arXiv research

New algorithm for online optimization over symmetric cones, unifying previous methods.

New algorithm provably converges to second-order stationary points in NMF.

Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $Ω(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The funda…

We show that a simple randomized sketch of the matrix multiplicative weight (MMW) update enjoys (in expectation) the same regret bounds as MMW, up to a small constant factor. Unlike MMW, where every step requires full matrix exponentiation, our steps require only a single product of the form $e^A b$, which the Lanczos …

Paper proves multiplicative weight updates can train neural networks without learning rate tuning.

The (stochastic) gradient descent and the multiplicative update method are probably the most popular algorithms in machine learning. We introduce and study a new regularization which provides a unification of the additive and multiplicative updates. This regularization is derived from an hyperbolic analogue of the entr…

Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.

New NMF algorithm uses Toeplitz matrix for facial recognition.

Online learning makes sequence of decisions with partial data arrival where next movement of data is unknown. In this paper, we have presented a new technique as multiple times weight updating that update the weight iteratively forsame instance. The proposed technique analyzed with popular state-of-art algorithms from …

NMF with specific constraints is equivalent to LDA.

Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic nonnegative matrix factorization (NMF) to extract short-lived temporal motifs from a long …

Many convex problems in machine learning and computer science share the same form: \begin{align*} \min_{x} \sum_{i} f_i( A_i x + b_i), \end{align*} where $f_i$ are convex functions on $\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \in \mathbb{R}^{n_i \times d}$, $b_i \in \mathbb{R}^{n_i}$ and $\sum_i n_i = n$. This probl…

An algorithm for computing positive semidefinite factorizations of matrices.

In this paper, we extend the $β$-CNMF to two dimensions and derive exact multiplicative updates for its factors. The new updates generalize and correct the nonnegative matrix factor deconvolution previously proposed by Schmidt and Mørup. We show by simulation that the updates lead to a monotonically decreasing $β$-dive…

MetaGrad adapts multiple learning rates for faster online optimization.

The online problem of computing the top eigenvector is fundamental to machine learning. In both adversarial and stochastic settings, previous results (such as matrix multiplicative weight update, follow the regularized leader, follow the compressed leader, block power method) either achieve optimal regret but run slow,…

The paper introduces MU for NMF with $β$-divergences and disjoint constraints.

Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…

Pion optimizes LLMs by preserving weight matrix singular values.

Regression problems that have closed-form solutions are well understood and can be easily implemented when the dataset is small enough to be all loaded into the RAM. Challenges arise when data is too big to be stored in RAM to compute the closed form solutions. Many techniques were proposed to overcome or alleviate the…

New algorithm speeds up NMF with $β$-divergence.

The decremented learning algorithms are required in machine learning, to prune redundant nodes and remove obsolete inline training samples. In this paper, an efficient decremented learning algorithm to prune redundant nodes is deduced from the incremental learning algorithm 1 proposed in [9] for added nodes, and two de…

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and sho…

Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simp…

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficu…

BiQGEMM efficiently multiplies quantized DNN weights using lookup tables.

The SCMU algorithm computes cone factorizations for symmetric cones, improving upon existing methods.

DMFAW improves multi-view clustering with adaptive weights and feature selection.

Efficiently factorizes coupled matrix tensor data for better accuracy and speed.

Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To cir…

The multiplicative update (MU) algorithm has been extensively used to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizers. However, theoretical convergence guarantees have only been derived for a few special divergences withou…

MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.

New hierarchical tensor decomposition model for complex data.

New insights into neural network feature learning through multi-step gradient descent.

Paper presents a rank-1 approximation method for natural policy gradients in deep RL.

Algorithm learns Sherrington-Kirkpatrick model parameters at low temperatures.

A new method estimates parameters in heavy-tailed corrupted regression with unknown covariance and heterogeneous noise.

Improved accuracy in neural networks using CTF memory with RPU.

New method enhances model fine-tuning with minimal data.

BatchEnsemble reduces ensemble costs by 3X in training and testing.

Paper adapts multiplicative weights method to Gaussian graphical models.

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squ…

MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown…

Paper proposes efficient weight updates for edge nodes with minimal communication.

This paper presents a novel multitask multiple kernel learning framework that efficiently learns the kernel weights leveraging the relationship across multiple tasks. The idea is to automatically infer this task relationship in the \textit{RKHS} space corresponding to the given base kernels. The problem is formulated a…

Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new type of nonnegative matrix factorization method, which learns local similarity …