frac{\partial C}{\partial w_j} &= -\frac{1}{n} \sum_x \left(
\frac{y }{\sigma(z)} -\frac{(1-y)}{1-\sigma(z)} \right)
\frac{\partial \sigma}{\partial w_j} \label{eq:58}\tag{58}\\
&= -\frac{1}{n} \sum_x \left(
\frac{y}{\sigma(z)}
-\frac{(1-y)}{1-\sigma(z)} \right)\sigma'(z) x_j \label{eq:59}\tag{59}
\end{align}
\begin{equation}
\frac{\partial C}{\partial w_j} = \frac{1}{n} \sum_x \frac{\sigma'(z)
x_j}{\sigma(z) (1-\sigma(z))} (\sigma(z)-y)
\label{eq:60}\tag{60}
\end{equation}
$\sigma(z) = 1/(1+e^{-z})$ $\sigma'(z) =
\sigma(z)(1-\sigma(z))$
$\sigma'(z)$ $\sigma(z)(1-\sigma(z))$
\begin{equation}
\frac{\partial C}{\partial w_j} = \frac{1}{n} \sum_x x_j(\sigma(z)-y)
\label{eq:61}\tag{61}
\end{equation}
\gls*{weight} $\sigma(z)-y$
\gls*{cost-func}\gls*{cost-func} $\sigma'(z)$
~\eqref{eq:55}$\sigma'(z)$
\gls*{bias}
\begin{equation}
\frac{\partial C}{\partial b} = \frac{1}{n} \sum_x (\sigma(z)-y)
\label{eq:62}\tag{62}
\end{equation}
,\gls*{cost-func}~\eqref{eq:56} $\sigma'(z)$
\subsection*{}
\begin{itemize}
\item $\sigma'(z) = \sigma(z)(1-\sigma(z))$
\end{itemize}
\gls*{weight} $0.6$\gls*{bias} $0.9$
\begin{center}
\includegraphics{saturation3-0}
\end{center}
\begin{center}
\includegraphics{saturation3-50}\includegraphics{saturation3-100}\\
\includegraphics{saturation3-150}\includegraphics{saturation3-200}\\
\includegraphics{saturation3-250}\includegraphics{saturation3-300}
\end{center}
\hyperref[saturation2_anchor]{}\gls*{weight}%
\gls*{bias}$2.0$
\begin{center}
\includegraphics{saturation4-0}
\end{center}
\begin{center}
\includegraphics{saturation4-50}\includegraphics{saturation4-100}\\
\includegraphics{saturation4-150}\includegraphics{saturation4-200}\\
\includegraphics{saturation4-250}\includegraphics{saturation4-300}
\end{center}
\gls*{cost-func}\gls*{cost-func}
\gls*{learning-rate}\gls*{cost-func}
$\eta = 0.15$\gls*{learning-rate}
\gls*{cost-func}\gls*{learning-rate}
\gls*{cost-func}
\gls*{learning-rate}
$\eta = 0.005$
\gls*{learning-rate}%
\gls*{learning-rate}
\gls*{cost-func}
\gls*{cost-func}%
\textbf{}
\gls*{learning-rate}
$y = y_1, y_2, \ldots$
$a^L_1, a^L_2, \ldots$
\begin{equation}
C = -\frac{1}{n} \sum_x \sum_j \left[y_j \ln a^L_j + (1-y_j) \ln (1-a^L_j) \right]
\label{eq:63}\tag{63}
\end{equation}
$\sum_j$
~\eqref{eq:57}
~\eqref{eq:63}
\gls*{cost-func}%
\gls*{sigmoid-neuron}
\gls*{weight}\gls*{bias}
~~ $1$
$0$\gls*{cost-func}
\gls*{weight}
\subsection*{}
\begin{itemize}
\item $y$ $a$
$-[y \ln a + (1-y) \ln (1-a)]$
$-[a \ln y + (1-a) \ln (1-y)]$ $y=0$ $1$
\item $\sigma(z) \approx y$
$y$ $1$ $0$
$y$ $0$ $1$
$\sigma(z) = y$
\begin{equation}
C = -\frac{1}{n} \sum_x [y \ln y+(1-y) \ln(1-y)]
\label{eq:64}\tag{64}
\end{equation}
$-[y \ln y+(1-y)\ln(1-y)]$ %
\href{path_to_url}{}
\end{itemize}
\subsection*{}
\begin{itemize}
\item \textbf{}\quad %
\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}
\gls*{cost-func}\gls*{weight}
\begin{equation}
\frac{\partial C}{\partial w^L_{jk}} = \frac{1}{n}
\sum_x a^{L-1}_k (a^L_j-y_j) \sigma'(z^L_j)
\label{eq:65}\tag{65}
\end{equation}
$\sigma'(z^L_j)$
\gls*{cost-func} $x$ $\delta^L$
\begin{equation}
\delta^L = a^L-y
\label{eq:66}\tag{66}
\end{equation}
\gls*{weight}
\begin{equation}
\frac{\partial C}{\partial w^L_{jk}} = \frac{1}{n} \sum_x
a^{L-1}_k (a^L_j-y_j)
\label{eq:67}\tag{67}
\end{equation}
$\sigma'(z^L_j)$
\gls*{bias}
\item \textbf{\gls*{cost-func}}\quad
\textbf{} \gls*{sigmoid-func}
$a^L_j = z^L_j$\gls*{cost-func}
$x$
\begin{equation}
\delta^L = a^L-y
\label{eq:68}\tag{68}
\end{equation}
\gls*{weight}\gls*{bias}
\begin{align}
\frac{\partial C}{\partial w^L_{jk}} &= \frac{1}{n} \sum_x
a^{L-1}_k (a^L_j-y_j) \label{eq:69}\tag{69}\\
\frac{\partial C}{\partial b^L_{j}} &= \frac{1}{n} \sum_x
(a^L_j-y_j) \label{eq:70}\tag{70}
\end{align}
\gls*{cost-func}
\gls*{cost-func}
\end{itemize}
\subsection{ MNIST }
% \hyperref[sec:handwriting_recognition_revisited_the_code]{}%
\hyperref[sec:implementing_our_network_to_classify_digits]{}
\lstinline!network.py! \lstinline!network2.py!
\footnote{
\href{path_to_url}{GitHub}
} MNIST
$30$ \gls*{mini-batch}
$10$\gls*{learning-rate} $\eta=0.5$ \footnote{
$\eta = 3.0$ \gls*{learning-rate}
\gls*{cost-func}
\gls*{learning-rate}
\gls*{learning-rate}
$\sigma' =
\sigma(1-\sigma)$ $\sigma$ $\int_0^1 d\sigma
\sigma(1-\sigma) = 1/6$%
\gls*{learning-rate} $6$
\gls*{learning-rate} $6$
} $30$ \gls*{epoch}
\lstinline!network2.py! \lstinline!network.py!
\lstinline!help(network2.Network.SGD)!
\lstinline!network2.py!
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
>>> import network2
>>> net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)
>>> net.large_weight_initializer()
>>> net.SGD(training_data, 30, 10, 0.5, evaluation_data=test_data,
... monitor_evaluation_accuracy=True)
\end{lstlisting}
\lstinline!net.large_weight_initializer()!
\gls*{weight}\gls*{bias}
\gls*{weight}
95.49\% \gls*{cost-func}
95.42\%
$100$
96.82\% \gls*{cost-func} 96.59\%
3.41\% 3.18\%
$1/14$
\gls*{cost-func}
\gls*{mini-batch}
MNIST
~~%
\hyperref[sec:overfitting_and_regularization]{\gls*{regularization}}
\gls*{cost-func}
\subsection{}
~\eqref{eq:55} ~\eqref{eq:56} $\sigma'(z)$
$\sigma'(z)$
$x$ $C = C_x$
\begin{align}
\frac{\partial C}{\partial w_j} &= x_j(a-y) \label{eq:71}\tag{71}\\
\frac{\partial C}{\partial b } &= (a-y) \label{eq:72}\tag{72}
\end{align}
\gls*{cost-func}
\begin{equation}
\frac{\partial C}{\partial b} = \frac{\partial C}{\partial a}
\sigma'(z)
\tag{73}
\end{equation}
$\sigma'(z) = \sigma(z)(1-\sigma(z)) = a(1-a)$
\begin{equation}
\frac{\partial C}{\partial b} = \frac{\partial C}{\partial a}
a(1-a)
\label{eq:74}\tag{74}
\end{equation}
~\eqref{eq:72}
\begin{equation}
\frac{\partial C}{\partial a} = \frac{a-y}{a(1-a)}
\label{eq:75}\tag{75}
\end{equation}
$a$
\begin{equation}
C = -[y \ln a + (1-y) \ln (1-a)]+ {\rm constant}
\label{eq:76}\tag{76}
\end{equation}
{\rm constant} $x$ \gls*{cost-func}
\gls*{cost-func}
\begin{equation}
C = -\frac{1}{n} \sum_x [y \ln a +(1-y) \ln(1-a)] + {\rm constant}
\label{eq:77}\tag{77}
\end{equation}
~\eqref{eq:71}
~\eqref{eq:72}
$x
\rightarrow y = y(x)$ $x \rightarrow a = a(x)$
$a$ $y = 1$ $1-a$ $y=0$
$y$
%
\href{path_to_url#Motivation}{}
\href{path_to_url}{Cover and Thomas}
Kraft
\subsection*{}
\begin{itemize}
\item \gls*{cost-func}
~\eqref{eq:61} $x_j$
$x_j$ $0$ \gls*{weight} $w_j$
\gls*{cost-func} $x_j$
\end{itemize}
\subsection{}
\label{subsec:softmax}
\textbf{\gls{softmax}}
\gls*{softmax}%
\gls*{softmax}%
\hyperref[ch:Deeplearning]{}\gls*{softmax}
\gls*{softmax} S
\footnote{\gls*{softmax}%
\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}
} $z^L_j = \sum_{k} w^L_{jk} a^{L-1}_k +
b^L_j$\gls*{sigmoid-func}
\text{\gls{softmax-func}} $z^L_j$ $j$
$a^L_j$
\begin{equation}
a^L_j = \frac{e^{z^L_j}}{\sum_k e^{z^L_k}}
\label{eq:78}\tag{78}
\end{equation}
\gls*{softmax-func}~\eqref{eq:78}
~\eqref{eq:78}
$z^L_1, z^L_2, z^L_3$ $z^L_4$
$z^L_4$
\begin{center}
\includegraphics{softmax}
\end{center}
$z^L_4$ $a^L_4$
$z^L_4$ $2$
\begin{center}
\includegraphics{softmax-1}
\end{center}
$z^L_4$ $5$
\begin{center}
\includegraphics{softmax-2}
\end{center}
$z^L_4$ $a^L_4$
$z^L_4$ $-2$
\begin{center}
\includegraphics{softmax-3}
\end{center}
$z^L_4$ $-5$
\begin{center}
\includegraphics{softmax-4}
\end{center}
$a^L_4$ $1$
~\eqref{eq:78}
\begin{equation}
\sum_j a^L_j = \frac{\sum_j e^{z^L_j}}{\sum_k e^{z^L_k}} = 1
\label{eq:79}\tag{79}
\end{equation}
$a^L_4$
$1$
~\eqref{eq:78}
$1$
$a^L_j$
$j$ MNIST
$a^L_j$ $j$
S
S
S
\subsection*{}
\begin{itemize}
\item S $a^L_j$
$1$
\end{itemize}
~\eqref{eq:78} ~\eqref{eq:78}
\gls*{softmax} $1$
$z^L_j$
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{softmax}}\quad $j=k$ $\partial a^L_j /
\partial z^L_k$ $j \neq k$ $z^L_j$
$a^L_j$
\item \textbf{\gls*{softmax}}\quad S $a^L_j$
$a^L_j = \sigma(z^L_j)$ \gls*{softmax}
$a^L_j$ \textbf{}
\end{itemize}
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{softmax}}\quad \gls*{softmax}
$a^L_j$ $z^L_j = \ln
a^L_j + C$ $C$ $j$
\end{itemize}
\textbf{}
\textbf{\gls{log-likelihood}}\gls*{cost-func} $x$ $y$
\gls*{log-likelihood}\gls*{cost-func}
\begin{equation}
C \equiv -\ln a^L_y
\label{eq:80}\tag{80}
\end{equation}
MNIST $7$ %
\gls*{log-likelihood} $-\ln a_7^L$
$7$ $a_7^L$
$1$ $-\ln a_7^L$
$a_7^L$ $-\ln a_7^L$ \gls*{cost-func}
\gls*{cost-func}
$\partial C /
\partial w^L_{jk}$ $\partial C / \partial b^L_j$
~~~~
\footnote{ $y$
$y$ 7 $7$
$y$ $7$
7 $1$ $0$ }
\begin{align}
\frac{\partial C}{\partial b^L_j} &= a^L_j-y_j \label{eq:81}\tag{81}\\
\frac{\partial C}{\partial w^L_{jk}} &= a^{L-1}_k (a^L_j-y_j) \label{eq:82}\tag{82}
\end{align}
~\eqref{eq:82} ~\eqref{eq:67}
%
\gls*{log-likelihood}\gls*{softmax} S
S
S
\hyperref[ch:Deeplearning]{}
MNIST
\subsection*{}
\begin{itemize}
\item ~\eqref{eq:81} ~\eqref{eq:82}
\item \textbf{}\quad
\begin{equation}
a^L_j = \frac{e^{c z^L_j}}{\sum_k e^{c z^L_k}}
\label{eq:83}\tag{83}
\end{equation}
$c$ $c=1$
$c$
$c$
$c\rightarrow \infty$ $a_j^L$
$c=1$
\item \textbf{\gls*{bp}}\quad S
\gls*{bp}
$\delta^L_j \equiv \partial C / \partial z^L_j$
\begin{equation}
\delta^L_j = a^L_j -y_j
\label{eq:84}\tag{84}
\end{equation}
\gls*{bp}
\end{itemize}
\section{}
\label{sec:overfitting_and_regularization}
4
\footnote{
\href{path_to_url}{Freeman
Dyson}
%
\href{path_to_url}{}%
}
MNIST 30
24,000 100
80,000
30
23,860 50,000 MNIST
1,000
\gls*{cost-func}\gls*{learning-rate} $\eta = 0.5$ \gls*{mini-batch}
$10$ 400 \gls*{epoch}
\lstinline!network2! \gls*{cost-func}
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
>>> import network2
>>> net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)
>>> net.large_weight_initializer()
>>> net.SGD(training_data[:1000], 400, 10, 0.5, evaluation_data=test_data,
... monitor_evaluation_accuracy=True, monitor_training_cost=True)
\end{lstlisting}
\footnote{
\href{path_to_url}{overfitting.py}
}
\begin{center}
\includegraphics[width=.6\textwidth]{overfitting1}
\end{center}
\gls*{cost-func}
$200$ $399$ \gls*{epoch}
\begin{center}
\includegraphics[width=.6\textwidth]{overfitting2}
\end{center}
200 \gls*{epoch}
82\% 280 \gls*{epoch}
\gls*{epoch} 280 \gls*{epoch}
280 \gls*{epoch}
280 \gls*{epoch}%
\textbf{\gls{overfitting}}\textbf{\gls{overtraining}}
\textbf{}
\textbf{}
\begin{center}
\includegraphics[width=.6\textwidth]{overfitting3}
\end{center}
15 \gls*{epoch}
\gls*{overfitting}
15 280 \gls*{epoch}\gls*{overfitting}
280 \gls*{epoch}
\gls*{overfitting}
\gls*{overfitting}
\begin{center}
\includegraphics[width=.6\textwidth]{overfitting4}
\end{center}
100\% $1000$
82.27\%
\gls*{overfitting}\gls*{weight}
\gls*{bias}\gls*{overfitting}
\gls*{overfitting}
\gls*{overfitting}~~
\gls*{overfitting}
\gls*{overfitting}
MNIST
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
\end{lstlisting}
\lstinline!training_data! \lstinline!test_data!
\lstinline!validation_data!\lstinline!validation_data! $10,000$
MNIST $50,000$
$10,000$ \lstinline!validation_data!
\lstinline!test_data! \gls*{overfitting} \lstinline!test_data!
\gls*{epoch} \lstinline!validation_data!
\textbf{
}
\footnote{
280 \gls*{epoch}
400 \gls*{epoch}
}
\label{validation_explanation}
\lstinline!validation_data! \lstinline!test_data! \gls*{overfitting}
\lstinline!validation_data! \gls*{epoch}\gls*{learning-rate}
%
\hyperref[sec:how_to_choose_a_neural_network's_hyper-parameters]{}
\lstinline!validation_data!
\lstinline!test_data! \gls*{overfitting}
\lstinline!validation_data! \lstinline!test_data!
\lstinline!test_data! \gls*{overfitting}
\lstinline!test_data!
\lstinline!test_data!
\lstinline!validation_data!
\lstinline!test_data!
\lstinline!test_data!
\textbf{hold out} \lstinline!validation_data!
\lstinline!traning_data!
\lstinline!test_data!
~~~~
\gls*{overfitting} \lstinline!test_data!
\lstinline!training_data!\lstinline!validation_data!
\lstinline!test_data! Hold-Out
$1,000$ \gls*{overfitting}
50,000 $30$
\gls*{learning-rate} $0.5$\gls*{mini-batch} $10$\gls*{epoch} 30
\begin{center}
\includegraphics[width=.6\textwidth]{code_samples/fig/overfitting_full}
\end{center}
$1,000$
97.86\% 95.33\%
1.53\% 17.73\%\gls*{overfitting}
\gls*{overfitting}
\gls*{overfitting}
\subsection{}
\gls*{overfitting}\gls*{overfitting}
\gls*{overfitting}
\textbf{\gls{regularization}}\gls*{regularization}
~~\textbf{\gls{weight-decay}} \textbf{L2 \gls*{regularization}}L2 \gls*{regularization}
\gls*{cost-func}\textbf{\gls{regularization-term}}\gls*{regularization}
\begin{equation}
C = -\frac{1}{n} \sum_{xj} \left[ y_j \ln a^L_j+(1-y_j) \ln
(1-a^L_j)\right] + \frac{\lambda}{2n} \sum_w w^2
\label{eq:85}\tag{85}
\end{equation}
\gls*{weight}
$\lambda / 2n$ $\lambda > 0$ \textbf{\gls*{regularization}} $n$
$\lambda$ \gls*{regularization}\textbf{}\gls*{bias}
\gls*{cost-func}\gls*{regularization}\gls*{cost-func}\gls*{regularization}
\begin{equation}
C = \frac{1}{2n} \sum_x \|y-a^L\|^2 + \frac{\lambda}{2n} \sum_w w^2
\label{eq:86}\tag{86}
\end{equation}
\begin{equation}
C = C_0 + \frac{\lambda}{2n} \sum_w w^2
\label{eq:87}\tag{87}
\end{equation}
$C_0$ \gls*{cost-func}
\gls*{regularization}\gls*{weight}
\gls*{weight}\gls*{cost-func}\gls*{regularization}
\gls*{weight}\gls*{cost-func} $\lambda$
$\lambda$ \gls*{cost-func}\gls*{weight}
\gls*{overfitting}
\gls*{regularization}\gls*{overfitting}
\gls*{sgd}\gls*{regularization}
\gls*{weight}\gls*{bias} $\partial
C/\partial w$ $\partial C/\partial b$~\eqref{eq:87}
\begin{align}
\frac{\partial C}{\partial w} & = \frac{\partial C_0}{\partial w} +
\frac{\lambda}{n} w \label{eq:88}\tag{88} \\
\frac{\partial C}{\partial b} & = \frac{\partial C_0}{\partial b} \label{eq:89}\tag{89}
\end{align}
$\partial C_0/\partial w$ $\partial C_0/\partial b$ \gls*{bp}
\hyperref[ch:HowTheBackpropagationAlgorithmWorks]{}
\gls*{regularization}\gls*{cost-func}\gls*{bp}
$\frac{\lambda}{n} w$ \gls*{weight}\gls*{bias}\gls*{bias}
\begin{equation}
b \rightarrow b -\eta \frac{\partial C_0}{\partial b}
\label{eq:90}\tag{90}
\end{equation}
\gls*{weight}
\begin{align}
w & \rightarrow w-\eta \frac{\partial C_0}{\partial
w}-\frac{\eta \lambda}{n} w \label{eq:91}\tag{91}\\
& = \left(1-\frac{\eta \lambda}{n}\right) w -\eta \frac{\partial
C_0}{\partial w} \label{eq:92}\tag{92}
\end{align}
$1-\frac{\eta\lambda}{n}$
\gls*{weight} $w$\textbf{\gls*{weight}}\gls*{weight}
\gls*{weight} $0$\gls*{cost-func}
\gls*{weight}
\gls*{sgd}\gls*{regularization}
$m$ \gls*{mini-batch} $\partial C_0/\partial
w$\gls*{sgd}\gls*{regularization}~\eqref{eq:20}
\begin{equation}
w \rightarrow \left(1-\frac{\eta \lambda}{n}\right) w -\frac{\eta}{m}
\sum_x \frac{\partial C_x}{\partial w}
\label{eq:93}\tag{93}
\end{equation}
\gls*{mini-batch} $x$ $C_x$ \gls*{regularization}%
\gls*{sgd}\gls*{weight}
$1-\frac{\eta \lambda}{n}$\gls*{bias}\gls*{regularization}
\gls*{regularization}~\eqref{eq:21}
\begin{equation}
b \rightarrow b - \frac{\eta}{m} \sum_x \frac{\partial C_x}{\partial b}
\label{eq:94}\tag{94}
\end{equation}
\gls*{mini-batch} $x$
\gls*{regularization} $30$ \gls*{mini-batch}
$10$\gls*{learning-rate} $0.5$\gls*{regularization}%
$\lambda = 0.1$ \lstinline!lmbda!
Python \lstinline!lambda!
\lstinline!test_data! \lstinline!validation_data!
\lstinline!validation_data!
\gls*{regularization}
\lstinline!validation_data!
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
>>> import network2
>>> net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)
>>> net.large_weight_initializer()
>>> net.SGD(training_data[:1000], 400, 10, 0.5,
... evaluation_data=test_data, lmbda = 0.1,
... monitor_evaluation_cost=True, monitor_evaluation_accuracy=True,
... monitor_training_cost=True, monitor_training_accuracy=True)
\end{lstlisting}
\gls*{cost-func}\gls*{regularization}\footnote{
\href{path_to_url}{overfitting.py}
}
\begin{center}
\includegraphics[width=.6\textwidth]{regularized1}
\end{center}
400 \gls*{epoch}
\begin{center}
\includegraphics[width=.6\textwidth]{regularized2}
\end{center}
\gls*{regularization}\gls*{overfitting}
87.1\% 82.27\% 400 \gls*{epoch}
\gls*{regularization}
\gls*{overfitting}
1,000 50,000
\gls*{overfitting}%
\gls*{regularization}30 \gls*{epoch}, \gls*{learning-rate} 0.5,
\gls*{mini-batch} 10\gls*{regularization}
$n=1,000$ $n=50,000$\gls*{weight}
$1-\frac{\eta\lambda}{n}$ $\lambda = 0.1$ \gls*{weight}
\gls*{regularization} $\lambda = 5.0$
\gls*{weight}
\begin{lstlisting}[language=Python]
>>> net.large_weight_initializer()
>>> net.SGD(training_data, 30, 10, 0.5,
... evaluation_data=test_data, lmbda = 5.0,
... monitor_evaluation_accuracy=True, monitor_training_accuracy=True)
\end{lstlisting}
\begin{center}
\includegraphics[width=.6\textwidth]{code_samples/fig/regularized_full}
\end{center}
\gls*{regularization}
95.49\% 96.49\%
\gls*{overfitting}
100 \gls*{regularization} $\lambda = 5.0$
L2 \gls*{regularization}
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 100, 10], cost=network2.CrossEntropyCost)
>>> net.large_weight_initializer()
>>> net.SGD(training_data, 30, 10, 0.5, lmbda=5.0,
... evaluation_data=validation_data,
... monitor_evaluation_accuracy=True)
\end{lstlisting}
97.92\% 30
\label{chap3_98_04_percent}60 \gls*{epoch}
$\eta=0.1$ $\lambda = 5.0$ 98\%98.04\%
\label{98percent} 152
\gls*{regularization}\gls*{overfitting}
\gls*{weight} MNIST
\gls*{regularization}\gls*{cost-func}
\gls*{regularization}
\gls*{cost-func}\gls*{regularization}\gls*{weight}
\gls*{weight}
\gls*{cost-func}
\subsection{}
% I produce the 3 graphs in MATLAB:
%
% for simple_model:
% x = [0.976923076923080,1.48461538461538,1.99230769230769,2.58461538461538,2.83846153846154,3.43076923076923,3.60000000000000,3.72692307692308,4.10769230769231,4.53076923076923];
% y = [2.51111111111111,2.82222222222222,4.22222222222222,5,5.85555555555556,6.55555555555556,6.86666666666667,7.33333333333333,8.18888888888889,8.88888888888889];
% plot(x,y,'.k','MarkerSize', 20);
% xlabel('\it x','FontSize',16,'FontWeight','bold')
% ylabel('\it y','FontSize',16,'FontWeight','bold')
%
% for polynomial_fit:
% p = polyfit(x, y, 9);
% x1 = 0.95:0.05:4.55;
% y1 = polyval(p, x1);
% figure
% plot(x,y,'.k','MarkerSize', 20)
% hold on
% plot(x1,y1,'b')
% hold off
%
% for linear_fit:
% x2 = [0, 5];
% y2 = [0, 10];
% figure
% plot(x,y,'.k','MarkerSize', 20)
% hold on
% plot(x2,y2,'b')
% hold off
\gls*{regularization}\gls*{overfitting}
\gls*{weight}
\begin{center}
\includegraphics[width=.55\textwidth]{simple_model.eps}
\end{center}
$x$ $y$
$y$ $x$
$9$ $y=a_0x^9 + a_1x^8 + ... + a_9$
\footnote{
Numpy \lstinline!polyfit! %
\href{path_to_url}{
} 14 \lstinline!p(x)!
}
\begin{center}
\includegraphics[width=.55\textwidth]{polynomial_fit.eps}
\end{center}
$y=2x$
\begin{center}
\includegraphics[width=.55\textwidth]{linear_fit.eps}
\end{center}
19
2 $y=2x$
$x$ $y$
9 $x^9$
\gls*{weight}
\gls*{weight}
\gls*{regularization}
\gls*{regularization}
\gls*{weight}\gls*{regularization}%
\gls*{weight}
\gls*{regularization}
1940 Marcel Schein
GE
Hans Bethe Bethe Schein Schein
plate Bethe
Schein Bethe plateBethe
Schein
$1/5$ Bethe $5$ plate
Schein plateplate
plate Bethe
Bethe
Schein \footnote{ Richard Feynman
Charles Weiner %
\href{path_to_url}{}%
}
1859 Urbain Le Verrier
1916
\gls*{regularization}\gls*{regularization}
empirical fact\gls*{regularization}%
\gls*{regularization}\gls*{regularization}
\gls*{regularization}
~~\gls*{regularization}
\footnote{
\href{path_to_url}{problem of
induction} David Hume
\href{path_to_url}{"An Enquiry Concerning Human
Understanding"} 1748 David Wolpert
William Macready 1997%
\href{path_to_url}{}%
}
~~~~
\gls*{regularization}
\gls*{regularization}
100
80,000 50,000 80,000
50,000 \gls*{overfitting}
\footnote{
\href{path_to_url}{Gradient-Based
Learning Applied to Document Recognition} Yann LeCun Lon Bottou
Yoshua Bengio Patrick Haffner 1998}\gls*{regularization}
\gls*{regularization}
L2 \gls*{regularization}\gls*{bias}
\gls*{regularization}\gls*{bias}
\gls*{bias}\gls*{regularization}
\gls*{bias}\gls*{weight}
\gls*{bias}\gls*{bias}
~~\gls*{bias}
\gls*{bias}\gls*{regularization}
\subsection{}
L2 \gls*{regularization}
\gls*{overfitting}L1 \gls*{regularization}\gls*{dropout}
\gls*{regularization}\\
\textbf{L1 \gls*{regularization}} \gls*{regularization}\gls*{cost-func}
\begin{equation}
C = C_0 + \frac{\lambda}{n} \sum_w |w|
\label{eq:95}\tag{95}
\end{equation}
L2 \gls*{regularization}\gls*{weight}\gls*{weight}
L1 \gls*{regularization} L2 \gls*{regularization} L1 \gls*{regularization}
L1 \gls*{regularization} L2 \gls*{regularization}
\gls*{cost-func} \eqref{eq:95}
\begin{equation}
\frac{\partial C}{\partial w} = \frac{\partial C_0}{\partial w}
+ \frac{\lambda}{n} \, {\rm sgn}(w)
\label{eq:96}\tag{96}
\end{equation}
${\rm sgn}(w)$ $w$ $w$ $+1$ $w$
$-1$\gls*{bp} L1 \gls*{regularization}
L1 \gls*{regularization}
\begin{equation}
w \rightarrow w' = w-\frac{\eta \lambda}{n} \mbox{sgn}(w) - \eta \frac{\partial
C_0}{\partial w}
\label{eq:97}\tag{97}
\end{equation}
\gls*{mini-batch} $\partial C_0/\partial w$
L2 \gls*{regularization}~\eqref{eq:93}
\begin{equation}
w \rightarrow w' = w\left(1 - \frac{\eta \lambda}{n} \right)
- \eta \frac{\partial C_0}{\partial w}
\label{eq:98}\tag{98}
\end{equation}
\gls*{regularization}\gls*{weight}\gls*{regularization}
\gls*{weight} L1 \gls*{regularization}\gls*{weight} $0$ L2
\gls*{regularization}\gls*{weight} $w$ \gls*{weight}
$|w|$ L1 \gls*{regularization}\gls*{weight} L2 \gls*{regularization}
$|w|$ L1 \gls*{regularization}\gls*{weight} L2 \gls*{regularization}
L1 \gls*{regularization}\gls*{weight}\gls*{weight}
$0$
~~ $w=0$ $\partial
C/\partial w$ $|w|$ $w=0$
\gls*{regularization}\gls*{sgd}
$w=0$ \gls*{regularization}\gls*{weight}
$0$ \gls*{weight}
~\eqref{eq:96} ~\eqref{eq:97} $\mbox{sgn}(0) = 0$
L1 \gls*{regularization}\gls*{sgd}\\
\textbf{\gls{dropout}} \gls*{dropout}
L1L2 \gls*{regularization}\gls*{dropout}\gls*{cost-func}\gls*{dropout}
\gls*{dropout}
\begin{center}
\includegraphics{tikz30}
\end{center}
$x$ $y$
$x$ \gls*{bp}\gls*{dropout}
\gls*{dropout}
\begin{center}
\includegraphics{tikz31}
\end{center}
$x$\gls*{bp}
\gls*{mini-batch}\gls*{weight}\gls*{bias}
\gls*{dropout}
\gls*{mini-batch}\gls*{weight}\gls*{bias}
\gls*{weight}\gls*{bias}\gls*{weight}\gls*{bias}
\gls*{dropout}
\gls*{weight}
\gls*{dropout}\gls*{regularization}%
\gls*{dropout}
33
\gls*{overfitting}
\gls*{overfitting}\gls*{overfitting}
\gls*{dropout}\gls*{dropout}
\gls*{dropout}
\gls*{overfitting}\gls*{dropout}\gls*{overfitting}
\label{dropout_explanation}
\footnote{\href{path_to_url}{ImageNet
Classification with Deep Convolutional Neural Networks} Alex Krizhevsky
Ilya Sutskever Geoffrey Hinton 2012}
\gls*{dropout}
\gls*{dropout} L1L2 \gls*{regularization}\gls*{weight}
\gls*{dropout}
\footnote{\href{path_to_url}{Improving neural networks
by preventing co-adaptation of feature detectors} Geoffrey Hinton Nitish
Srivastava Alex Krizhevsky Ilya Sutskever Ruslan Salakhutdinov
2012 }
\gls*{dropout} MNIST
98.4\% \gls*{dropout} L2 \gls*{regularization}
98.7\%
\gls*{dropout}
\\
\textbf{} MNIST 1,000
80\%
30
\gls*{mini-batch} $10$%
\gls*{learning-rate} $\eta=0.5$\gls*{regularization} $\lambda=5.0$\gls*{cost-func}
30 \gls*{epoch}
\gls*{epoch}\gls*{weight}
\gls*{regularization} $\lambda = 5.0$
$\lambda$ \footnote{
\href{path_to_url}{\lstinline!more_data.py!}
}
\begin{center}
\includegraphics[width=.6\textwidth]{more_data}
\end{center}
\begin{center}
\includegraphics[width=.6\textwidth]{more_data_log}
\end{center}
~~ 50,000~~
5 MNIST
\begin{center}
\includegraphics[height=32pt]{more_data_5}
\end{center}
$15^{\circ}$
\begin{center}
\includegraphics[height=32pt]{more_data_rotated_5}
\end{center}
MNIST
\textbf{} MNIST
\textbf{}
\footnote{\href{path_to_url}{Best Practices
for Convolutional Neural Networks Applied to Visual Document Analysis}
Patrice Simard Dave Steinkraus John Platt 2003}
MNIST
~~ 800
MNIST 98.4\%
98.9\%
99.3\%
~~
\subsection*{}
\begin{itemize}
\item MNIST
\end{itemize}
\textbf{}
\begin{center}
\includegraphics[width=.6\textwidth]{more_data_log}
\end{center}
SVM%
\hyperref[ch:UsingNeuralNetsToRecognizeHandwrittenDigits]{}
SVM
\href{path_to_url}{scikit-learn } SVM
SVM
\footnote{
\href{path_to_url}{\lstinline!more_data.py!}
}
\begin{center}
\includegraphics[width=.6\textwidth]{more_data_comparison}
\end{center}
SVM
scikit-learn
SVM
50,000 94.48\% 5,000
93.24\%
A
B A B
B~~~~
\footnote{
\href{path_to_url}{Scaling to very very large
corpora for natural language disambiguation} Michele Banko Eric
Brill 2001} A B
Y X
\textbf{}
\subsection*{}
\begin{itemize}
\item \textbf{}
\end{itemize}
\textbf{} \gls*{overfitting}\gls*{regularization}
\gls*{overfitting}
\gls*{regularization}
\section{}
\label{sec:weight_initialization}
\gls*{weight}\gls*{bias}%
\hyperref[ch:UsingNeuralNetsToRecognizeHandwrittenDigits]{}
\gls*{weight}\gls*{bias}
$0$ $1$\textbf{}
\gls*{weight}\gls*{bias}
$1,000$
\gls*{weight}\gls*{weight}
\begin{center}
\includegraphics{tikz32}
\end{center}
$x$ $1$ $0$
$z=\sum_j w_j x_j + b$ $500$ $x_j$ $0$
$z$ $501$ $500$ \gls*{weight}
$1$ \gls*{bias} $z$ $0$ $\sqrt{501} \approx
22.4$$z$
\begin{center}
\includegraphics{wide_gaussian}
\end{center}
$|z|$ $z \gg 1$ $z \ll
-1$ $\sigma(z)$ $1$ $0$
\gls*{weight}
\gls*{cost-func}\gls*{weight}
\footnote{%
\hyperref[sec:the_four_fundamental_equations_behind_backpropagation]{\gls*{bp}
}\gls*{weight}}
\gls*{cost-func}
\gls*{weight}
\gls*{weight} $0$
$1$
$n_{\rm in}$ \gls*{weight} $0$
$1/\sqrt{n_{\rm in}}$ \gls*{weight}
$0$ $1$
\gls*{bias} $z = \sum_j w_j x_j
+ b$ $0$ $500$
$0$ $500$ $1$ $z$ $0$
$\sqrt{3/2} = 1.22\ldots$
\begin{center}
\includegraphics{narrow_gaussian}
\end{center}
\subsection*{}
\begin{itemize}
\item $z = \sum_j w_j x_j + b$ $\sqrt{3/2}$
ab
\end{itemize}
\gls*{bias} $0$
$1$ \gls*{bias}
\gls*{bias}
\gls*{bias} $0$\gls*{bias}
MNIST \gls*{weight} $30$
\gls*{mini-batch} $10$\gls*{regularization} $\lambda = 5.0$
\gls*{learning-rate} $\eta=0.5$ $0.1$
\gls*{weight}
\begin{lstlisting}[language=Python]
`python
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
>>> import network2
>>> net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)
>>> net.large_weight_initializer()
>>> net.SGD(training_data, 30, 10, 0.1, lmbda = 5.0,
... evaluation_data=validation_data,
... monitor_evaluation_accuracy=True)
\end{lstlisting}
\gls*{weight}
\lstinline!network2!
\lstinline!net.large_weight_initializer()!
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)
>>> net.SGD(training_data, 30, 10, 0.1, lmbda = 5.0,
... evaluation_data=validation_data,
... monitor_evaluation_accuracy=True)
\end{lstlisting}
\footnote{
\href{path_to_url}{\lstinline!weight_initialization.py!}
}
\begin{center}
\includegraphics[width=.6\textwidth]{weight_initialization_30}
\end{center}
96\%
87\%
93\%\gls*{weight}
$100$
\begin{center}
\includegraphics[width=.6\textwidth]{weight_initialization_100}
\end{center}
%
\gls*{epoch}
\gls*{weight}
$1/\sqrt{n_{\rm in}}$ \gls*{weight}
$1/\sqrt{n_{\rm in}}$ \gls*{weight}
$1/\sqrt{n_{\rm in}}$
2012 Yoshua Bengio
\footnote{\href{path_to_url}{Practical
Recommendations for Gradient-Based Training of Deep Architectures}
Yoshua Bengio 2012} 14 15
\subsection*{}
\begin{itemize}
\item \textbf{\gls*{regularization}\gls*{weight}} L2 \gls*{regularization}
\gls*{weight}
1 $\lambda$ \gls*{epoch}\gls*{weight}
2 $\eta \lambda \ll n$\gls*{weight} $\exp(-\eta \lambda / m)$
\gls*{epoch}3 $\lambda$ \gls*{weight}\gls*{weight} $1/\sqrt{n}$
$n$ \gls*{weight}
\end{itemize}
\section{}
\label{sec:handwriting_recognition_revisited_the_code}
\lstinline!network2.py!
\hyperref[sec:implementing_our_network_to_classify_digits]{} \lstinline!network.py!
\lstinline!network.py! $74$
\lstinline!network.py! \lstinline!Network!
\lstinline!sizes!
\lstinline!cost!
\begin{lstlisting}[language=Python]
class Network(object):
def __init__(self, sizes, cost=CrossEntropyCost):
self.num_layers = len(sizes)
self.sizes = sizes
self.default_weight_initializer()
self.cost=cost
\end{lstlisting}
\lstinline!__init__! \lstinline!network.py!
\lstinline!default_weight_initializer! %
\hyperref[sec:weight_initialization]{\gls*{weight}}
$0$ $1/\sqrt{n}$$n$
$0$ $1$ \gls*{bias}
\begin{lstlisting}[language=Python]
def default_weight_initializer(self):
self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
self.weights = [np.random.randn(y, x)/np.sqrt(x)
for x, y in zip(self.sizes[:-1], self.sizes[1:])]
\end{lstlisting}
\lstinline!np! Numpy
\lstinline!import! Numpy\gls*{bias}
\gls*{bias}
\lstinline!network.py!
\lstinline!default_weight_initializer!
\lstinline!large_weight_initializer!
\gls*{weight}\gls*{bias} \lstinline!default_weight_initializer!
\begin{lstlisting}[language=Python]
def large_weight_initializer(self):
self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(self.sizes[:-1], self.sizes[1:])]
\end{lstlisting}
\lstinline!larger_weight_initializer!
\lstinline!__init__!
\lstinline!cost!
\footnote{ Python \lstinline!@staticmethod!
\lstinline!fn! \lstinline!delta!
\lstinline!@staticmethod! Python
\lstinline!self!
\lstinline!fn! \lstinline!delta!}
\begin{lstlisting}[language=Python]
class CrossEntropyCost(object):
@staticmethod
def fn(a, y):
return np.sum(np.nan_to_num(-y*np.log(a)-(1-y)*np.log(1-a)))
@staticmethod
def delta(z, a, y):
return (a-y)
\end{lstlisting}
Python Python \gls*{cost-func}
$a$
$y$ \lstinline!CrossEntropyCost.fn!
\lstinline!np.nan_to_num! Numpy $0$
\gls*{cost-func}%
\hyperref[sec:the_four_fundamental_equations_behind_backpropagation]{}
\gls*{bp}$\delta^L$
\gls*{cost-func}\gls*{cost-func}
~\eqref{eq:66}
\begin{equation}
\delta^L = a^L-y
\label{eq:99}\tag{99}
\end{equation}
\lstinline!CrossEntropyCost.delta!
\lstinline!network2.py! \gls*{cost-func}
\lstinline!QuadraticCost.fn! $a$ $y$
\lstinline!QuadraticCost.delta! \gls*{cost-func}
~\eqref{eq:30}
\begin{lstlisting}[language=Python]
class QuadraticCost(object):
@staticmethod
def fn(a, y):
return 0.5*np.linalg.norm(a-y)**2
@staticmethod
def delta(z, a, y):
return (a-y) * sigmoid_prime(z)
\end{lstlisting}
\lstinline!network2.py! \lstinline!network.py!
L2 \gls*{regularization}%
\gls*{regularization} \lstinline!network2.py!
\lstinputlisting[language=Python]{code_samples/src/network2.py}
L2 \gls*{regularization}
\lstinline!lmbda!
\lstinline!Network.SGD!
\lstinline!Network.update_mini_batch!
\gls*{weight}
\gls*{regularization}
\gls*{sgd}
\lstinline!False!
\lstinline!True! \lstinline!Network!
\lstinline!network2.py! \lstinline!Network.SGD!
\begin{lstlisting}[language=Python]
>>> evaluation_cost, evaluation_accuracy,
... training_cost, training_accuracy = net.SGD(training_data, 30, 10, 0.5,
... lmbda = 5.0,
... evaluation_data=validation_data,
... monitor_evaluation_accuracy=True,
... monitor_evaluation_cost=True,
... monitor_training_accuracy=True,
... monitor_training_cost=True)
\end{lstlisting}
\lstinline!evaluation_cost! $30$
\gls*{epoch}\gls*{cost-func}
\lstinline!Network.save!
\lstinline!Network!
JSON Python \lstinline!pickle! \lstinline!cPickle! ~~
Python JSON
\lstinline!Network! sigmoid
\lstinline!Network.__init__!
pickle \lstinline!load! JSON
Network \lstinline!load!
\lstinline!network.py!
$74$ $152$
\subsection*{}
\begin{itemize}
\item L1 \gls*{regularization} L1 \gls*{regularization} $30$
MNIST \gls*{regularization}\gls*{regularization}
\item \href{path_to_url}{\lstinline!network.py!} \lstinline!Network.cost_derivative!
\gls*{cost-func}\gls*{cost-func}
\lstinline!network2.py!
\lstinline!Network.cost_derivative!
`CrossEntropyCost.delta`
\end{itemize}
\section{}
\label{sec:how_to_choose_a_neural_network's_hyper-parameters}
\gls*{learning-rate} $\eta$\gls*{regularization} $\lambda$
MNIST
\gls*{learning-rate} $\eta=10.0$ \gls*{regularization} $\lambda=1000.0$
\begin{lstlisting}[language=Python]
>>> import mnist_loader
>>> training_data, validation_data, test_data = \
... mnist_loader.load_data_wrapper()
>>> import network2
>>> net = network2.Network([784, 30, 10])
>>> net.SGD(training_data, 30, 10, 10.0, lmbda = 1000.0,
... evaluation_data=validation_data, monitor_evaluation_accuracy=True)
Epoch 0 training complete
Accuracy on evaluation data: 1030 / 10000
Epoch 1 training complete
Accuracy on evaluation data: 990 / 10000
Epoch 2 training complete
Accuracy on evaluation data: 1009 / 10000
...
Epoch 27 training complete
Accuracy on evaluation data: 1009 / 10000
Epoch 28 training complete
Accuracy on evaluation data: 983 / 10000
Epoch 29 training complete
Accuracy on evaluation data: 967 / 10000
\end{lstlisting}
\gls*{learning-rate}\gls*{regularization}
$30$
$100$
$300$
minibatch
\gls*{cost-func}\gls*{weight}
\\
\textbf{} \textbf{}
MNIST
$0$ $1$ $0$ $1$ $10$
80\% $5$
$[784, 10]$
$[784, 30 ,10]$
\lstinline!network2.py!
$50,000$
~~ $[784, 30, 10]$ $10$
$10$
$1,000$ $10,000$
$100$
\lstinline!network2.py!
$1,000$ MNIST
0 1
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 10])
>>> net.SGD(training_data[:1000], 30, 10, 10.0, lmbda = 1000.0, \
... evaluation_data=validation_data[:100], \
... monitor_evaluation_accuracy=True)
Epoch 0 training complete
Accuracy on evaluation data: 10 / 100
Epoch 1 training complete
Accuracy on evaluation data: 10 / 100
Epoch 2 training complete
Accuracy on evaluation data: 10 / 100
...
\end{lstlisting}
10
$\lambda=1000.0$
$\lambda$ \gls*{weight}
$\lambda = 20.0$
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 10])
>>> net.SGD(training_data[:1000], 30, 10, 10.0, lmbda = 20.0, \
... evaluation_data=validation_data[:100], \
... monitor_evaluation_accuracy=True)
Epoch 0 training complete
Accuracy on evaluation data: 12 / 100
Epoch 1 training complete
Accuracy on evaluation data: 14 / 100
Epoch 2 training complete
Accuracy on evaluation data: 25 / 100
Epoch 3 training complete
Accuracy on evaluation data: 18 / 100
...
\end{lstlisting}
\gls*{learning-rate}
$\eta$ $100.0$:
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 10])
>>> net.SGD(training_data[:1000], 30, 10, 100.0, lmbda = 20.0, \
... evaluation_data=validation_data[:100], \
... monitor_evaluation_accuracy=True)
Epoch 0 training complete
Accuracy on evaluation data: 10 / 100
Epoch 1 training complete
Accuracy on evaluation data: 10 / 100
Epoch 2 training complete
Accuracy on evaluation data: 10 / 100
Epoch 3 training complete
Accuracy on evaluation data: 10 / 100
...
\end{lstlisting}
\gls*{learning-rate}
$\eta$ $\eta=1.0$
\begin{lstlisting}[language=Python]
>>> net = network2.Network([784, 10])
>>> net.SGD(training_data[:1000], 30, 10, 1.0, lmbda = 20.0, \
... evaluation_data=validation_data[:100], \
... monitor_evaluation_accuracy=True)
Epoch 0 training complete
Accuracy on evaluation data: 62 / 100
Epoch 1 training complete
Accuracy on evaluation data: 42 / 100
Epoch 2 training complete
Accuracy on evaluation data: 43 / 100
Epoch 3 training complete
Accuracy on evaluation data: 61 / 100
...
\end{lstlisting}
$\eta$
$10$ $\eta$ $\lambda$
$20$
hold out
~~
$\eta$L2 \gls*{regularization}
$\lambda$\gls*{mini-batch}
\gls*{regularization} momentum
co-efficient \\
\textbf{\gls*{learning-rate}} \gls*{learning-rate}$\eta=0.025$
$\eta=0.25$$\eta=2.5$ MNIST
$30$ minibatch $10$ $\lambda = 5.0$
$50,000$
\begin{center}
\includegraphics[width=.6\textwidth]{multiple_eta}
\end{center}
$\eta=0.025$\gls*{cost-func} $\eta=0.25$
$20$
$\eta=2.5$
\gls*{cost-func}
\begin{center}
\includegraphics{valley_with_ball}
\end{center}
$\eta$
$\eta=2.5$ $\eta=0.25$
$\eta=0.025$
$30$ %
\gls*{learning-rate}~~\gls*{sgd}
$\eta=0.25$$\eta=0.025$
\gls*{learning-rate}
\gls*{learning-rate}$\eta$
$\eta$
$\eta$
$\eta=0.01$
$\eta=0.1, 1.0,...$ $\eta$
$\eta=0.01$
$\eta=0.001, 0.0001,...$
\gls*{learning-rate}
$\eta$ $\eta=0.5$ $\eta=0.2$
$\eta$ $\eta$
MNIST \gls*{learning-rate} $\eta$
$0.1$ $\eta=0.5$
\gls*{learning-rate} $\eta=0.25$
$\eta=0.5$ $30$ \gls*{learning-rate}
\gls*{cost-func} $\eta$
\gls*{regularization}
minibatch \gls*{learning-rate}
\gls*{learning-rate}\gls*{learning-rate}%
\\
\textbf{\label{early_stopping}\gls*{epoch}}
\gls*{overfitting}
\gls*{regularization}
MNIST
$10$
$10$ MNIST
~~
$10$
$20$ $50$
MNIST $10$
MNIST
\lstinline!network2.py!
\subsection*{}
\begin{itemize}
\item \lstinline!network2.py! $n$
$n$
\item $n$
\lstinline!network2.py! $10$
\end{itemize}
\textbf{\gls*{learning-rate}} \gls*{learning-rate}
\gls*{learning-rate}\gls*{weight}
\gls*{learning-rate}\gls*{weight}
\gls*{learning-rate}
\gls*{learning-rate}
\gls*{learning-rate}
\gls*{learning-rate}$10$ $2$%
\gls*{learning-rate} $1/1024$$1/1000$
\gls*{learning-rate}
~~
\gls*{learning-rate}
\subsection*{}
\begin{itemize}
\item \lstinline!network2.py! $10$
\gls*{learning-rate}\gls*{learning-rate}
$1/128$
\end{itemize}
\textbf{\gls*{regularization}} \gls*{regularization}$\lambda=0.0$ $\eta$
$\eta$ $\lambda$
$\lambda=1.0$ $10$
$\lambda$
$\eta$
\subsection*{}
\begin{itemize}
\item
$\lambda$ $\eta$
\end{itemize}
\textbf{}
$\eta$ $\lambda$
\gls*{cost-func}\gls*{cost-func}\gls*{weight}
\gls*{regularization}
\\
\label{mini_batch_size}
\textbf{\gls*{mini-batch}} \gls*{mini-batch}
$1$ %
\gls*{mini-batch}
\gls*{mini-batch}
\gls*{cost-func}
$10-20$
%
\hyperref[ch:]{}
\gls*{mini-batch}
$50$ $100$
$100$ \gls*{mini-batch};
\begin{equation}
w \rightarrow w' = w-\eta \frac{1}{100} \sum_x \nabla C_x
\label{eq:100}\tag{100}
\end{equation}
\gls*{mini-batch}
\begin{equation}
w \rightarrow w' = w-\eta \nabla C_x
\label{eq:101}\tag{101}
\end{equation}
$50$
\gls*{mini-batch}\gls*{learning-rate} $100$
\begin{equation}
w \rightarrow w' = w-\eta \sum_x \nabla C_x
\label{eq:102}\tag{102}
\end{equation}
$100$ $50$
100 \gls*{mini-batch} $\nabla C_x$
\gls*{weight}%
\gls*{mini-batch}
\gls*{mini-batch}
\gls*{weight}
\gls*{mini-batch}
%
\gls*{mini-batch}
\gls*{mini-batch}
$\eta$
\gls*{mini-batch}\gls*{mini-batch}
%
\gls*{mini-batch}\gls*{mini-batch} $10$
\gls*{mini-batch}
\gls*{mini-batch}$1$
\gls*{mini-batch}
\gls*{mini-batch}\\
\textbf{}
\textbf{}\textbf{grid search}
James Bergstra Yoshua
Bengio $2012$
\footnote{\href{path_to_url}{Random search for
hyper-parameter optimization} James Bergstra Yoshua Bengio
2012}
2012
\footnote{\href{path_to_url}{Practical
Bayesian optimization of machine learning algorithms} Jasper Snoek
Hugo Larochelle Ryan Adams}%
\href{path_to_url}{}
\\
\textbf{}
$\eta$
$\lambda$ $\eta$
,
,
Yoshua Bengio 2012 \footnote{\href{path_to_url}{Practical
recommendations for gradient-based training of deep architectures}
Yoshua Bengio 2012}\gls*{bp}
Bengio
1998 Yann LeCunLon
BottouGenevieve Orr Klaus-Robert Mller
\footnote{\href{path_to_url}{Efficient
BackProp} Yann LeCun Lon Bottou Genevieve Orr Klaus-Robert
Mller 1998} 2012
\footnote{\href{path_to_url}{Neural
Networks: Tricks of the Trade} Grgoire Montavon Genevive
Orr Klaus-Robert Mller }
SVM
\section{}
\label{sec:other_techniques}
\subsection{}
\gls*{bp}\gls*{sgd} MNIST
\gls*{cost-func}
Hessian momentum \\
\textbf{Hessian }
\gls*{cost-func} $C$ $C$
$w=w_1,w_2,\ldots$ $C=C(w)$\gls*{cost-func} $w$
\begin{align}
C(w+\Delta w) &= C(w) + \sum_j \frac{\partial C}{\partial w_j} \Delta w_j \nonumber \\
& \quad + \frac{1}{2} \sum_{jk} \Delta w_j \frac{\partial^2 C}{\partial w_j \partial w_k} \Delta w_k + \ldots \label{eq:103}\tag{103}
\end{align}
\begin{equation}
C(w+\Delta w) = C(w) + \nabla C \cdot \Delta w +
\frac{1}{2} \Delta w^T H \Delta w + \ldots
\label{eq:104}\tag{104}
\end{equation}
$\nabla C$ $H$ \textbf{Hessian }
$jk$ $\partial^2 C/\partial w_j\partial w_k$
$C$
\begin{equation}
C(w+\Delta w) \approx C(w) + \nabla C \cdot \Delta w +
\frac{1}{2} \Delta w^T H \Delta w
\label{eq:105}\tag{105}
\end{equation}
\footnote{
Hessian
$C$ }
\begin{equation}
\Delta w = -H^{-1} \nabla C
\label{eq:106}\tag{106}
\end{equation}
~\eqref{eq:105} \gls*{cost-func} $w$
$w+\Delta w = w - H^{-1}\nabla C$ \gls*{cost-func}
\gls*{cost-func}
\begin{itemize}
\item $w$
\item $w$ $w' = w - H_{-1}\nabla C$ Hessian $H$ $\nabla C$
$w$
\item $w'$ $w = w' - H'^{-1}\nabla' C$ Hessian $H'$
$\nabla' C$ $w'$
\item $\ldots$
\end{itemize}
\eqref{eq:105}
$\Delta w = -\eta H^{-1} \nabla C$ $w$ $\eta$
\gls*{learning-rate}
\gls*{cost-func} \textbf{Hessian } \textbf{Hessian }
Hessian
\gls*{cost-func} Hessian
pathologies\gls*{bp} Hessian
Hessian Hessian
Hessian $10^7$ \gls*{weight}\gls*{bias}
Hessian $10^7 \times 10^7=10^{14}$
$H^{-1}\nabla C$
Hessian
momentum \\
\textbf{ momentum } Hessian
momentum
momentum
momentum
velocity
momentum
$v = v_1, v_2, \ldots$
$w_j$ \footnote{$w_j$ \gls*{weight}
} $w\rightarrow w'=w-\eta\nabla C$
\begin{align}
v \rightarrow v' &= \mu v - \eta \nabla C \label{eq:107}\tag{107}\\
w \rightarrow w' &= w+v' \label{eq:108}\tag{108}
\end{align}
$\mu$
$\mu=1$ $\nabla
C$ $v$ $w$
\begin{center}
\includegraphics{valley_with_ball}
\end{center}
momentum
~\eqref{eq:107} $\mu$ $\mu$
$1-\mu$ $\mu=1$
$\nabla C$ $\mu=0$
~\eqref{eq:107}~\eqref{eq:108}
$w\rightarrow w'=w-\eta \nabla C$ $0$ $1$ $\mu$
hold out
$\mu$ $\eta$ $\lambda$
$\mu$ $\mu$
\textbf{moment co-efficient} $\mu$
momentum
momentum
\gls*{bp} minibatch
Hessian ~~
momentum
\subsection*{}
\begin{itemize}
\item $\mu > 1$
\item $\mu < 0$
\end{itemize}
\subsection*{}
\begin{itemize}
\item momentum \gls*{sgd} \lstinline!network2.py!
\end{itemize}
\textbf{\gls*{cost-func}} \gls*{cost-func}
\footnote{\href{path_to_url}{Efficient
BackProp} Yann LeCun Lon Bottou Genevieve Orr and Klaus-Robert
Mller 1998} BFGS
limited memory BFGS
\href{path_to_url}{L-BFGS}
\footnote{
\href{path_to_url~hinton/absps/momentum.pdf}{On the
importance of initialization and momentum in deep learning} Ilya
Sutskever James Martens George Dahl Geoffrey Hinton 2012}
Nesterov momentum
\gls*{sgd} momentum
\subsection{}
\label{subsec:other_models_of_artificial_neuron}
\gls*{sigmoid-neuron}
S
\gls{tanh-neuron}\gls{hyperbolic-tangent} \gls*{sigmoid-func} $x$
$w$\gls*{bias} $b$ \gls*{tanh-neuron}
\begin{equation}
\tanh(w \cdot x+b)
\label{eq:109}\tag{109}
\end{equation}
\gls*{sigmoid-neuron} $\tanh$
\begin{equation}
\tanh(z) \equiv \frac{e^z-e^{-z}}{e^z+e^{-z}}
\label{eq:110}\tag{110}
\end{equation}
\begin{equation}
\sigma(z) = \frac{1+\tanh(z/2)}{2}
\label{eq:111}\tag{111}
\end{equation}
$\tanh$ \gls*{sigmoid-func}
$\tanh$
\begin{center}
\includegraphics{tanh_function}
\end{center}
$\tanh$ $(-1, 1)$ $(0,
1)$ $\tanh$
sigmoid
\gls*{sigmoid-neuron}\gls*{tanh-neuron}
$(-1, 1)$ \footnote{ tanh \gls*{sigmoid-neuron}
}\gls*{bp}\gls*{sgd}
\gls*{tanh-neuron}
\subsection*{}
\begin{itemize}
\item ~\eqref{eq:111}
\end{itemize}
\gls*{tanh} S
\gls*{tanh}\footnote{
\href{path_to_url}{Efficient
BackProp} Yann LeCun Lon Bottou Genevieve Orr Klaus-Robert
Mller 1998
\href{path_to_url}{Understanding
the difficulty of training deep feedforward networks} Xavier Glorot
Yoshua Bengio 2010}\gls*{tanh}
\gls*{sigmoid-neuron}\gls*{weight}
$w_{jk}^{l+1}$ $l+1$ $j$ \gls*{bp}%
\hyperref[eq:bp4]{} $a_k^l\delta_j^{l+1}$
$\delta_j^{l+1}$
$\delta_j^{l+1}$ $w_{jk}^{l+1}$
$\delta_j^{l+1}$ \gls*{weight} $w_{jk}^{l+1}$
\gls*{weight}
\gls*{weight}
\gls*{tanh}
\gls*{tanh} $0$ $\tanh(-z) = -\tanh(z)$
\gls*{weight}
\gls*{bias}
\gls*{tanh} \gls*{sigmoid-func} \gls*{sigmoid-neuron}
\gls*{tanh}
\textbf{\gls{reln}}\textbf{\gls{relu}} ReLU
$x$\gls*{weight} $w$\gls*{bias} $b$ ReLU
\begin{equation}
\max(0, w \cdot x+b)
\label{eq:112}\tag{112}
\end{equation}
$\max(0,z)$
\begin{center}
\includegraphics{max_function}
\end{center}
sigmoid tanh ReLU
\gls*{bp}\gls*{sgd}
ReLU
\footnote{
\href{path_to_url}{What is the
Best Multi-Stage Architecture for Object Recognition?} Kevin Jarrett
Koray Kavukcuoglu Marc'Aurelio Ranzato Yann LeCun 2009
\href{path_to_url}{Deep Sparse
Rectier Neural Networks} Xavier GlorotAntoine Bordes Yoshua
Bengio 2011
\href{path_to_url}{ImageNet
Classification with Deep Convolutional Neural Networks} Alex
Krizhevsky Ilya Sutskever Geoffrey Hinton 2012
\gls*{cost-func}\gls*{regularization}
\href{path_to_url~hinton/absps/reluICML.pdf}{Rectified Linear
Units Improve Restricted Boltzmann Machines} Vinod Nair Geoffrey
Hinton 2010}
ReLU \gls*{tanh-neuron}
ReLU sigmoid
$0$ $1$
$\sigma'$ Tanh
ReLU
ReLU
\gls*{sigmoid-neuron}
\subsection{}
\begin{quote}
{\itshape \textbf{}
}
\textbf{}
-- {\itshape Yann LeCun %
\href{path_to_url}{
}}
\end{quote}
...
...
......
~~~~
~~
~~
\hyperref[dropout_explanation]{}\gls*{dropout}
\footnote{
\href{path_to_url}{ImageNet
Classification with Deep Convolutional Neural Networks} Alex
KrizhevskyIlya Sutskever Geoffrey Hinton 2012}
dropout dropout
~~~~
``` | /content/code_sandbox/chap3.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 20,037 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\crossEntropyCostLearning{2.0}{2.0}{0.005}{100}
\end{document}
``` | /content/code_sandbox/images/saturation4-100.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage[default]{cjkfonts}
\usetikzlibrary{calc,positioning}
\input{../westernfonts}
\begin{document}
\begin{tikzpicture}
\foreach \x in {0,...,26}
\draw (\x * 0.4,0) -- (\x * 0.4, 1);
\coordinate (layer1bottom) at (5.2,1);
\coordinate (layer2top) at (5.2,0);
\node(layer1) [above,rectangle,draw,minimum width=11cm,inner sep=6pt] at (layer1bottom) {
\texttt{AND}, \texttt{OR}, \texttt{NOT}
};
\node(layer2) [below,rectangle,draw,minimum width=11cm,inner sep=6pt] at (layer2top) {
};
\node(input) [above=of layer1] {
\begin{tabular}{c}
\\
\end{tabular}
};
\node(output) [below=of layer2] {
\begin{tabular}{c}
\\
\end{tabular}
};
\coordinate (t0) at (layer1.north);
\coordinate (t1) at (layer1.north east);
\coordinate (t2) at (layer1.north west);
\coordinate (i0) at (input.south);
\coordinate (i1) at (input.south east);
\coordinate (i2) at (input.south west);
\draw (i0) to (t0);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (i0)!\x!(i1) $) to ($ (t0)!\x!(t1) $);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (i0)!\x!(i2) $) to ($ (t0)!\x!(t2) $);
\coordinate (b0) at (layer2.south);
\coordinate (b1) at (layer2.south east);
\coordinate (b2) at (layer2.south west);
\coordinate (o0) at (output.north);
\coordinate (o1) at (output.north east);
\coordinate (o2) at (output.north west);
\draw (b0) to (o0);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (b0)!\x!(b1) $) to ($ (o0)!\x!(o1) $);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (b0)!\x!(b2) $) to ($ (o0)!\x!(o2) $);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/shallow_circuit.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 727 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{axis}[
view={-30}{15},
axis background/.style={fill=blue!5},
xlabel=$x$,
ylabel=$y$,
xtick distance=1,
ytick distance=1,
ztick distance=1,
xtick={1},
ytick={1},
ztick={2}, % big number to disable
title={Many towers},
colormap={simple}{rgb255=(235,95,95) rgb255=(255,155,145)},
declare function={
g(\z)=floor(\z * 4.999);
f(\x,\y)=(g(\x)*g(\x) + g(\y) * g(\y))/50;
}]
\addplot3[surf,domain=0:1] {
f(x,y)
};
\end{axis}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/many_towers.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 297 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=middle,
axis y line=left,
ymin=-2.2,
ymax=2.2,
xmax=1.1,
xlabel=$x$,
xtick distance=1,
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\h,\s,\e) = \h * (sigma(300 * (\x - \s)) - sigma(300 * (\x - \e)));
}]
\addplot[red!50,thick,domain=0.08:0.32,samples=51] {
f(x, -1.55/2, 0.1, 0.3)
};
\addplot[green!50,thick,domain=0.28:0.52,samples=51] {
f(x, -1.15/2, 0.3, 0.5)
};
\addplot[blue!50,thick,domain=0.48:0.72,samples=51] {
f(x, -0.7/2, 0.5, 0.7)
};
\addplot[violet!50,thick,domain=0.68:0.92,samples=51] {
f(x, -0.6/2, 0.7, 0.9)
};
\addplot[orange!50,thick,domain=0.88:0.99,samples=51] {
f(x, 0.3, 0.9, 1.1)
};
\end{axis}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/shifted_bumps.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 440 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm},
font=\footnotesize
]
\node(l0) [neuron] {};
\node(m0) [neuron,right=1.5 of l0] {};
\node(m1) [neuron,above=0.6 of m0] {};
\node(m2) [neuron,above=0.6 of m1] {};
\node(m3) [neuron,above=0.6 of m2] {};
\node(l2) [neuron,left=1.5 of m3] {};
\node(r0) [neuron,right=1.5 of m0] {};
\node(r2) [neuron,right=1.5 of m3] {};
\coordinate (lc) at ($(l0)!0.5!(l2)$);
\node(l1) at (lc) [neuron] {};
\coordinate (rc) at ($(r0)!0.5!(r2)$);
\node(r1) at (rc) [neuron] {};
\foreach \x in {0,1,2}
\node(tl\x) [left=0.1 of l\x] {$\ldots$};
\foreach \x in {0,1,2}
\node(tr\x) [right=0.1 of r\x] {$\ldots$};
\node (n0) [neuron,right=5 of m1] {};
\node (n1) [neuron,right=5 of m2] {};
\coordinate (nc) at ($(n0)!0.5!(n1)$);
\node (c) [right=1.5 of nc] {$C$};
\node(tn0) [left=0.1 of n0] {$\ldots$};
\node(tn1) [left=0.1 of n1] {$\ldots$};
% connections:
\foreach \x in {0,1,2}
\foreach \y in {0,...,3}
\draw[->] (l\x) to (m\y);
\foreach \x in {0,...,3}
\foreach \y in {0,1,2}
\draw[->] (m\x) to (r\y);
\draw[->] (n0) to (c);
\draw[->] (n1) to (c);
% mark:
\coordinate (p) at ($(l1)!0.5!(m3)$);
\draw[->,very thick,blue] (p) to (m3);
\draw[->,very thick,blue] (m3) to (r0);
\draw[->,very thick,blue] (m3) to (r1);
\draw[->,very thick,blue] (m3) to (r2);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz24.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 731 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=1.6mm}
]
\foreach \x in {0,...,27}
\foreach \y in {0,...,27}
\node (x\x y\y) [neuron,gray] at (\x * 0.25,\y * 0.25) {};
\node [above] at (3.5,7) {input neurons};
\foreach \x in {0,...,23}
\foreach \y in {0,...,23}
\node (m\x n\y) [neuron,gray] at (\x * 0.25 + 9, \y * 0.25 + 0.5) {};
\node [above] at (12, 6.5) {first hidden layer};
\node(hidden) [neuron,orange,thick] at (m0n23) {};
\foreach \x in {0,...,4}
\foreach \y in {22,23,...,27}
{\node (a\x b\y) [neuron,orange,thick] at (\x * 0.25,\y * 0.25) {};
\draw[->,orange] (a\x b\y) to (hidden);
}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz44.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 365 |
```postscript
%!PS-Adobe-3.0 EPSF-3.0
%%Title: /home/zhanggyb/overfitting3.eps
%%Creator: matplotlib version 1.3.1, path_to_url
%%CreationDate: Wed Feb 17 11:16:53 2016
%%Orientation: portrait
%%BoundingBox: 13 175 598 616
%%EndComments
%%BeginProlog
/mpldict 8 dict def
mpldict begin
/m { moveto } bind def
/l { lineto } bind def
/r { rlineto } bind def
/c { curveto } bind def
/cl { closepath } bind def
/box {
m
1 index 0 r
0 exch r
neg 0 r
cl
} bind def
/clipbox {
box
clip
newpath
} bind def
%!PS-Adobe-3.0 Resource-Font
%%Title: DejaVu Sans
%%Creator: Converted from TrueType to type 3 by PPR
25 dict begin
/_d{bind def}bind def
/_m{moveto}_d
/_l{lineto}_d
/_cl{closepath eofill}_d
/_c{curveto}_d
/_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d
/_e{exec}_d
/FontName /DejaVuSans def
/PaintType 0 def
/FontMatrix[.001 0 0 .001 0 0]def
/FontBBox[-1021 -415 1681 1167]def
/FontType 3 def
/Encoding [ /space /period /zero /one /two /three /four /five /six /seven /eight /nine /C /E /a /c /d /e /h /n /o /p /s /t ] def
/FontInfo 10 dict dup begin
/FamilyName (DejaVu Sans) def
/FullName (DejaVu Sans) def
/Weight (Book) def
/Version (Version 2.34) def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -130 def
/UnderlineThickness 90 def
end readonly def
/CharStrings 24 dict dup begin
/space{318 0 0 0 0 0 _sc
}_d
/period{318 0 107 0 210 124 _sc
107 124 _m
210 124 _l
210 0 _l
107 0 _l
107 124 _l
_cl}_d
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318 742 _m
399 742 461 709 505 645 _c
548 580 570 486 570 364 _c
570 241 548 147 505 83 _c
461 19 399 -13 318 -13 _c
236 -13 173 19 130 83 _c
87 147 66 241 66 364 _c
66 486 87 580 130 645 _c
173 709 236 742 318 742 _c
_cl}_d
/one{636 0 110 0 544 729 _sc
124 83 _m
285 83 _l
285 639 _l
110 604 _l
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383 729 _l
383 83 _l
544 83 _l
544 0 _l
124 0 _l
124 83 _l
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/two{{636 0 73 0 536 742 _sc
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536 83 _l
536 0 _l
73 0 _l
73 83 _l
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426 479 433 504 433 528 _c
433 566 419 598 392 622 _c
365 646 330 659 286 659 _c
255 659 222 653 188 643 _c
154 632 117 616 78 594 _c
78 694 _l
118 710 155 722 189 730 _c
223 738 255 742 284 742 _c
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532 504 526 475 515 449 _c
504 422 484 390 454 354 _c
446 344 420 317 376 272 _c
332 227 271 164 192 83 _c
_cl}_e}_d
/three{{636 0 76 -13 556 742 _sc
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542 298 556 258 556 212 _c
556 140 531 84 482 45 _c
432 6 362 -13 271 -13 _c
240 -13 208 -10 176 -4 _c
144 1 110 10 76 22 _c
76 117 _l
103 101 133 89 166 81 _c
198 73 232 69 268 69 _c
330 69 377 81 409 105 _c
441 129 458 165 458 212 _c
458 254 443 288 413 312 _c
383 336 341 349 287 349 _c
}_e{202 349 _l
202 430 _l
291 430 _l
339 430 376 439 402 459 _c
428 478 441 506 441 543 _c
441 580 427 609 401 629 _c
374 649 336 659 287 659 _c
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169 644 135 635 98 623 _c
98 711 _l
135 721 170 729 203 734 _c
235 739 266 742 296 742 _c
370 742 429 725 473 691 _c
517 657 539 611 539 553 _c
539 513 527 479 504 451 _c
481 423 448 403 406 393 _c
_cl}_e}_d
/four{636 0 49 0 580 729 _sc
378 643 _m
129 254 _l
378 254 _l
378 643 _l
352 729 _m
476 729 _l
476 254 _l
580 254 _l
580 172 _l
476 172 _l
476 0 _l
378 0 _l
378 172 _l
49 172 _l
49 267 _l
352 729 _l
_cl}_d
/five{{636 0 77 -13 549 729 _sc
108 729 _m
495 729 _l
495 646 _l
198 646 _l
198 467 _l
212 472 227 476 241 478 _c
255 480 270 482 284 482 _c
365 482 429 459 477 415 _c
525 370 549 310 549 234 _c
549 155 524 94 475 51 _c
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``` | /content/code_sandbox/images/overfitting3.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 15,458 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm},
font=\footnotesize
]
\node (neuron) [neuron] {};
\node (input) [left=2 of neuron] {};
\node (output) [right=1.5 of neuron] {};
\node [above] at (neuron.north) {bias $b$};
\draw[->] (input) to node [above] {weight $w$} (neuron);
\draw[->] (neuron) to (output);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz28.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 202 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm},
font=\footnotesize
]
% left layers:
\foreach \y in {0,...,3}
\node (l\y) at (0, \y * 1.25 + 1 * 1.25) [neuron] {};
% right layers:
\foreach \y in {0,...,2}
\node (r\y) at (2, \y * 1.25 + 1 * 1.25) [neuron,dotted] {};
\node (r3) at (2, 3 * 1.25 + 1.25) [neuron] {};
% right text:
\foreach \y in {0,...,3}
\node (tr\y) [right=0.5 of r\y] {$\ldots$};
% bottom text:
\node [below=0.5 of l0,rotate=-90,yshift=1.5mm] {$\ldots$};
\node [below=0.5 of r0,rotate=-90,yshift=1.5mm] {$\ldots$};
\node [below=0.5 of tr0,rotate=-45,xshift=2mm] {$\ldots$};
\foreach \x in {0,...,3}
\draw [->] (l\x) to (r3);
\foreach \x in {0,...,3}
\foreach \y in {0,...,2}
\draw [dotted,->] (l\x) to (r\y);
% \draw[->] (r0) -- ++(1,0);
% \draw[->] (r1) -- ++(1,0);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz32.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 479 |
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``` | /content/code_sandbox/images/polynomial_fit.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 8,694 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{positioning}
\input{../plots}
\begin{document}
\manipulateTiGraph{8}{-5}
\end{document}
``` | /content/code_sandbox/images/ti_graph.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 83 |
```postscript
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showpage
``` | /content/code_sandbox/images/training_speed_3_layers.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 20,214 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\usepackage{pgfplots}
\usepackage[default]{cjkfonts}
\input{../westernfonts}
\input{../plots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel={\normalsize $x$},
axis lines=left,
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
legend style={font=\tiny},
xtick distance=1,
ytick distance=1,
xtick={0},
ytick={1},
% minor tick num=1,
legend entries={$w=8,b=-4$\\$w=8,b=4$\\$w=3,b=4$\\$w=105,b=4$\\},
legend style={
at={(0.8,0.5)},
anchor=west
},
title={},
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\w,\b) = sigma(\w * \x + \b);
}
]
\addplot[
gray,
thick,
dotted,
domain=-5:5,
samples=101
] {
f(x, 8, -4)
};
\addplot[
orange!40!gray,
domain=-5:5,
samples=101
] {
f(x, 8, 4)
};
\addplot[
orange!80,
domain=-5:5,
samples=101
] {
f(x, 3, 4)
};
\addplot[
orange,
thick,
domain=-5:5,
samples=401
] {
f(x, 105, 4)
};
\end{axis}
\end{tikzpicture}%
\end{document}
``` | /content/code_sandbox/images/create_step_function.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 472 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\node (x1) at (-6, 1.2) {$x_1$};
\node (x2) at (-6, -1.2) {$x_2$};
\node (pl1) at (-4, 0) [neuron] {};
\node (pm1) at (-2, 1.2) [neuron] {};
\node (pm2) at (-2, -1.2) [neuron] {};
\node (pm3) at (-2, -2.5) [neuron] {};
\node (pr1) at (0, 0) [neuron] {};
\node (sum) at (2.5, 0) {\ sum: $x_1 \oplus x_2$};
\node (carrybit) at (2.5, -2.5) {\ carry bit: $x_1x_2$};
\draw [->] (-5.75, 1.2) to (pl1);
\draw [->] (-5.75, -1.2) to (pl1);
\draw [->] (-5.75, 1.2) to (pm1);
\draw [->] (-5.75, -1.2) to (pm2);
\draw [->] (pl1) to (pm1);
\draw [->] (pl1) to (pm2);
\draw [->] (pl1) to node [below,xshift=-2mm] {$-4$} (pm3);
\draw [->] (pm1) to (pr1);
\draw [->] (pm2) to (pr1);
\draw [->] (pr1) to (sum);
\draw [->] (pm3) to (carrybit);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz5.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 496 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\node (x1) at (-6, 1.2) {$x_1$};
\node (x2) at (-6, -1.2) {$x_2$};
\node (pl1) at (-4, 0) [neuron] {};
\node (pm1) at (-2, 1.2) [neuron] {};
\node (pm2) at (-2, -1.2) [neuron] {};
\node (pm3) at (-2, -2.5) [neuron] {};
\node (pr1) at (0, 0) [neuron] {};
\node (sum) at (2.5, 0) {\ sum: $x_1 \oplus x_2$};
\node (carrybit) at (2.5, -2.5) {\ carry bit: $x_1x_2$};
\draw [->] (-5.75, 1.2) to (pl1);
\draw [->] (-5.75, -1.2) to (pl1);
\draw [->] (-5.75, 1.2) to (pm1);
\draw [->] (-5.75, -1.2) to (pm2);
\draw [->] (pl1) to (pm1);
\draw [->] (pl1) to (pm2);
\draw [->] (pl1.-60) to (pm3);
\draw [->] (pl1.-70) to (pm3.180);
\draw [->] (pm1) to (pr1);
\draw [->] (pm2) to (pr1);
\draw [->] (pr1) to (sum);
\draw [->] (pm3) to (carrybit);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz4.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 503 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
inputlayer/.style={rectangle,draw,fill=white,inner sep=0pt,minimum size=30mm},
hiddenlayer/.style={rectangle,draw,fill=white,inner sep=0pt,minimum size=22mm},
poolinglayer/.style={rectangle,draw,fill=white,inner sep=0pt,minimum size=15mm},
neuron/.style={circle,draw,inner sep=0pt,minimum size=5mm}
]
\node (input) [inputlayer,anchor=south west] at (0,0) {};
\node (hidden0) [hiddenlayer,anchor=south west] at (4,0) {};
\node (hidden1) [hiddenlayer,anchor=south west,xshift=6mm,yshift=6mm] at (hidden0.south west) {};
\node (hidden2) [hiddenlayer,anchor=south west,xshift=1mm,yshift=1mm] at (hidden1.south west) {};
\node (hidden3) [hiddenlayer,anchor=south west,xshift=1mm,yshift=1mm] at (hidden2.south west) {};
\draw[dashed] (hidden0.north west) -- (hidden1.north west);
\draw[dashed] (hidden0.south west) -- (hidden1.south west);
\draw[dashed] (hidden0.south east) -- (hidden1.south east);
\foreach \x in {0,1,2,3}
\node (pooling\x) [poolinglayer,anchor=west,right=1.8 of hidden\x] {};
\draw[dashed] (pooling0.north west) -- (pooling1.north west);
\draw[dashed] (pooling0.south west) -- (pooling1.south west);
\draw[dashed] (pooling0.south east) -- (pooling1.south east);
\foreach \x in {0,...,7}
\node(s\x) [neuron] at (12, 0.75 * \x - 1.125) {};
\foreach \x in {0,...,4}
\node(o\x) [neuron] at (14.2, 0.75 * \x + 0.375) {};
\node [above] at (input.north) {$28 \times 28$};
\node [above,xshift=-6mm] at (hidden3.north) {
\begin{tabular}{c}
convolution layer\\
$20 \times 24 \times 24$
\end{tabular}
};
\node [above,xshift=-5mm] at (pooling2.north) {
\begin{tabular}{c}
pooling layer\\
$20 \times 12 \times 12$
\end{tabular}
};
\node [above] at (s7.north) {
\begin{tabular}{c}
100 sigmoid\\
neurons
\end{tabular}
};
\node [above] at (o4.north) {
\begin{tabular}{c}
10 neurons\\
output layer\\
(softmax)
\end{tabular}
};
\node [below,rotate=-90,xshift=5mm,yshift=1.75mm] at (s0.south) {$\ldots$};
\node [below,rotate=-90,xshift=5mm,yshift=1.75mm] at (o0.south) {$\ldots$};
\coordinate(a0) at (input.east);
\draw[->] (a0) -- ++(1.4,0);
\draw[->] (a0)++(4,0) -- ++(1.4,0);
\draw[->] (a0)++(7.3,0) -- ++(1.45,0);
\draw[->] (a0)++(9.25,0) -- ++(1.65,0);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/simple_conv.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 981 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\usepackage{pgfplots}
\usepackage{cjkfonts}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0) [neuron,right=of l0,yshift=-1.5cm] {};
\node (m1) [neuron,right=of l0,yshift=1.5cm] {};
\node (r0) [neuron,right=of m0,yshift=1.5cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0);
\draw[->] (l0) to (m1);
\draw[->] (m0) to (r0);
\draw[->] (m1) to (r0);
\node(b) [blue,above] at (m1.north) {$s = 0.40$};
\end{scope}
\begin{scope}[xshift=6cm]
\begin{axis}[
width=5.6cm,
height=5.6cm,
xlabel={\normalsize $x$},
axis lines=left,
tick label style={font=\tiny},
label style={font=\tiny},
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``` | /content/code_sandbox/images/step_parameterization.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 493 |
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``` | /content/code_sandbox/images/regularized2.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 13,625 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{circuits.logic.US,positioning,decorations.pathreplacing,math}
\begin{document}
\begin{tikzpicture}[
circuit logic US, large circuit symbols,
contact/.style={circle, fill=black, minimum size=4pt, inner sep=0pt}
]
\matrix [column sep=1cm,row sep=2mm] {
& \node [nand gate] (n1) {}; & \\
\node [nand gate] (n2) {}; & & \node [nand gate] (sum) {}; \\
& \node [nand gate] (n3) {}; & \\
& & \node [nand gate] (carry) {}; \\
};
\node (x1) [left=of n2,yshift=8mm] {$x_1$};
\node (x2) [left=of n2,yshift=-8mm] {$x_2$};
\node (text1) [right=of sum] {sum: $x_1 \oplus x_2$};
\node (text2) [right=of carry] {carry bit: $x_1x_2$};
% connections:
\draw (x1.east) -- ++(right:5mm) node [contact] (x1split) {} |- (n1.input 1);
\draw (x1split) |- (n2.input 1);
\draw (x2.east) -- ++(right:5mm) node [contact] (x2split) {} |- (n2.input 2);
\draw (x2split) |- (n3.input 2);
\draw (n2.output) -- ++(right:5mm) node [contact] (split1) [] {} |- (n1.input 2);
\draw (split1 |- n3.input 1) node[contact] (split2) {} -- (n3.input 1);
\draw (split2 |- carry.input 1) node[contact] (split3) {} -- (carry.input 1);
\draw (split1) -- (split2) -- (split3) |- (carry.input 2);
\draw (n1.output) -- ++(right:5mm) |- (sum.input 1);
\draw (n3.output) -- ++(right:5mm) |- (sum.input 2);
\draw (sum.output) -- (text1.west);
\draw (carry.output) -- (text2.west);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz3.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 617 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm}
]
% input label:
\node (input) at (-4.5, 0) {input};
% leftmost perceptrons:
\node (pl1) at (-2.25, 1.25) [neuron] {};
\node (pl2) at (-2.25, 0) [neuron] {};
\node (pl3) at (-2.25, -1.25) [neuron] {};
% middle perceptrons:
\node (pm1) at (0, 1.875) [neuron] {};
\node (pm2) at (0, 0.625) [neuron] {};
\node (pm3) at (0, -0.625) [neuron] {};
\node (pm4) at (0, -1.875) [neuron] {};
% rightmost perceptron:
\node (pr) at (2.25, 0) [neuron] {};
% output:
\node (output) at (4.5, 0) {\ output};
% connect nodes:
\draw [->] (-4, 1.5) to (pl1);
\draw [->] (-4, 1.5) to (pl2);
\draw [->] (-4, 1.5) to (pl3);
\draw [->] (-4, 0.75) to (pl1);
\draw [->] (-4, 0.75) to (pl2);
\draw [->] (-4, 0.75) to (pl3);
\draw [->] (-4, 0) to (pl1);
\draw [->] (-4, 0) to (pl2);
\draw [->] (-4, 0) to (pl3);
\draw [->] (-4, -0.75) to (pl1);
\draw [->] (-4, -0.75) to (pl2);
\draw [->] (-4, -0.75) to (pl3);
\draw [->] (-4, -1.5) to (pl1);
\draw [->] (-4, -1.5) to (pl2);
\draw [->] (-4, -1.5) to (pl3);
\draw [->] (pl1) to (pm1);
\draw [->] (pl1) to (pm2);
\draw [->] (pl1) to (pm3);
\draw [->] (pl1) to (pm4);
\draw [->] (pl2) to (pm1);
\draw [->] (pl2) to (pm2);
\draw [->] (pl2) to (pm3);
\draw [->] (pl2) to (pm4);
\draw [->] (pl3) to (pm1);
\draw [->] (pl3) to (pm2);
\draw [->] (pl3) to (pm3);
\draw [->] (pl3) to (pm4);
\draw [->] (pm1) to (pr);
\draw [->] (pm2) to (pr);
\draw [->] (pm3) to (pr);
\draw [->] (pm4) to (pr);
\draw [->] (pr) to (output);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz1.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 859 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\crossEntropyCostLearning{2.0}{2.0}{0.005}{50}
\end{document}
``` | /content/code_sandbox/images/saturation4-50.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```unknown
# Makefile to generate pdfs from tikz pictures
TEX := xelatex
RM := rm -f
TARGETS := $(patsubst %.tex,%.pdf,$(wildcard *.tex))
.PHONY: clean
all: $(TARGETS) ../plots.tex
%.pdf: %.tex
$(TEX) $(basename $<)
clean:
$(RM) *.pdf
$(RM) *.aux
$(RM) *.log
``` | /content/code_sandbox/images/Makefile | unknown | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 100 |
```postscript
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%%CreationDate: 2016-01-30T20:22:54
%%Pages: (atend)
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[1 0 0 -1 0 420] CT
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GS
1 GC
N
0 0 560 420 re
f
GR
GS
1 GC
N
0 0 560 420 re
f
GR
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1 GC
N
73 374 M
507 374 L
507 31 L
73 31 L
cp
f
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507 374 M
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[1 0 0 1 121.22222 378.20001] CT
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[1 0 0 1 0 0] CT
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0.149 GC
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[1 0 0 1 0 0] CT
-3.5 9 moveto
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(2) t
GR
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[1 0 0 1 265.88889 378.20001] CT
0.149 GC
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GS
[1 0 0 1 0 0] CT
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(2.5) t
GR
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[1 0 0 1 314.11111 378.20001] CT
0.149 GC
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[1 0 0 1 0 0] CT
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(3) t
GR
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[1 0 0 1 362.33334 378.20001] CT
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(3.5) t
GR
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[1 0 0 1 410.55554 378.20001] CT
0.149 GC
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GS
[1 0 0 1 0 0] CT
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[1 0 0 1 0 0] CT
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( x) t
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507 374 M
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GR
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1 LJ
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N
507 276 M
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GR
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0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 227 M
502.66 227 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 178 M
502.66 178 L
S
GR
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0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 129 M
502.66 129 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 80 M
502.66 80 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 31 M
502.66 31 L
S
GR
GS
[1 0 0 1 68.8 374] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(2) t
GR
GR
GS
[1 0 0 1 68.8 325] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(3) t
GR
GR
GS
[1 0 0 1 68.8 276] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(4) t
GR
GR
GS
[1 0 0 1 68.8 227] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(5) t
GR
GR
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[1 0 0 1 68.8 178] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(6) t
GR
GR
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[1 0 0 1 68.8 129] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
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(7) t
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[1 0 0 1 68.8 80] CT
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/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
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(8) t
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0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(9) t
GR
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[0 -1 1 0 56 208] CT
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/Helvetica-BoldItalic 12 F
GS
[1 0 0 1 0 0] CT
0 0 moveto
1 -1 scale
( y) t
GR
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[1 0 0 1 118.99658 348.95557] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 167.96068 333.71112] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 216.92479 265.11111] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 274.04959 227] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 298.53165 185.07777] CT
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3.333 0 M
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-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 355.6564 150.77779] CT
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1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
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[1 0 0 1 371.97778 135.53333] CT
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cp
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[1 0 0 1 420.94186 70.74446] CT
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cp
f
GR
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[1 0 0 1 461.7453 36.44442] CT
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3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
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%%Trailer
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%%EOF
``` | /content/code_sandbox/images/simple_model.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 7,593 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=middle,
axis y line=left,
ymin=-2.2,
ymax=2.2,
xmax=1.1,
xlabel=$x$,
xtick distance=1,
declare function={
sigma(\z) = 1/(1 + exp(-\z));
f(\x,\h,\s,\e) = \h * (sigma(300 * (\x - \s)) - sigma(300 * (\x - \e)));
}]
\addplot[red!50,thick,domain=0.0:0.22,samples=51] {
f(x, -1.3/2, 0.0, 0.2)
};
\addplot[green!50,thick,domain=0.18:0.42,samples=51] {
f(x, -1.8/2, 0.2, 0.4)
};
\addplot[blue!50,thick,domain=0.38:0.62,samples=51] {
f(x, -0.5/2, 0.4, 0.6)
};
\addplot[violet!50,thick,domain=0.58:0.82,samples=51] {
f(x, -0.9/2, 0.6, 0.8)
};
\addplot[orange!50,thick,domain=0.78:0.99,samples=51] {
f(x, 0.3/2, 0.8, 1.0)
};
\end{axis}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/half_bumps.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 442 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{positioning}
\input{../plots}
\begin{document}
\createTiGraphSurf{8}{-5}
\end{document}
``` | /content/code_sandbox/images/ti_graph-0.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 83 |
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showpage
``` | /content/code_sandbox/images/training_speed_4_layers.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 22,599 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}[
tick/.style={font=\scriptsize}
]
\draw (-6,0) -- (6,0);
\foreach \x in {-30, -20, -10, 0, 10, 20, 30}
\draw (\x / 5, 0) -- (\x / 5, -0.1) node[tick,below]{$\x$};
\draw (0,0) -- (0,1.8);
\draw (0,1.8) -- (-0.1, 1.8) node[tick,left] {$0.02$};
\tikzmath{
% Gaussian distribution:
function gaussian(\x, \m, \s) {
return (1 / (sqrt(2 * pi) * \s)) * exp(- (pow(\x - \m,2)) / (2 * pow(\s, 2)));
};
{\draw[blue,domain=-30:30,samples=101,xscale=0.2] plot (\x, {gaussian(\x, 0, 22.4) * 90});};
}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/wide_gaussian.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 324 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\crossEntropyCostLearning{2.0}{2.0}{0.005}{200}
\end{document}
``` | /content/code_sandbox/images/saturation4-200.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\node (x1) at (-6, 1.2) [neuron] {$x_1$};
\node (x2) at (-6, -1.2) [neuron] {$x_2$};
\node (pl1) at (-4, 0) [neuron] {};
\node (pm1) at (-2, 1.2) [neuron] {};
\node (pm2) at (-2, -1.2) [neuron] {};
\node (pm3) at (-2, -2.5) [neuron] {};
\node (pr1) at (0, 0) [neuron] {};
\node (sum) at (2.5, 0) {\ sum: $x_1 \oplus x_2$};
\node (carrybit) at (2.5, -2.5) {\ carry bit: $x_1x_2$};
\draw [->] (x1) to (pl1);
\draw [->] (x2) to (pl1);
\draw [->] (x1) to (pm1);
\draw [->] (x2) to (pm2);
\draw [->] (pl1) to (pm1);
\draw [->] (pl1) to (pm2);
\draw [->] (pl1) to node [below,xshift=-2mm] {$-4$} (pm3);
\draw [->] (pm1) to (pr1);
\draw [->] (pm2) to (pr1);
\draw [->] (pr1) to (sum);
\draw [->] (pm3) to (carrybit);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz6.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 480 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\quadraticCostLearning{2.0}{2.0}{0.15}{250}
\end{document}
``` | /content/code_sandbox/images/saturation2-250.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm},
font=\footnotesize
]
\node(l0) [neuron] {};
\node(m0) [neuron,right=1.5 of l0] {};
\node(m1) [neuron,above=0.6 of m0] {};
\node(m2) [neuron,above=0.6 of m1] {};
\node(m3) [neuron,above=0.6 of m2] {};
\node(l2) [neuron,left=1.5 of m3] {};
\node(r0) [neuron,right=1.5 of m0] {};
\node(r2) [neuron,right=1.5 of m3] {};
\coordinate (lc) at ($(l0)!0.5!(l2)$);
\node(l1) at (lc) [neuron] {};
\coordinate (rc) at ($(r0)!0.5!(r2)$);
\node(r1) at (rc) [neuron] {};
\foreach \x in {0,1,2}
\node(tl\x) [left=0.1 of l\x] {$\ldots$};
\foreach \x in {0,1,2}
\node(tr\x) [right=0.1 of r\x] {$\ldots$};
\node (n0) [neuron,right=5 of m1] {};
\node (n1) [neuron,right=5 of m2] {};
\coordinate (nc) at ($(n0)!0.5!(n1)$);
\node (c) [right=1.5 of nc] {$C$};
\node(tn0) [left=0.1 of n0] {$\ldots$};
\node(tn1) [left=0.1 of n1] {$\ldots$};
% connections:
\foreach \x in {0,1,2}
\foreach \y in {0,...,3}
\draw[->] (l\x) to (m\y);
\foreach \x in {0,...,3}
\foreach \y in {0,1,2}
\draw[->] (m\x) to (r\y);
\draw[->] (n0) to (c);
\draw[->] (n1) to (c);
% mark:
\coordinate (p) at ($(l1)!0.5!(m3)$);
\draw[->,very thick,blue] (p) to (m3);
\draw[->,very thick,blue] (m3) to (r0);
\draw[->,very thick,blue] (m3) to (r1);
\draw[->,very thick,blue] (m3) to (r2);
\draw[->,very thick,blue] (n0) to (c);
\draw[->,very thick,blue] (n1) to (c);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz25.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 769 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm},
font=\footnotesize
]
\node(l0) [neuron] {};
\node(m0) [neuron,right=1.5 of l0] {};
\node(m1) [neuron,above=0.6 of m0] {};
\node(m2) [neuron,above=0.6 of m1] {};
\node(m3) [neuron,above=0.6 of m2] {};
\node(l2) [neuron,left=1.5 of m3] {};
\node(r0) [neuron,right=1.5 of m0] {};
\node(r2) [neuron,right=1.5 of m3] {};
\coordinate (lc) at ($(l0)!0.5!(l2)$);
\node(l1) at (lc) [neuron] {};
\coordinate (rc) at ($(r0)!0.5!(r2)$);
\node(r1) at (rc) [neuron] {};
\foreach \x in {0,1,2}
\node(tl\x) [left=0.1 of l\x] {$\ldots$};
\foreach \x in {0,1,2}
\node(tr\x) [right=0.1 of r\x] {$\ldots$};
\node (n0) [neuron,right=5 of m1] {};
\node (n1) [neuron,right=5 of m2] {};
\coordinate (nc) at ($(n0)!0.5!(n1)$);
\node (c) [right=1.5 of nc] {$C$};
\node(tn0) [left=0.1 of n0] {$\ldots$};
\node(tn1) [left=0.1 of n1] {$\ldots$};
% connections:
\foreach \x in {0,1,2}
\foreach \y in {0,...,3}
\draw[->] (l\x) to (m\y);
\foreach \x in {0,...,3}
\foreach \y in {0,1,2}
\draw[->] (m\x) to (r\y);
\draw[->] (n0) to (c);
\draw[->] (n1) to (c);
% mark:
\coordinate (p) at ($(l1)!0.5!(m3)$);
\node(t) [blue,above=1.5 of p] {$\Delta w^l_{jk}$};
\draw[->,very thick,blue] (t) to (p);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz22.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 692 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
tick/.style={font=\footnotesize}
]
\draw (-5,0) -- (5,0) node [right] {Z};
\foreach \x in {-4, -3, -2, -1, 0, 1, 2, 3, 4}
\draw (\x, 0) -- (\x, -0.15) node[tick,below]{$\x$};
%\draw (-5, 0) -- (-5, -0.1);
\draw (5, 0) -- (5, -0.15);
\draw (-5,-3) -- (-5,3);
\foreach \y in {-1.0, -0.5, 0.0, 0.5, 1.0}
\draw (-5, \y * 3) -- (-5-0.15, \y * 3) node[tick,left]{$\y$};
\draw (0, 3) node[above] {tanh function};
\draw[blue,thick,domain=-10:10,xscale=0.5,samples=101] plot (\x, {6 * (1 + tanh(\x/2))/2 - 3});
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tanh_function.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 350 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\usepackage{pgfplots}
\usepackage{cjkfonts}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\begin{scope}
\node (l0) [neuron] {$x$};
\node (m0) [neuron,right=of l0,yshift=-1.5cm] {};
\node (m1) [neuron,right=of l0,yshift=1.5cm] {};
\node (r0) [neuron,right=of m0,yshift=1.5cm] {};
\draw[->] (r0) -- ++(1,0);
\draw[->] (l0) to (m0);
\draw[->] (l0) to node (w) [blue,above,xshift=-0.5cm] {$w = 100$} (m1);
\draw[->] (m0) to (r0);
\draw[->] (m1) to (r0);
\node(b) [blue,above] at (m1.north) {$b = -40$};
\end{scope}
\begin{scope}[xshift=6cm]
\begin{axis}[
width=5.6cm,
height=5.6cm,
xlabel={\normalsize $-b/w = 0.40$},
axis lines=left,
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
xtick distance=1,
ytick distance=1,
xmax=1.1,
ymax=1.1,
title={}
]
\draw[gray] (axis cs:0.4,0) -- (axis cs:0.4,1.0);
\draw[gray] (axis cs:0,1) -- (axis cs:1,1);
\addplot[
orange,
thick,
domain=0:1,
samples=101
] {
1/(1 + exp(-(100 * x + (-40))))
};
\end{axis}
\end{scope}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/step.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 566 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm}
]
% left layers:
\foreach \y in {0,...,2}
\node (l\y) at (0, \y * 1.875 + 2 * 1.25) [neuron] {};
% middle layers:
\foreach \y in {0,2,5}
\node (m\y) at (2.25, \y * 1.25 + 1 * 1.25) [neuron] {};
\foreach \y in {1,3,4}
\node (m\y) at (2.25, \y * 1.25 + 1 * 1.25) [neuron,dotted] {};
% right layer:
\node (r0) at (4.5, 5) [neuron] {};
\node (r1) at (4.5, 3.75) [neuron] {};
% connections:
\foreach \x in {0,...,2}
\foreach \y in {0,2,5}
\draw [->] (l\x) to (m\y);
\foreach \x in {0,...,2}
\foreach \y in {1,3,4}
\draw [dotted,->] (l\x) to (m\y);
\foreach \x in {0,2,5}
\foreach \y in {0,1}
\draw [->] (m\x) to (r\y);
\foreach \x in {1,3,4}
\foreach \y in {0,1}
\draw [dotted,->] (m\x) to (r\y);
\draw[->] (r0) -- ++(1,0);
\draw[->] (r1) -- ++(1,0);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz31.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 510 |
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f
GR
GS
1 GC
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0 0 560 420 re
f
GR
GS
1 GC
N
73 374 M
507 374 L
507 31 L
73 31 L
cp
f
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0.149 GC
2 setlinecap
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0.5 LW
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73 374 M
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73 369.66 L
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116.4 374 M
116.4 369.66 L
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GS
0.149 GC
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0.5 LW
N
159.8 374 M
159.8 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
203.2 374 M
203.2 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
246.6 374 M
246.6 369.66 L
S
GR
GS
0.149 GC
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1 LJ
0.5 LW
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290 374 M
290 369.66 L
S
GR
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0.149 GC
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N
333.4 374 M
333.4 369.66 L
S
GR
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0.149 GC
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0.5 LW
N
376.8 374 M
376.8 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
420.2 374 M
420.2 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
463.6 374 M
463.6 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 374 M
507 369.66 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 31 M
73 35.34 L
S
GR
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0.149 GC
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1 LJ
0.5 LW
N
116.4 31 M
116.4 35.34 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
159.8 31 M
159.8 35.34 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
203.2 31 M
203.2 35.34 L
S
GR
GS
0.149 GC
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1 LJ
0.5 LW
N
246.6 31 M
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S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
290 31 M
290 35.34 L
S
GR
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0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
333.4 31 M
333.4 35.34 L
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0.5 LW
N
376.8 31 M
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0.149 GC
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N
420.2 31 M
420.2 35.34 L
S
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463.6 31 M
463.6 35.34 L
S
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0.149 GC
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GS
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[1 0 0 1 0 0] CT
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( x) t
GR
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GS
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0.5 LW
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73 374 M
73 31 L
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2 setlinecap
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0.5 LW
N
507 374 M
507 31 L
S
GR
GS
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1 LJ
0.5 LW
N
73 374 M
77.34 374 L
S
GR
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0.149 GC
2 setlinecap
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0.5 LW
N
73 339.7 M
77.34 339.7 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 305.4 M
77.34 305.4 L
S
GR
GS
0.149 GC
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0.5 LW
N
73 271.1 M
77.34 271.1 L
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0.5 LW
N
73 236.8 M
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GR
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1 LJ
0.5 LW
N
73 202.5 M
77.34 202.5 L
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0.149 GC
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N
73 168.2 M
77.34 168.2 L
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GR
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0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 133.9 M
77.34 133.9 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 99.6 M
77.34 99.6 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 65.3 M
77.34 65.3 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
73 31 M
77.34 31 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 374 M
502.66 374 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 339.7 M
502.66 339.7 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 305.4 M
502.66 305.4 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 271.1 M
502.66 271.1 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 236.8 M
502.66 236.8 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 202.5 M
502.66 202.5 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 168.2 M
502.66 168.2 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 133.9 M
502.66 133.9 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 99.6 M
502.66 99.6 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 65.3 M
502.66 65.3 L
S
GR
GS
0.149 GC
2 setlinecap
1 LJ
0.5 LW
N
507 31 M
502.66 31 L
S
GR
GS
[1 0 0 1 68.8 374] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(0) t
GR
GR
GS
[1 0 0 1 68.8 339.70001] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(1) t
GR
GR
GS
[1 0 0 1 68.8 305.39999] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(2) t
GR
GR
GS
[1 0 0 1 68.8 271.10001] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(3) t
GR
GR
GS
[1 0 0 1 68.8 236.8] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
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(4) t
GR
GR
GS
[1 0 0 1 68.8 202.5] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(5) t
GR
GR
GS
[1 0 0 1 68.8 168.2] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(6) t
GR
GR
GS
[1 0 0 1 68.8 133.89999] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(7) t
GR
GR
GS
[1 0 0 1 68.8 99.6] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
-7 3 moveto
1 -1 scale
(8) t
GR
GR
GS
[1 0 0 1 68.8 65.3] CT
0.149 GC
/Helvetica 11 F
GS
[1 0 0 1 0 0] CT
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(9) t
GR
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[1 0 0 1 68.8 31] CT
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(10) t
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GS
[1 0 0 1 0 0] CT
0 0 moveto
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( y) t
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[1 0 0 1 157.79692 287.8689] CT
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3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 201.86461 277.19778] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 245.93231 229.17778] CT
N
3.333 0 M
3.333 1.841 1.841 3.333 0 3.333 C
-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
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cp
f
GR
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[1 0 0 1 297.34464 202.5] CT
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-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
1.841 -3.333 3.333 -1.841 3.333 0 C
cp
f
GR
GS
[1 0 0 1 319.37848 173.15445] CT
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-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
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cp
f
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[1 0 0 1 370.79077 149.14445] CT
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GR
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[1 0 0 1 385.47998 138.47333] CT
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-1.841 3.333 -3.333 1.841 -3.333 0 C
-3.333 -1.841 -1.841 -3.333 0 -3.333 C
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%%Trailer
%%Pages: 1
%%EOF
``` | /content/code_sandbox/images/linear_fit.eps | postscript | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 8,303 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\crossEntropyCostLearning{0.6}{0.9}{0.005}{250}
\end{document}
``` | /content/code_sandbox/images/saturation3-250.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{positioning}
\input{../plots}
\begin{document}
\createTiGraphSurf{50}{-5}
\end{document}
``` | /content/code_sandbox/images/ti_graph-1.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 83 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\usepackage{pgfplots}
\usepackage{cjkfonts}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
width=7cm,
height=7cm,
xlabel={\normalsize $x$},
axis lines=center,
tick label style={font=\tiny},
label style={font=\tiny},
title style={font=\scriptsize},
xtick={1},
ytick={-2,-1,0,1,2},
% minor tick num=1,
title={$\sigma^{-1} \circ f(x)$},
declare function={
sigmaInverse(\z)=ln(\z/(1-\z));
f(\x)=0.2+0.4*\x*\x+0.3*\x*sin(15*deg(\x))+0.05*cos(50*deg(\x));
},
]
\addplot[blue,domain=0:1,samples=201] {
sigmaInverse(f(x))
};
\end{axis}
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/inverted_function_2.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 289 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\usetikzlibrary{backgrounds,math}
\input{../plots}
\begin{document}
\quadraticCostLearning{2.0}{2.0}{0.15}{50}
\end{document}
``` | /content/code_sandbox/images/saturation2-50.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 94 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage[default]{cjkfonts}
\usetikzlibrary{calc,positioning}
\input{../westernfonts}
\begin{document}
\begin{tikzpicture}
\foreach \x in {0,...,26}
\coordinate (p\x) at (\x * 0.4,0);
\foreach \x in {0,...,26}
\draw (p\x) -- ++(0, 1);
\coordinate (layer1bottom) at (5.2,1);
\coordinate (layer2top) at (5.2,0);
\node(layer1) [above,rectangle,draw,minimum width=11cm,inner sep=6pt] at (layer1bottom) {
};
\node(layer2) [below,rectangle,draw,minimum width=11cm,inner sep=6pt] at (layer2top) {
};
\coordinate (layer2bottom) at ($ (layer2top)-(layer2.north)+(layer2.south) $);
\foreach \x in {0,...,26}
\draw ($ (p\x)-(layer2.north)+(layer2.south)$) -- ++(0, -1);
\coordinate (layer3top) at ($ (layer2bottom)-(0,1) $);
\node(layer3) [below,rectangle,draw,minimum width=11cm,inner sep=6pt] at (layer3top) {
};
\node(input) [above=of layer1] {
x y
};
\node(output) [below=of layer3] {
x.y
};
\coordinate (t0) at (layer1.north);
\coordinate (t1) at (layer1.north east);
\coordinate (t2) at (layer1.north west);
\coordinate (i0) at (input.south);
\coordinate (i1) at (input.south east);
\coordinate (i2) at (input.south west);
\draw (i0) to (t0);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (i0)!\x!(i1) $) to ($ (t0)!\x!(t1) $);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (i0)!\x!(i2) $) to ($ (t0)!\x!(t2) $);
\coordinate (b0) at (layer3.south);
\coordinate (b1) at (layer3.south east);
\coordinate (b2) at (layer3.south west);
\coordinate (o0) at (output.north);
\coordinate (o1) at (output.north east);
\coordinate (o2) at (output.north west);
\draw (b0) to (o0);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (b0)!\x!(b1) $) to ($ (o0)!\x!(o1) $);
\foreach \x in {0.15,0.35,0.6,0.95}
\draw ($ (b0)!\x!(b2) $) to ($ (o0)!\x!(o2) $);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/circuit_multiplication.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 821 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
tick/.style={font=\footnotesize}
]
\draw (-5,0) -- (5,0) node[right] {Z};
\foreach \x in {-4,...,5}
\draw (\x, 0) -- (\x, -0.15) node[tick,below]{$\x$};
% \draw (-5, 0) -- (-5, -0.1);
\draw (5, 0) -- (5, -0.15);
\draw (-5,-4) -- (-5,4);
\foreach \y in {-4,...,5}
\draw (-5, \y * 4 / 5) -- (-5-0.15, \y * 4 / 5) node[tick,left]{$\y$};
\draw (-5,-4) -- (-5-0.15,-4);
\draw (0, 4) node[above] {max(o,z)};
\draw[blue,thick] (-5, 0) -- (0, 0) -- (5, 4);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/max_function.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 315 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\node (perceptron) at (0, 0) [neuron] {$x_1$};
\node (output) at (2.25, 0) {};
\draw [->] (perceptron) to (output);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz7.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 144 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning,math}
\input{../plots}
\begin{document}
\manipulateSoftmaxBars{2.5}{-1}{3.2}{-5}
\end{document}
``` | /content/code_sandbox/images/softmax-4.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 87 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=10mm}
]
\node(n) [neuron] {};
\node(x) [neuron,left=1.25 of n,yshift=1.5cm] {$x$};
\node(y) [neuron,left=1.25 of n,yshift=-1.5cm] {$y$};
\draw[->] (x) -- node [yshift=2mm,xshift=2mm] {$w_1$} (n);
\draw[->] (y) -- node [yshift=-2mm,xshift=2mm] {$w_2$} (n);
\node [above] at (n.north) {$b$};
\draw[->] (n) -- ++(1cm, 0);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/two_inputs.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 263 |
```tex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[11pt,tikz,border=1]{standalone}
\usepackage[default]{cjkfonts}
\begin{document}
\begin{tikzpicture}[
neuron/.style={circle,draw,inner sep=0pt,minimum size=8mm}
]
% leftmost perceptrons:
\node (pl1) at (-2.25, 1.25) [neuron] {};
\node (pl2) at (-2.25, 0) [neuron] {};
\node (pl3) at (-2.25, -1.25) [neuron] {};
% middle perceptrons:
\node (pm1) at (0, 1.875) [neuron] {};
\node (pm2) at (0, 0.625) [neuron] {};
\node (pm3) at (0, -0.625) [neuron] {};
\node (pm4) at (0, -1.875) [neuron] {};
% rightmost perceptron:
\node (pr) at (2.25, 0) [neuron] {};
% output:
\node (output) at (5.5, 0) {\ $output + \Delta output$};
\node (weight) at (-1.125, 2.5) {$w + \Delta w$};
% connect nodes:
\draw [->] (pl1) to (pm1);
\draw [->] (pl1) to (pm2);
\draw [->] (pl1) to (pm3);
\draw [->] (pl1) to (pm4);
\draw [->] (pl2) to (pm1);
\draw [->] (pl2) to (pm2);
\draw [->] (pl2) to (pm3);
\draw [->] (pl2) to (pm4);
\draw [->] (pl3) to (pm1);
\draw [->] (pl3) to (pm2);
\draw [->] (pl3) to (pm3);
\draw [->] (pl3) to (pm4);
\draw [->] (pm1) to (pr);
\draw [->] (pm2) to (pr);
\draw [->] (pm3) to (pr);
\draw [->] (pm4) to (pr);
\draw [->] (pr) to (output);
\draw (weight) -- node [above] {
\begin{tabular}{c}
\footnotesize \\
\footnotesize
\end{tabular}
} (6.35, 2.5);
\draw [->] (6.35, 2.5) -- (6.35, 0.25);
% \draw [->] (weight) -- node (5.5, 2.5) to (output);
\end{tikzpicture}
\end{document}
``` | /content/code_sandbox/images/tikz8.tex | tex | 2016-01-20T08:40:07 | 2024-08-15T16:40:43 | nndl | zhanggyb/nndl | 1,208 | 704 |
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