Search Results for author:
Found 32 papers, 4 papers with code
GAIA: Categorical Foundations of Generative AI
In this paper, we propose GAIA, a generative AI architecture based on category theory.
Zero-th Order Algorithm for Softmax Attention Optimization
We demonstrate the convergence of our algorithm, highlighting its effectiveness in efficiently computing gradients for large-scale LLMs.
Randomized and Deterministic Attention Sparsification Algorithms for Over-parameterized Feature Dimension
It runs in $\widetilde{O}(\mathrm{nnz}(X) + n^{\omega} ) $ time, has $1-\delta$ succeed probability, and chooses $m = O(n \log(n/\delta))$.
An Over-parameterized Exponential Regression
Mathematically, we define the neural function $F: \mathbb{R}^{d \times m} \times \mathbb{R}^d \rightarrow \mathbb{R}$ using an exponential activation function.
A Layered Architecture for Universal Causality
At the second layer, causal models are defined by a graph-type category.
Privacy Aware Experiments without Cookies
We propose a two-stage experimental design, where the two brands only need to agree on high-level aggregate parameters of the experiment to test the alternate experiences.
Unifying Causal Inference and Reinforcement Learning using Higher-Order Category Theory
We present a unified formalism for structure discovery of causal models and predictive state representation (PSR) models in reinforcement learning (RL) using higher-order category theory.
Categoroids: Universal Conditional Independence
Categoroids are defined as a hybrid of two categories: one encoding a preordered lattice structure defined by objects and arrows between them; the second dual parameterization involves trigonoidal objects and morphisms defining a conditional independence structure, with bridge morphisms providing the interface between the binary and ternary structures.
On The Universality of Diagrams for Causal Inference and The Causal Reproducing Property
The second result, the Causal Reproducing Property (CRP), states that any causal influence of a object X on another object Y is representable as a natural transformation between two abstract causal diagrams.
Smoothed Online Combinatorial Optimization Using Imperfect Predictions
Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive rounds.
Universal Decision Models
Decision objects in a UDM correspond to instances of decision tasks, ranging from causal models and dynamical systems such as Markov decision processes and predictive state representations, to network multiplayer games and Witsenhausen's intrinsic models, which generalizes all these previous formalisms.
Asymptotic Causal Inference
Semantic entropy quantifies the reduction in entropy where edges are removed by causal intervention.
Causal Homotopy
Second, a diverse range ofgraphical models used to represent causal structures can be represented in a unified way in terms of a topological representation of the induced poset structure.
Causal Inference in Network Economics
Network economics is the study of a rich class of equilibrium problems that occur in the real world, from traffic management to supply chains and two-sided online marketplaces.
Multiscale Manifold Warping
Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination.
Finite-Sample Analysis of Proximal Gradient TD Algorithms
In this paper, we analyze the convergence rate of the gradient temporal difference learning (GTD) family of algorithms.
Regularized Off-Policy TD-Learning
We present a novel $l_1$ regularized off-policy convergent TD-learning method (termed RO-TD), which is able to learn sparse representations of value functions with low computational complexity.
Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity
In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms.
Optimizing for the Future in Non-Stationary MDPs
Most reinforcement learning methods are based upon the key assumption that the transition dynamics and reward functions are fixed, that is, the underlying Markov decision process is stationary.
Global Convergence to the Equilibrium of GANs using Variational Inequalities
In optimization, the negative gradient of a function denotes the direction of steepest descent.
A Unified Framework for Domain Adaptation using Metric Learning on Manifolds
We present a novel framework for domain adaptation, whereby both geometric and statistical differences between a labeled source domain and unlabeled target domain can be integrated by exploiting the curved Riemannian geometry of statistical manifolds.
Online Monotone Games
Algorithmic game theory (AGT) focuses on the design and analysis of algorithms for interacting agents, with interactions rigorously formalized within the framework of games.
A Manifold Approach to Learning Mutually Orthogonal Subspaces
Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging.
Generative Multi-Adversarial Networks
Generative adversarial networks (GANs) are a framework for producing a generative model by way of a two-player minimax game.
Ranked #67 on
Image Generation
on CIFAR-10
(Inception score metric)
Online Monotone Optimization
This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems.
Inverting Variational Autoencoders for Improved Generative Accuracy
Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$).
Deep Reinforcement Learning With Macro-Actions
Deep reinforcement learning has been shown to be a powerful framework for learning policies from complex high-dimensional sensory inputs to actions in complex tasks, such as the Atari domain.
Reasoning about Linguistic Regularities in Word Embeddings using Matrix Manifolds
In this paper, we introduce a new approach to capture analogies in continuous word representations, based on modeling not just individual word vectors, but rather the subspaces spanned by groups of words.
Proximal Reinforcement Learning: A New Theory of Sequential Decision Making in Primal-Dual Spaces
In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to design reliable, convergent, and robust reinforcement learning algorithms (ii) how to guarantee that reinforcement learning satisfies pre-specified "safety" guarantees, and remains in a stable region of the parameter space (iii) how to design "off-policy" temporal difference learning algorithms in a reliable and stable manner, and finally (iv) how to integrate the study of reinforcement learning into the rich theory of stochastic optimization.
Projected Natural Actor-Critic
Natural actor-critics are a popular class of policy search algorithms for finding locally optimal policies for Markov decision processes.
Basis Construction from Power Series Expansions of Value Functions
This paper explores links between basis construction methods in Markov decision processes and power series expansions of value functions.
