Machine Learning and Neural Networks - page 25

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MIT 6.S192 - Lecture 19: Easy 3D content creation with consistent neural fields, Ajay Jain

MIT 6.S192 - Lecture 19: Easy 3D content creation with consistent neural fields, Ajay Jain

In this lecture, Ajay Jain presents his work on neural scene representations, specifically focusing on the Neural Radiance Fields model which uses sparsely sampled input views to construct a representation of a scene's 3D geometry and color. Jain discusses the challenges of fitting a Neural Radiance Field to a single scene, as well as ways to improve the data efficiency of the training process by adding photometric loss and semantic consistency loss. He also talks about using CLIP to remove artifacts in NeRF and generate 3D objects from captions in the project Dream Fields. Other topics include creating consistent foreground objects in scenes, acquiring captioned 3D object datasets, reducing rendering costs, and optimizing the system's performance.

• 00:00:00 In this section of the video, Ajay Jain talks about his journey and research interests in generative models and AI tools. He also discusses the different types of scene representations, focusing on volumetric approaches which are easier to train and use in a learning context compared to mesh representations commonly used in graphics applications. Jain also highlights the recent interest in neural scene representations.
  
  
• 00:05:00 In this section, the speaker discusses the concept of neural scene representations, specifically focusing on a model called Neural Radiance Fields. This model addresses the problem of view synthesis, where sparsely sampled input views of a scene are used to construct a representation of the scene's 3D geometry and color, allowing for rendering from new perspectives. The Neural Radiance Field is estimated from these images and allows for smooth interpolation of the sparsely sampled views. The model is also able to model view-dependent effects such as specularities on shiny surfaces. The neural network is represented as a function mapping from 3D space coordinates and viewing direction and predicts color and density for each coordinate. Rendering is done through ray tracing and volume rendering.
  
  
• 00:10:00 In this section, the speaker discusses the process of rendering color according to the neural scene representation in order to optimize weights of the neural network to achieve the desired colors. They explain that the MLP that encodes the scene allows for differentiable rendering of viewpoints making it easier to optimize. This process is called inverse graphics and involves going from 2D space to optimizing for the underlying 3D representation that will reconstruct those views. The speaker also explains how the input coordinates are fed into the neural network using a sinusoidal positional encoding approach that projects the 5-dimensional input into a higher dimensional space.
  
  
• 00:15:00 In this section, the video discusses the challenges of fitting a Neural Radiance Field to a single scene, as it generally requires a large amount of data to train. The video showcases one synthetic scene that required a hundred images to fit the field, while some outdoor scenes required fewer images. The video then discusses a way to improve the data efficiency of the training process by adding an additional loss to the Neural Radiance Field training, called photometric loss, at unobserved positions. This allows for the rendering of novel views even before the scene has converged.
  
  
• 00:20:00 In this section, the speaker discusses the concept of semantic consistency loss, which allows for the regularization of scenes from any perspective during training. Using a visual encoder, each input view is represented in feature space, which allows for the encoding of object identity and other features that are consistent across viewpoints. The feature choice is crucial, as it should encode the object's identity and properties instead of low-level details like pixel colors. The speaker proposes using the CLIP network because it has learned to match images to their associated captions, which allows it to encode classes of objects, poses of objects, and details about the entire scene. The speaker shows that the cosine similarity of embeddings from the image encoder of CLIP within a particular scene from different camera poses is highly similar, yet very different in pixel space.
  
  
• 00:25:00 In this section of the video, the speaker talks about their experiments on using CLIP to remove artifacts in NeRF by maximizing feature space similarity, and then discusses using CLIP to generate 3D objects from just a caption in their second work, Dream Fields. They optimize a shared scene representation to look similar to a diet NeRF with additional regularizers, and then render out new views for each perspective. They use the text encoder of CLIP to maximize similarity in feature space between the scene and the caption instead of optimizing for feature similarity in image feature space. They note that automatic captioning with CLIP is challenging due to the difficulty of the search and optimization process.
  
  
• 00:30:00 In this section, Ajay Jain discusses the process of creating consistent foreground objects in 3D scenes using Dream Fields. By randomly sampling poses in the scene and rendering images, they try to ensure that semantic features match the caption features. However, naive application of this approach without regularization can lead to degenerate scenes. Therefore, they regularize the scene by composited randomly sampled backgrounds and highly transparent foreground objects to encourage sparsity in the scene. With this regularization, they are able to create more consistent foreground objects in the scene. Additionally, they experiment with different caption templates to measure the compositional generalization of the model.
  
  
• 00:35:00 In this section, the speaker discusses the challenges of acquiring captioned 3D object datasets and how they addressed this issue by using CLIP, a pre-trained 2D image and text encoder. The Dream Fields project lifts this 2D representation into 3D through a shared representation of geometry. The speaker also talks about the techniques used to improve the quality of generated 3D objects and the cost of the optimization process. The goal of the project is to make 3D content creation easier and generate assets that are useful for downstream applications, and the code is available for anyone who wants to try it out.
  
  
• 00:40:00 In this section, Ajay Jain explains that the 3D structure of objects only emerges because of the shared representation, which satisfies CLIP from any perspective. There is no prior on the 3D structure learned from data, so some consistency on the 3D data is missing, and that is an opportunity for future work. Jain also mentions that when the underlying geometry is not visible, the consistency is not preserved, leading to repeated structures. The neural net generated from the function mapping from coordinates must be post-processed, which involves converting the output of the neural field to an .fbx file or mesh, with some algorithms allowing for this conversion.
  
  
• 00:45:00 In this section, the speaker discusses strategies to reduce rendering costs in neural radiance field volumetric representations, including rendering images at low resolution and using a single low memory GPU to significantly speed up the process. They also explain how transparent objects can be handled within this type of representation and mention future steps to make this approach more practical for 3D artists, such as synthesizing deformable objects and incorporating human feedback during training. Finally, they share a Colab notebook to implement the system and adjust quality settings for different prompts.
  
  
• 00:50:00 In this section, the speaker discusses the learning curves and optimization process involved in creating 3D content using consistent neural fields. They explain different factors that impact the optimization process, such as the transparency of pixels in the scene and the number of data augmentations per iteration. They also suggest tweaking the configuration parameters to reduce memory usage, which includes reducing the number of samples and using the CLIP b32 instead of the default CLIP b16. Finally, they mention the option of parallelizing across multiple GPUs to optimize performance.

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MIT 6.S192 - Lecture 20: Generative art using diffusion, Prafulla Dhariwal

MIT 6.S192 - Lecture 20: Generative art using diffusion, Prafulla Dhariwal

In this lecture, Prafulla Dhariwal from OpenAI discusses the progress of generative modeling for hard creative tasks, particularly with diffusion models. The process involves starting with an image and slowly adding Gaussian noise to it, then reversing the process by taking some noised damage and de-noising it to create less noisy images. The generative model is obtained by training a model to reverse noise like this, producing an image from pure noise at test time by running the model step-by-step backwards. The reverse prediction of the process also looks like a Gaussian distribution when the amount of noise added is very small, which is used to predict the mean and variance of the model. Dhariwal also discusses how to use diffusion models for in-painting and addressing the potential dangers of AI-generated content.

• 00:00:00 In this section of the video, Prafulla Dhariwal from OpenAI discusses his background and motivations for conducting AI research. He also showcases some examples of powerful creative ML models, such as GPT-3 and JukeBox, which can generate poetry and music, respectively, from just a few examples. The video also includes a sample output from JukeBox, which generated the music and lyrics together, as they are interdependent. Viewers are encouraged to ask questions at any point during the presentation.
  
  
• 00:05:00 In this section, Prafulla Dhariwal discusses the progress of generative modeling for hard creative tasks. The speaker explains that one way of understanding whether models are really learning something is by seeing if they can create complex and hard to understand things. Training models to create images, audio, and video is one of the hardest tasks in these domains, but there has been a lot of progress in trying to create things from models or generative modeling. Dhariwal discusses how generative models work, what inputs they require, and how they are evaluated. The speaker also talks about the recent progress of diffusion models, which can generate realistic faces and different categories of images. Dhariwal shows that these models are better than GANs at generating images.
  
  
• 00:10:00 In this section of the lecture, Prafulla Dhariwal discusses generative art through the use of diffusion models. The models work by starting with an image and slowly adding Gaussian noise to it, trying to reverse the process by taking some noised damage and de-noising it to create less noisy images. The generative model is obtained by training a model to reverse noise like this, producing an image from pure noise at test time by running the model step-by-step backwards. The reverse prediction of the process also looks like a Gaussian distribution when the amount of noise added is very small, which is used to predict the mean and variance of the model.
  
  
• 00:15:00 In this section, Prafulla Dhariwal discusses the process of using diffusion to reverse the noise added to an image. The process involves predicting a Gaussian in the reverse direction and using training tricks to simplify the process. The model takes in an image x0, random noise, and a combination of the two to produce a noised x_t, and the network is trained to predict the noise that was added to the image using L2 loss. The models used for this task are usually convolutional UNet style models, which downsample the image and learn features at different levels of granularity before up-sampling it back into a prediction of noise. The process can be used to obtain a generative model by predicting the mean of the reverse process.
  
  
• 00:20:00 In this section, we learn about how to make the diffusion model class conditional by providing labels to the model during training time, so the model can produce an image from p of x given y, the distribution of images represented by a label. Additionally, the model can be conditioned on low-resolution images, and up-sample them to high-resolution images. However, this type of model produces incoherent samples, so the trick of guidance is introduced. This involves training a classifier on noisy images and then taking the gradient of the classifier to guide the diffusion model towards generating images more likely to be classified as the desired label.
  
  
• 00:25:00 In this section, Dhariwal explains the necessity of keeping the classifier around in the sampling process, as gradients are directly used from the classifier. The modified reverse process uses a term with additional variance, which is the step size control in the process, with scaling from the extra parameter, s. The s parameter helps the model focus on the modes of the distribution and narrower outcomes. A small value of s does not influence the classifier much, while a large value influences it greatly. The scale factor controls the guidance received from the classifier and affects the distribution in which it collapses.
  
  
• 00:30:00 In this section, Prafulla Dhariwal discusses using diffusion models to generate art based on text descriptions. By conditioning the diffusion models on text descriptions, the model can be nudged towards producing images that align with the text. CLIP can be used to measure how close the image and the text align, and a gradient can be taken to direct the model's generation process towards the text description. Alternatively, classifier-free guidance can be used to train a diffusion model with and without labels, and then the difference between the two predictions can be used as a nudging direction during test time. The scale parameter is used to control the amount of nudging towards the label-based distribution.
  
  
• 00:35:00 In this section, the speaker discusses a form of guidance for text conditional models called classifier-free guidance. This method involves using the diffusion model itself for guidance by asking the model to predict which way it should go to increase the probability of the generated image being from the correct class. The speaker also addresses a question about gradually adding elements to an image and suggests two possible methods for achieving this, one of which involves modifying the generated image iteratively using noise and re-running the process with new prompts. The speaker presents samples comparing the effectiveness of CLIP guidance and classifier-free guidance, with the latter producing the best results.
  
  
• 00:40:00 In this section, Prafulla Dhariwal discusses a new model class for generating images that uses a diffusion technique. He explains that this model is not doing things autoregressively, but rather generating a whole image, which allows for more complicated tasks, such as in-painting. In-painting involves masking out a portion of an image and then using the model to fill in that portion. This can also be accomplished with text condition in-painting, where a text label is provided to tell the model how to in-paint the region. Iterative in-painting can be used to add things to the image one by one, such as adding a painting of a corgi on a wall above a couch. The model generated more realistic samples than older models such as DALL·E, and used fewer parameters.
  
  
• 00:45:00 In this section of the lecture, Prafulla Dhariwal discusses how in-painting can be used to remove objects from an image or fill in any missing information. He also explains out-painting, which involves moving the rectangle outside the image and asking the model to fill in that area. Additionally, Dhariwal notes that the released notebooks use a filtered GLIDE model as the original could generate problematic images. Despite the performance gap, the smaller model can still generate realistic looking images. He demonstrates examples of artwork generated by users on Twitter by finding cool prompts and expanding them with the out-painting technique. Lastly, there is a question regarding the danger created by the original GLIDE model, to which Dhariwal recommends reading the paper for further details.
  
  
• 00:50:00 In this section, the speaker discusses the trade-offs between the usefulness of the models and the potential danger of the generated content. The speaker highlights the difficulty of ensuring that models only produce safe content, given that they are powerful tools that could easily create misleading or violent data. To filter out unsafe portions of the model, the team must train classifiers to identify potentially problematic data points. The speaker goes on to discuss practical concerns when deploying the model, such as choosing the scales and time steps for the diffusion process, as well as how to add custom masks to image files to in-paint a specific area.
  
  
• 00:55:00 In this section, Prafulla Dhariwal recommends further reading for those interested in the theory behind the models used in generative art. He suggests reading the "de-noising diffusion probabilistic models paper" by Jonathan Ho, as well as their own paper on "Diffusion Models beat GANs on Image Synthesis" for more information on CLIP guidance and classifier-free guidance. Additionally, Dhariwal recommends the paper by Yang Song, "Generative Modeling by Estimating Gradients of the Data Distribution," which approaches the problem from a different perspective of score matching, a different lens for understanding diffusion models. During the Q&A, Dhariwal notes that there is a relationship between the two-dimensional noise used and the outputs of the model, but it is indirect. He suggests sampling the noise once at the start and then running a deterministic reverse process to sample from the model as a way to make this relationship more clear.
  
  
• 01:00:00 In this section, the speakers discuss the process of de-noising and the role of text conditioning in generating images without CLIP. They explain that training a model without text labels makes it difficult to generate a sample for a given text distribution, but the diffusion model is trained to be text conditional. While guidance can be used on top of both unconditional and conditional models, the original model can also use guidance to improve its ability to produce an image given text. The speakers encourage viewers to read blogs and explore other Colab notebooks for more information.

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MIT 6.S192 - Lecture 21: Between Art, Mind, & Machines, Sarah Schwettmann

MIT 6.S192 - Lecture 21: Between Art, Mind, & Machines, Sarah Schwettmann

In this lecture, Sarah Schwettmann discusses the intersection between art, mind, and machines. She delves into visual perception and the challenge of experiencing a rich 3D world through a 2D canvas, which requires the brain to solve an inverse problem and construct a best explanation of the incoming information. Schwettmann also talks about projects involving deep generative models trained on artworks, such as the use of GAN inversion to embed Met collection images into a foundation model's feature space to understand the structure of human creativity, and the creation of a visual concept vocabulary for an arbitrary GAN latent space by sampling the space of salient or possible transformations and using those sample directions as a screen to project human perceptual judgments. Human interaction and labeling are important in this process, and the resulting vocabulary can be applied to other models and used to manipulate images in various ways. Despite noise in the data due to varying word choice, their method of distilling vocabularies using any size of annotation library can be scaled up and may involve training a captioner to label directions automatically.

Sarah Schwettmann also discusses various ways to explore and assign meaning to directions within models trained on human creation. She presents an experiment capturing and learning visual directions without language, which allows humans to define the transformation they want purely visually by interacting with a small batch of images sampled from latent space or feature space. This method is useful for labeling and understanding images with nuanced, hard-to-explain features. Moreover, latent space can become a screen onto which human experiences can be projected, allowing researchers to better understand aspects of human perception that are otherwise difficult to formalize.

• 00:00:00 In this section, Sarah Schwettmann discusses her background in neuroscience and how she became interested in the meeting point between the self and the world, specifically in the areas where visual art and higher-level aspects of cognition intersect. She describes visual perception as fundamentally constructive, requiring a bit of creativity to solve ill-posed inverse problems, and notes that the back of the human eye is a 2D flat canvas made up of a hierarchy of cells that constitute a 2D canvas that takes in incoming image data and represents images in terms of patterns of activations via a mosaic of cells.
  
  
• 00:05:00 In this section of the lecture, Sarah Schwettmann discusses the challenge of experiencing a rich 3D world while viewing it through a 2D canvas. While classical computer vision problems can recognize the 3D structure of an object, it can't convey the associated meanings and associations that come with it. Our brain has to solve an inverse problem to get from low two-dimensional information to rich 3D, which is an ill-posed problem because there are infinitely many configurations that could cause the same 2D projection. Perception is fundamentally constructive and requires the brain to construct a best explanation of the incoming information, making it an act of creation. One popular way to solve this inference problem is by using models of the world, such as bayesian or deep learning approaches. Schwettmann then provides an example of a live demo where the visual information is constrained to a single line of red laser light, forcing the audience to infer what is sitting on a table covered in black velvet.
  
  
• 00:10:00 In this section of the video, Sarah Schwettmann discusses how our mental models about shapes and forms can help inform our perception. She presents an example where a single line of laser light moves over the surface of several different shapes, and how we can infer what those shapes are based on how the light bends around the surface. This leads to a discussion of intuitive physics and how the brain represents physical properties like mass, which could be used as input to an abstract generalized engine for physical simulation. Schwettmann also touches on the topic of models in art, explaining how it's difficult to develop a computational formalism for certain works of art where the underlying dimensions are unclear.
  
  
• 00:15:00 In this section, Dr. Sarah Schwettmann discusses the Vision in Art and Neuroscience course that MIT offers. It is an in-depth seminar that delves into the principles underlying vision through neuroscience literature, computation, and art practice. Schwettmann presents examples from Minor White's photography and discusses how different factors can affect veridical perception. The course also includes a studio section where students explore how to externalize and visualize principles of vision in artistic contexts. Additionally, coursework culminates in developing an art exhibition piece, providing students with a unique opportunity to showcase their own artwork.
  
  
• 00:20:00 In this section, Sarah Schwettmann discusses a project that focused on how deep generative models could be used to understand the structure of human creativity. The Metropolitan Museum of Art provided a data set of a few hundred thousand digital images of works in their collection. The researchers asked whether they could build deep generative models associated with these archives which embedded created work in their cultural context. They used GAN (generative adversarial network) inversion to embed each image in the dataset into the feature space of a foundation model. This allowed them to define subspaces of these big models that they could interact with, rather than having to retrain a model on their data set. The project aimed to experiment with cultural history on a timeline that allowed for rapid evolution in the present.
  
  
• 00:25:00 In this section, Schwettmann discusses a project she worked on involving the Met collection and BigGAN ImageNet. They selected categories that were shared between the two and created a two-part loss to maximize the similarity between the Met image and the BigGAN image at the pixel and semantic levels. They were able to visualize individual embeddings and do interpolations between existing images on the graph to create hypothetical or dreamlike images that exist between the spaces of existing works in the collection. The project was exhibited in the Met and a web app version was made available. The project continues to evolve with the use of StyleGAN2-ADA to train on smaller datasets.
  
  
• 00:30:00 In this section, Schwettmann talks about a project that involves creating layered oil paintings from short walks in latent space using a robotic oil painter to visually represent the steerability work covered in the course. This project is being exhibited at the University of North Texas' contemporary art gallery. She also discusses the importance of understanding and interpreting the dimensions underlying generative models trained on bodies of artistic work from museum digital collections, with the goal of creating alternate and imaginary histories of art built from unique latent walks. The aim is to understand shared aspects of picture language that may be present across vastly different genres of art.
  
  
• 00:35:00 In this section, Schwettmann discusses the intersection between modeling creativity and machine learning, particularly with regard to modeling individual art-making techniques and styles. She also notes that generative models trained on artworks can offer insights into the structure underlying creativity, and can be used as tools for collaboration. Schwettmann then goes on to explore ways in which humans can interact with generative models in order to learn more about human vision and to build shared vocabularies, such as designing experiments that allow the visualization and interaction of latent walks. The human interaction in this process involves a selection of representative images for training data sets and selecting arbitrary walks through latent space, with the next step being to create a more systematic language for the different walks.
  
  
• 00:40:00 In this section, Sarah Schwettmann discusses the use of human interaction in the labeling and selection of different walks through latent space to produce nuanced changes in the development of art. She highlights the importance of directly engaging models, rather than relying on an intermediary captioner, and pulling different kinds of humans into the loop to use their knowledge to create a unique synthesis with the generative model. Schwettmann then discusses a project focused on building a visual concept vocabulary for an arbitrary GAN latent space, which involves sampling the space of salient or possible transformations and using those sample directions as a screen to project human perceptual judgments. The goal is to disentangle the concepts into a vocabulary of open-ended compositional visual concepts and define a shared vocabulary between deep features in a model's representation and concepts meaningful to humans in visual scene understanding.
  
  
• 00:45:00 In this section of the lecture, Sarah Schwettmann discusses how humans can be used to label a data set for a vocabulary that is both diverse and specific. By defining mutually orthogonal layer selective directions that minimize the change in feature representation at some layer of BigGAN, Schwettmann is able to capture focused changes and changes at different levels of abstraction. These minimal meaningful transformations are then labeled by human viewers, which Schwettmann then decomposes into a visual concept vocabulary consisting of single directions labeled with single words. Over 2000 concepts are found to correspond to many different types of visual changes, allowing for manipulations such as zoom, rotation, color, and even mood changes. Through this process, Schwettmann is able to disentangle transformations that correspond to viewer-labeled concepts, such as making a kitchen seem more modern, and applying these transformations to other images.
  
  
• 00:50:00 In this section, Sarah Schwettmann discusses the composable and generalizable nature of their proposed method to find dimensions of visual interest that are meaningful to humans in the latent space of a model trained on real world images. They conducted a set of behavioral experiments to evaluate the success of their method and found that adding concepts learned in one category to a different category is possible. The method is model agnostic and can be applied to other models, including those trained on archives of art images. There are also different methods that can be used to sample the latent space, but the layer selection method was found to be the most effective in isolating specific changes. Human intervention is still necessary for annotation, but future work may involve training a captioner on a larger labeled dataset or using something like CLIP for automatic annotations while preserving the opportunity for experts to annotate specialized models.
  
  
• 00:55:00 In this section of the video, Sarah Schwettmann discusses the annotation process for the project and the decision-making behind choosing which directions to visualize. The team collected at least two annotations for each direction to measure inter-subject agreement and used BLEU and BERTScores for inter-annotator agreement. They visualized 64 z per category and a bunch of different minimal meaningful directions for them. The decision was somewhat ad hoc, but the method they used can distill vocabularies using any size of annotation library. They are now deciding whether to scale up and collect more annotations to train a captioner to label the directions automatically. In terms of labeling, there were no standards for the annotators in terms of word choice, which resulted in some noise in the data. Though they did a practice run and looked at examples before the annotations, the inter-annotator agreement was based solely on the raw window into perception that their word choice provided.
  
  
• 01:00:00 In this section, the speaker discusses their research on evaluating the vocabulary used to describe changes in the sky. They found that using BERTScores to evaluate semantic similarity of annotations was more effective than just looking at word-based correspondence. They also discuss the idea of collapsing similar annotations under one umbrella to increase power, but note the beauty in the different words used to describe changes. The speaker and audience member then discuss non-linear walks through subspaces in latent spaces and the lack of normalization in the visual meaning corresponding to adjectives. The speaker concludes with a beta method for building a shared vocabulary between humans and models.
  
  
• 01:05:00 In this section, Sarah Schwettmann describes her experiment of capturing and learning visual directions without language. This method is inspired by "steerability work" and allows humans to define the transformation they want purely visually by interacting with a small batch of images sampled from latent space or feature space. Users can sort images in the direction of the particular visual feature they want to define, and the method is simpatico with the steerability work. They have defined a transformation purely by learning a hyperplane that separates different classes of images and sampled images from latent space. It is possible to discern these directions with some degree of reliability using a few images in each category, making it simple for the user to interact with such systems. This method is handy for labelling and understanding images that have nuanced, hard-to-explain features.
  
  
• 01:10:00 In this section of the lecture, Sarah Schwettmann discusses latent space and how it can be used to explore and assign meaning to directions found within models that have been trained on human creation. By examining how a model learns visual differences between categories, researchers can learn meaningful dimensions such as fullness, which can be applied to scenes beyond what the model was trained on. Through this process, latent space can become a screen onto which human experiences can be projected, allowing researchers to better understand aspects of human perception that are otherwise difficult to formalize. The result is a collaboration between human and machine that can produce exquisite outputs.
  
  
• 01:15:00 In this section, Sarah Schwettmann discusses the idea of latent spaces and the connection between our imagination and the models that we create. She expresses her appreciation for this relationship and then ends the video by allowing for any remaining questions from the audience.

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MIT 6.S192 - Lecture 22: Diffusion Probabilistic Models, Jascha Sohl-Dickstein

MIT 6.S192 - Lecture 22: Diffusion Probabilistic Models, Jascha Sohl-Dickstein

In this lecture, Jascha Sohl-Dickstein discusses diffusion models, which are used to learn tasks that are separate from the training data. The models are probabilistic and can be used to encode or decode data. The forward diffusion process is a fixed process, and the reverse process is also true.

This lecture discusses diffusion probabilistic models and explains that, while there is a one-to-one correspondence between the latent space and the image space, it is possible to work with multiple classes within the same model. The lecture then goes on to explain how to use these models to generate new images.

• 00:00:00 In this talk, Jascha Sohl-Dickstein discusses diffusion models, which are used to generate images in a variety of disciplines, including art. He also shares examples of how diffusion models are being used in conjunction with text to produce better images.
  
  
• 00:05:00 In this lecture, Jascha Sohl-Dickstein discusses the physical intuition behind diffusion models, and shows how they can be used to generate samples from a data distribution. He then discusses connections between diffusion models and neural ODEs.
  
  
• 00:10:00 In this video, Professor Jascha Sohl-Dickstein of the MIT Department of Electrical Engineering discusses diffusion models, which are used to study the behavior of systems over time. One of the key advantages of diffusion models is that they can be used to generate data samples that represent the system as it evolves over time, without losing information about the system's underlying structure.
  
  
• 00:15:00 In this lecture, Jascha Sohl-Dickstein explains how diffusion models work. First, he shows how a 1D example is illustrated in three million dimensions. Next, he explains how diffusion models work in 2D and 3D. Finally, he demonstrates how diffusion models can be used to learn functions that describe the mean and covariance of a sequence of Gaussians.
  
  
• 00:20:00 In this lecture, Jascha Sohl-Dickstein covers the mathematical foundations of diffusion models, explaining how to train them using a variational bound. He also discusses Jensen's inequality and how to lower bound the log likelihood of the model. If the forward and reverse distributions over trajectories exactly overlap, the log likelihood can be written down as a sum over KL divergences, which both distributions are Gaussian.
  
  
• 00:25:00 In this lecture, Dr. Sohl-Dickstein discusses the KL divergence between two probability distributions, explaining its importance for supervised learning. He goes on to say that, in general, KL is computed from data to model, and that it is connected to the log likelihood of the data. He also notes that it can be difficult to compute the KL divergence in the opposite direction.
  
  
• 00:30:00 In this lecture, Jascha Sohl-Dickstein explains how to use stochastic differential equations (SDEs) to model the diffusion of noise into a data distribution. He explains how to transform the diffusion process into a stochastic differential equation, and how to use the gradient of the log-likelihood score function to train an approximation of theta to the score function.
  
  
• 00:35:00 This lecture discusses the diffusive modeling algorithm and its advantages over other modelling techniques. The algorithm is described in terms of a discrete-time SDE and a score function, and the sampling process is described in terms of a neural network. The lecture ends with a demonstration of some sample generation techniques.
  
  
• 00:40:00 This lecture covers the difference between stochastic and deterministic models and how to convert between the two. The lecture also discusses the benefits and drawbacks of using an SDE vs. ODE for modeling.
  
  
• 00:45:00 In this lecture, Jascha Sohl-Dickstein covers the theory behind diffusion models, explaining how they differ from ordinary linear models and how they can be used for various purposes, such as controlling the generation of noise samples under controlled conditions. He also mentions Bayes' rule, which can be used to train the second term of the diffusion model without requiring prior knowledge of the conditional distribution.
  
  
• 00:50:00 In this lecture, Jascha Sohl-Dickstein explains how diffusion models can be used to generate plausible in-paintings or colors in images. He also mentions that the encoding of the model is uniquely identifiable, which is a positive or negative depending on how you look at it. Finally, he shows how the model can be used to generate novel artistic creations without having to retrain the model.
  
  
• 00:55:00 This lecture discusses diffusion models, which are used to learn tasks that are separate from the training data. The models are probabilistic and can be used to encode or decode data. The forward diffusion process is a fixed process, and the reverse process is also true.
  
  
• 01:00:00 This lecture discusses diffusion probabilistic models and explains that, while there is a one-to-one correspondence between the latent space and the image space, it is possible to work with multiple classes within the same model.

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GenRep: Generative Models as a Data Source for Multiview Representation Learning in ICLR2022

Code: https://github.com/ali-design/GenRep

GenRep: Generative Models as a Data Source for Multiview Representation Learning in ICLR2022

The presenters discuss the concept of model zoos, where pre-trained generative models are made accessible without access to the underlying data. By utilizing contrastive learning, researchers can create different views of the same object, which will fall into the same neighborhood within the representation space. They found that simple gaussian transformations in the latent space were effective and that generating more samples from IGMs leads to better representations. Expert IGMs, such as StyleGAN Car in specific domains, can outperform representations learned from real data. The project website and Github code are available for further exploration.

• 00:00:00 In this section, the presenters discuss the concept of model zoos, where pre-trained generative models are made accessible without access to the underlying data. They go on to explain how implicit generative models can be steered to offer many transformations of generated images. By utilizing contrastive learning, researchers can create different views of the same object, which will fall into the same neighborhood within the representation space. By shifting in the latent space, creating different views for the anchor, and combining transformations together, researchers can learn representations from these IGMs. This research showed that if both transformations that IGMs offer are applied, they can get closer to the real data's performance and rival them. The results were surprisingly higher than real data in the case of StyleGAN Car.
  
  
• 00:05:00 In this section, the speaker discusses the use of contrastive learning and steerability in creating different views for representation learning. They found that simple gaussian transformations in the latent space were effective and that generating more samples from IGMs leads to better representations. They also found that expert IGMs, such as StyleGAN Car in specific domains, can outperform representations learned from real data. The project website and Github code are available for further exploration.

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An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Gilbert Strang, a renowned mathematician, emphasizes the importance of projects over exams in teaching deep learning, a crucial part of machine learning that heavily relies on linear algebra. He believes that projects allow students to understand how to apply deep learning in the real world and are a more effective way of learning. Strang also emphasizes that teaching is about learning and working with the students rather than solely grading them. He advises new professors to use large chalk and to take their time to stay with the class in order to be successful in teaching.

• 00:00:00 In this section, Gilbert Strang discusses how he got involved in teaching deep learning, an important part of machine learning that heavily depends on linear algebra. He also emphasizes that projects are far better than exams as they give students an idea of how to use deep learning in real-world situations, and are a more effective way of learning. By having the students ask their own questions and write their own programs, they're able to create projects that are interesting and memorable. However, Strang admits that he had no idea what to expect when he first started teaching the course in this way, and it took some time to figure out the logistics of facilitating the projects.
  
  
• 00:05:00 In this section of the video, Gilbert Strang discusses his philosophy regarding grading students' work. He believes that his main job as a teacher is to teach or learn alongside the students, not to grade them. He acknowledges that grading is important, but it is not his main concern. He advises new professors to use large chalk and not to rush, but to stay with the class. He believes that teaching is the best job possible.

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MIT 18.065. Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Course Introduction of  by Professor Strang

Professor Strang introduces his new course 18.065, which covers four key topics: linear algebra, deep learning, optimization, and statistics. The course will focus on the best matrices, symmetric and orthogonal matrices and their relation to linear algebra. It will also cover deep learning, which is foundational to linear algebra and involves complex calculations that can require the use of GPUs over days or even weeks. The course will touch on statistics, which plays a role in keeping the numbers in the learning function within a good range, and optimization and probability theory which, are important in learning algorithms, and differential equations which play a key role in science and engineering applications. The course includes exercises, problems, and discussions to provide a complete presentation of the subject matter.

• 00:00:00 In this section, Professor Strang introduces his new course 18.065 and the new textbook on linear algebra and learning from data. He explains that the course covers two essential and two supplementary, but important mathematical subjects. The first big subject is linear algebra, which has become increasingly important in practice, and Professor Strang focuses on the best matrices, symmetric and orthogonal matrices, and their relation. The second important topic is deep learning which deals with creating a learning function that recognizes patterns in inputs and produces output, using matrix multiplications and a very simple nonlinear function. The course also covers optimization and probability theory, which are important in learning algorithms, and differential equations, which play a key role in science and engineering applications.
  
  
• 00:05:00 In this section, Professor Strang introduces four key topics that will be covered in the course: linear algebra, deep learning, optimization, and statistics. Linear algebra is foundational to understanding deep learning, which involves complex calculations that can require the use of GPUs over days or even weeks. The course will also touch on statistics, which plays a role in keeping the numbers in the learning function within a good range. While this course will not be focused on statistics, it will be used within the context of deep learning. The course covers a wide range of materials beyond just videos, including exercises, problems, and discussions to provide a complete presentation of the subject matter.

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Lecture 1: The Column Space of A Contains All Vectors Ax

Lecture 1: The Column Space of A Contains All Vectors Ax

This lecture focuses on the concept of the column space of a matrix, which is a collection of all the vectors that can be obtained by multiplying the matrix with all possible vectors. The lecturer explains that the column space depends on the matrix and could be the whole space of R3 or a smaller subset of it. The professor further discusses the concepts of row space, column rank, and row rank, as well as the relationship between these ranks. The lecture also briefly touches upon the first great theorem in linear algebra, which states that the column rank of a matrix equals the row rank of the matrix. Additionally, the professor discusses methods for matrix multiplication and the number of multiplications required for the process. Overall, the lecture offers an introduction to linear algebra and its importance in learning from data.

• 00:00:00 In this section, the professor introduces himself and the course, which focuses on learning from data and involves a lot of linear algebra. He mentions a public site with a table of contents for the upcoming book, as well as the fact that there will be no quizzes, only homework assignments that will cover both linear algebra questions and practical applications such as recognizing handwriting and stitching images together. The professor then starts with the basics of linear algebra by demonstrating the correct way to multiply a matrix by a vector and will explore multiplying matrices by matrices later on.
  
  
• 00:05:00 In this section, the lecturer explains the importance of thinking of a matrix as a whole object that multiplies a vector to give another vector. He introduces the concept of the column space of a matrix, which is a collection of all the vectors that can be obtained by multiplying the matrix with all possible vectors. He explains that the column space depends on the matrix and could be the whole space of R3 or a smaller subset of it. Ultimately, the lecturer emphasizes that linear algebra provides a way to answer questions about collections of vectors, such as the column space of a matrix.
  
  
• 00:10:00 In this section, the lecturer explains that the column space of a random 3x3 matrix may not necessarily be all of our three, but instead could be a plane or even a line. He gives an example of a matrix whose column space is just a line, and another example of a matrix whose third column is a combination of the first two, making its column space a plane instead of the whole space. He then introduces rank one matrices, which are building blocks of linear algebra and data science, and shows how they can be thought of as a column times a row multiplication.
  
  
• 00:15:00 In this section, the lecturer discusses the column space of a matrix, which is the set of all possible combinations of its columns. He explains the concept of independent columns and how many independent columns a matrix has, which is known as its rank. The rank is the number of independent columns that fill the space, and a basis is made up of the independent columns. The lecturer demonstrates how to find a natural way to create a basis for the column space by looking for vectors that are not combinations of those already chosen. He showcases a matrix with three columns, two of which are independent and form the basis for the column space, while the third is not independent and cannot be part of the basis.
  
  
• 00:20:00 In this section of the lecture, the instructor explains the process of matrix factorization and introduces the first matrix factorization, which is a famous one in teaching near algebra. The process involves producing a matrix R that tells the user how to get the columns of one matrix from the columns of another matrix. The shape of R is determined by the original matrix, and the instructor goes on to explain how to put in the right numbers to get the correct matrix factorization. The lecture also briefly touches upon the first great theorem in linear algebra, which states that the column rank of a matrix equals the row rank of the matrix.
  
  
• 00:25:00 In this section, the lecturer introduces the concept of row space and its relationship with column space. He explains that the row space of a matrix is the combination of its rows, while the column space of a matrix is the combination of its columns. He further explains that the dimension of the row space is the row rank of the matrix, which can be determined by finding a basis for the row space. The lecturer points out the importance of this fact and offers a proof, showing that the rows of a matrix can form a basis for its row space.
  
  
• 00:30:00 In this section of the lecture, the professor explains how to check if two vectors are a basis for the row space by verifying if they are independent and if their combinations produce all the rows. He demonstrates this through an example involving matrix multiplication and shows that the factorization a = CR is the key idea in finding the row space. The column space, also known as the range, is also discussed with the emphasis on varying languages and different ways of expressing fundamental mathematical concepts.
  
  
• 00:35:00 In this section, the lecturer discusses the concepts of column rank and row rank, which are the number of columns and rows respectively in a matrix that are linearly independent, as well as the relationship between these two ranks. He explains that for a large matrix, it is not practical to examine all entries, and random sampling must be used, for example by taking a random vector X and looking at its corresponding ax. The lecturer also touches on factorizations such as taking columns or rows of a matrix, and the row reduced echelon form of a matrix.
  
  
• 00:40:00 In this section of the video, Professor Gilbert Strang explains that linear algebra problems will be part of the homework of the course. However, what makes this course special is the other online homeworks, which can be done using MATLAB, Python, or Julia. He talks about how the concepts of the course are credited to Professor Rao, University of Michigan, who had previously created online homework problems for a successful course in EE at Michigan. Professor Johnson, a part of this course, gives a tutorial on Julia every semester, which the students can attend. While MATLAB has issued an on-ramp to deep learning, Julia is also becoming a popular language for deep learning owing to its ease of use.
  
  
• 00:45:00 In this section of the lecture, the instructor covers the topic of multiplying a matrix by a vector. While this may seem simple to many, the instructor explores a deeper way of understanding matrix multiplication, where it becomes a combination of columns times rows. This approach is a generalization of the AX= B idea, where AB is the sum of outer products. The lecture briefly touches on the number of individual multiplications required for an M by N matrix multiplied by an N by P matrix.
  
  
• 00:50:00 In this section, the lecturer discusses the number of multiplications required for matrix multiplication by using the example of an old method and a new method. In the old method, n multiplications are required to do a dot product, and there are m and p dot products in the answer, resulting in m and p multiplies overall. However, the new method requires mp multiplies for each column and row multiplication, and there are n of these, leading to mp times n multiplies. Despite the different methodologies, both methods result in the same answer, and the lecturer indicates he will discuss this further on Friday.

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Lecture 2: Multiplying and Factoring Matrices

Lecture 2: Multiplying and Factoring Matrices

This lecture covers the basics of multiplying and factoring matrices. The author explains how matrices have dimensions in both the row and column spaces, and how the row space has dimension R while the null space has dimension M minus R. The lecture also discusses the relationship between rows and solutions to an equation, as well as the orthogonality of vectors in two-dimensional space. Finally, the author explains the fundamental theorem of linear algebra, which states that the dimensions of a space come out right when the geometry is worked out.

• 00:00:00 In this lecture, Gilbert Strang explains how to multiply matrices using column times row as a method. She also explains the five key factorizations of matrices, and how they are important in mathematics. Finally, she shows how to make matrices and discuss their importance in linear algebra.
  
  
• 00:05:00 In this lecture, the author discusses the concept of orthogonal matrices and their significance. He goes on to explain the rule for matrix multiplication and shows how it can be applied to two simple examples. He then proceeds to discuss the rank of a matrix and how it is related to the columns and rows of the matrix. Finally, the author demonstrates how to multiply a matrix by its diagonal matrix.
  
  
• 00:10:00 In this lecture, Professor Gilbert Strang provides a brief overview of the symmetric eigenvalue problem and its various applications. He then demonstrates how splitting a matrix into rank-1 pieces can provide the correct eigenvectors and eigenvalues.
  
  
• 00:15:00 In this lecture, Professor Gilbert Strang covers the fundamental factorizations of matrices, including the Singular Value Decomposition (SVD). He also discusses elimination, and explains how it is expressed by L times U. Finally, he demonstrates how this can be applied to a matrix invertible, and shows how it factors into lower triangular times upper triangular.
  
  
• 00:20:00 In this lecture, Professor Gilbert Strang explains the concept of elimination and how it is used in solving equations. He goes on to show how elimination can be applied to a two by two matrix, and provides an example illustrating the process.
  
  
• 00:25:00 The fundamental theorem of linear algebra states that there are four subspaces of a matrix, each with a different dimension. The subspaces are the row space, the column space, the vector space of all linear transformations on the matrix, and the space of all matrices.
  
  
• 00:30:00 The null space of a matrix is the set of solutions to the word "null" (a vector with all its components equal to zero). This space is closed, meaning that it does not contain any solutions to "ax equals zero" that are not also solutions to "e". In addition, the null space of a transpose is the set of solutions to the word "null" that are also solutions to "x transpose y".
  
  
• 00:35:00 The fundamental theorem of linear algebra states that there are typically independent solutions to equations in a system if the dimensions of the two spaces involved are equal. This theorem is often used to determine the dimensions of a system of equations.
  
  
• 00:40:00 The Multiplying and Factoring Matrices lecture covers the fundamentals of multiplying and factoring matrices. The lecture explains that matrices have dimensions in both the row and column spaces, and that the row space has dimension R while the null space has dimension M minus R. The final section of the lecture discusses the geometry of the matrix spaces and demonstrates how to find vectors that solve for a particular equation in a matrix.
  
  
• 00:45:00 In this lecture, the author explains the relationship between rows and solutions to an equation, as well as the orthogonality of vectors in two-dimensional space. He also discusses the fundamental theorem of linear algebra, which states that the dimensions of a space come out right when the geometry is worked out.

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Lecture 3. Orthonormal Columns in Q Give Q'Q = I

3. Orthonormal Columns in Q Give Q'Q = I

This section of the video explains the concept of orthogonal matrices and their significance in numerical linear algebra. The speaker proves that the length squared of QX must be the same as X transpose QX using the fact that Q transpose Q equals the identity. The video also discusses constructing orthogonal matrices using various methods such as Gordan matrices and Householder matrices. The importance and construction of wavelets is also explained, along with the concept of using orthogonal eigenvectors in signal processing. Finally, the speaker talks about how to test orthogonal vectors with complex numbers and mentions that orthogonal matrices have orthogonal eigenvectors with different eigenvalues.

• 00:00:00 In this section, the topic is on matrices Q, which are named after their orthonormal columns. The key fact in matrices Q is that orthonormal columns translate into the simple fact that Q transpose Q equals the identity matrix. The explanation for this is that the length squared of each vector in the normal part of the matrix is 1, resulting in a one in the identity matrix. The orthogonal part of the matrix has zeros, producing a simple identity. For square matrices Q, Q transpose is equal to the identity matrix, making Q an orthogonal matrix. If Q is rectangular, one example of getting an orthogonal 2 by 2 matrix is through cos and sine theta. The matrix represents a rotation.
  
  
• 00:05:00 In this section of the video, the speaker discusses the important property of orthogonal matrices, which is that they do not change the length of any vector. This property makes them popular for numerical algorithms as there is never any underflow or overflow when multiplying by orthogonal matrices. The speaker proves that the length squared of QX must be the same as X transpose QX using the fact that Q transpose Q equals the identity. The speaker also mentions that orthogonal matrices are also called orthonormal matrices, and poses a couple of examples of two-by-two orthogonal matrices.
  
  
• 00:10:00 In this section, the speaker discusses the concept of a reflection matrix, which is obtained after making a minor change to a rotation matrix. The resulting matrix is symmetric and has a determinant of -1. When applied to the unit vectors (1,0) and (0,1), the matrix reflects them across a line and perpendicular to the first column, respectively. The speaker also mentions that larger matrices like these are called Householder reflections.
  
  
• 00:15:00 In this section, the transcript discusses the concept of orthogonal matrices and their significance in numerical linear algebra. The Householder matrix is introduced as an important orthogonal matrix. A Householder matrix is created by starting with a unit vector and subtracting two times the product of the unit vector and its transpose, resulting in a symmetric and orthogonal matrix. The transcript explains that these matrices are useful in making things orthogonal and notes that they are better than the Gram-Schmidt method. The process of checking if the Householder matrix is orthogonal is also demonstrated, concluding that it is a reliable family of symmetric orthogonal matrices.
  
  
• 00:20:00 In this section, the speaker discusses constructing orthogonal matrices using the concept of Gordan matrices, which are matrices consisting of only ones and negatives ones. He constructs challenging examples of Gordan matrices with each column being orthogonal to each other. The speaker notes that this concept can be useful in encoding theory and suggests that there is an orthogonal 12x12 matrix consisting of ones and negatives ones, leading to a conjecture that every matrix size (besides 1x1 and 3x3) can be constructed in this way.
  
  
• 00:25:00 In this section, the speaker discusses the conjecture around whether there is a possible ones and minus ones orthogonal matrix with orthogonal columns of every size n. While no systematic way has been found to prove this, it's suggested that every multiple of four could be a possibility. The speaker also discusses the importance and construction of wavelets, which are simple yet significant constructions that help produce orthogonal vectors, particularly for symmetric matrices. The speaker illustrates this concept by drawing out a four-by-four case matrix of four quadrants, each made up of orthogonal vectors that follow a pattern of ones and minus ones.
  
  
• 00:30:00 In this section, the speaker discusses wavelets and the construction of the Haar wavelet matrix, which was developed many years before the term "wavelets" was invented. The Haar matrix has very simple functions that make it usable, and it consists of ones and minus ones followed by zeros. The matrix has the advantage of being sparse and is involved in taking the average and differences between values at different scales. Wavelets were further developed by Ingrid Dobashi, who found families of orthogonal matrices that had good properties. This discussion leads to the next lecture on eigenvalues, eigenvectors, and positive definite matrices.
  
  
• 00:35:00 In this section, the speaker talks about the importance of orthogonal eigenvectors. Eigenvectors of symmetric and orthogonal matrices are automatically orthogonal, simplifying the search for orthogonal vectors. The most important eigenvector is the discrete Fourier transform, which goes into the fast Fourier transform. The speaker demonstrates how the Eigenvectors of Q are orthogonal and reiterates that the discrete Fourier transform is immensely useful in signal processing because it helps in splitting vectors into their frequencies. Permutation matrices are a reordering of the identity matrix, and their columns are orthogonal, making them winners. The speaker concludes by talking about how Wednesday's discussion will focus on eigenvectors and eigenvalues of a queue.
  
  
• 00:40:00 In this section, the speaker discusses orthogonal matrices, rotations, reflections, and eigenvectors. The video explains how the eigenvectors of permutation matrices work, and that the first column is orthogonal to the second (or in frequency terms, the zeroth column is orthogonal to the first column). The video goes on to show how every one of the four columns is an eigenvector of the permutation, and how they are orthogonal to each other. Finally, the video mentions that this is similar to discrete Fourier stuff but instead of e to the I, II to the IX, there are vectors.
  
  
• 00:45:00 In this section of the video, the speaker talks about how to test orthogonal vectors with complex numbers. He mentions that taking the dot product without the complex conjugate may not be accurate, but using the complex conjugate can show orthogonality. The speaker also mentions that the eigenvectors of an orthogonal matrix with different eigenvalues should be orthogonal.