S. Sathiya Keerthi

Saurav Manchanda, Khoa Doan, Pranjul Yadav et al.

This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been applied for regression and has shown to be advantageous over the other standard approaches like Gaussian Process Regression, given its ability to implicitly model complex noise forms. However, the current CGAN implementation for regression uses the classical generator-discriminator architecture with the minimax optimization approach, which is notorious for being difficult to train due to issues like training instability or failure to converge. In this paper, we take another step towards regression models that implicitly model the noise, and propose a solution which directly optimizes the optimal transport cost between the true probability distribution $p(y|x)$ and the estimated distribution $\hat{p}(y|x)$ and does not suffer from the issues associated with the minimax approach. On a variety of synthetic and real-world datasets, our proposed solution achieves state-of-the-art results. The code accompanying this paper is available at "https://github.com/gurdaspuriya/ot_regression".

Aman Gupta, Shao Tang, Qingquan Song et al.

Reinforcement Learning with Human Feedback (RLHF) and its variants have made huge strides toward the effective alignment of large language models (LLMs) to follow instructions and reflect human values. More recently, Direct Alignment Algorithms (DAAs) have emerged in which the reward modeling stage of RLHF is skipped by characterizing the reward directly as a function of the policy being learned. Some popular examples of DAAs include Direct Preference Optimization (DPO) and Simple Preference Optimization (SimPO). These methods often suffer from likelihood displacement, a phenomenon by which the probabilities of preferred responses are often reduced undesirably. In this paper, we argue that, for DAAs the reward (function) shape matters. We introduce \textbf{AlphaPO}, a new DAA method that leverages an $α$-parameter to help change the shape of the reward function beyond the standard log reward. AlphaPO helps maintain fine-grained control over likelihood displacement and over-optimization. Compared to SimPO, one of the best performing DAAs, AlphaPO leads to about 7\% to 10\% relative improvement in alignment performance for the instruct versions of Mistral-7B and Llama3-8B while achieving 15\% to 50\% relative improvement over DPO on the same models. The analysis and results presented highlight the importance of the reward shape and how one can systematically change it to affect training dynamics, as well as improve alignment performance.

Aman Gupta, Rafael Celente, Abhishek Shivanna et al.

The Muon optimizer, based on matrix orthogonalization, has recently shown faster convergence and up to 2x computational efficiency over AdamW in LLM pretraining. Like AdamW, Muon is stateful, requiring storage of both model weights and accumulated gradients. While 8-bit AdamW variants mitigate this overhead using blockwise quantization, they are typically stable only under dynamic quantization - which improves stability on linear quantization for extreme values. In this paper, we introduce the 8-bit Muon optimizer using blockwise quantization, supporting both linear and dynamic schemes. We demonstrate that 8-bit Muon maintains stability under both, while delivering $\sim$74\% reduction in memory footprint compared to full-precision Muon. In extensive experiments, 8-bit Muon closely matches the performance of Muon while outperforming AdamW and 8-bit AdamW in pre-training a 1.6B model on 4B FineWeb tokens. It also shows competitive results when fine-tuning the Llama 3.2 3B model on post-training data. We also provide a theoretical perspective to help explain this robustness under quantization.

Aman Gupta, Rohan Ramanath, Jun Shi et al.

Over-parameterized deep networks trained using gradient-based optimizers are a popular choice for solving classification and ranking problems. Without appropriately tuned $\ell_2$ regularization or weight decay, such networks have the tendency to make output scores (logits) and network weights large, causing training loss to become too small and the network to lose its adaptivity (ability to move around) in the parameter space. Although regularization is typically understood from an overfitting perspective, we highlight its role in making the network more adaptive and enabling it to escape more easily from weights that generalize poorly. To provide such a capability, we propose a method called Logit Attenuating Weight Normalization (LAWN), that can be stacked onto any gradient-based optimizer. LAWN controls the logits by constraining the weight norms of layers in the final homogeneous sub-network. Empirically, we show that the resulting LAWN variant of the optimizer makes a deep network more adaptive to finding minimas with superior generalization performance on large-scale image classification and recommender systems. While LAWN is particularly impressive in improving Adam, it greatly improves all optimizers when used with large batch sizes

Khoa D. Doan, Saurav Manchanda, Fengjiao Wang et al.

For a given image generation problem, the intrinsic image manifold is often low dimensional. We use the intuition that it is much better to train the GAN generator by minimizing the distributional distance between real and generated images in a small dimensional feature space representing such a manifold than on the original pixel-space. We use the feature space of the GAN discriminator for such a representation. For distributional distance, we employ one of two choices: the Fréchet distance or direct optimal transport (OT); these respectively lead us to two new GAN methods: Fréchet-GAN and OT-GAN. The idea of employing Fréchet distance comes from the success of Fréchet Inception Distance as a solid evaluation metric in image generation. Fréchet-GAN is attractive in several ways. We propose an efficient, numerically stable approach to calculate the Fréchet distance and its gradient. The Fréchet distance estimation requires a significantly less computation time than OT; this allows Fréchet-GAN to use much larger mini-batch size in training than OT. More importantly, we conduct experiments on a number of benchmark datasets and show that Fréchet-GAN (in particular) and OT-GAN have significantly better image generation capabilities than the existing representative primal and dual GAN approaches based on the Wasserstein distance.

Saurav Manchanda, Pranjul Yadav, Khoa Doan et al.

An average adult is exposed to hundreds of digital advertisements daily (https://www.mediadynamicsinc.com/uploads/files/PR092214-Note-only-150-Ads-2mk.pdf), making the digital advertisement industry a classic example of a big-data-driven platform. As such, the ad-tech industry relies on historical engagement logs (clicks or purchases) to identify potentially interested users for the advertisement campaign of a partner (a seller who wants to target users for its products). The number of advertisements that are shown for a partner, and hence the historical campaign data available for a partner depends upon the budget constraints of the partner. Thus, enough data can be collected for the high-budget partners to make accurate predictions, while this is not the case with the low-budget partners. This skewed distribution of the data leads to "preferential attachment" of the targeted display advertising platforms towards the high-budget partners. In this paper, we develop "domain-adaptation" approaches to address the challenge of predicting interested users for the partners with insufficient data, i.e., the tail partners. Specifically, we develop simple yet effective approaches that leverage the similarity among the partners to transfer information from the partners with sufficient data to cold-start partners, i.e., partners without any campaign data. Our approaches readily adapt to the new campaign data by incremental fine-tuning, and hence work at varying points of a campaign, and not just the cold-start. We present an experimental analysis on the historical logs of a major display advertising platform (https://www.criteo.com/). Specifically, we evaluate our approaches across 149 partners, at varying points of their campaigns. Experimental results show that the proposed approaches outperform the other "domain-adaptation" approaches at different time points of the campaigns.

Karan Aggarwal, Matthieu Kirchmeyer, Pranjul Yadav et al.

In recent years, impressive progress has been made in the design of implicit probabilistic models via Generative Adversarial Networks (GAN) and its extension, the Conditional GAN (CGAN). Excellent solutions have been demonstrated mostly in image processing applications which involve large, continuous output spaces. There is almost no application of these powerful tools to problems having small dimensional output spaces. Regression problems involving the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$, with $m$ small (e.g., $m=1$ or just a few) is one good case in point. The standard approach to solve regression problems is to probabilistically model the output $y$ as the sum of a mean function $m(x)$ and a noise term $z$; it is also usual to take the noise to be a Gaussian. These are done for convenience sake so that the likelihood of observed data is expressible in closed form. In the real world, on the other hand, stochasticity of the output is usually caused by missing or noisy input variables. Such a real world situation is best represented using an implicit model in which an extra noise vector, $z$ is included with $x$ as input. CGAN is naturally suited to design such implicit models. This paper makes the first step in this direction and compares the existing regression methods with CGAN. We notice however, that the existing methods like mixture density networks (MDN) and XGBoost do quite well compared to CGAN in terms of likelihood and mean absolute error, respectively. Both these methods are comparatively easier to train than CGANs. CGANs need more innovation to have a comparable modeling and ease-of-training with respect to the existing regression solvers. In summary, for modeling uncertainty MDNs are better while XGBoost is better for the cases where accurate prediction is more important.

Chien-Chih Wang, Kent Loong Tan, Chun-Ting Chen et al.

Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but the calculation of function, gradient, and Hessian is expensive. In particular, the communication and the synchronization cost may become a bottleneck. In this paper, we focus on situations where the model is distributedly stored, and propose a novel distributed Newton method for training deep neural networks. By variable and feature-wise data partitions, and some careful designs, we are able to explicitly use the Jacobian matrix for matrix-vector products in the Newton method. Some techniques are incorporated to reduce the running time as well as the memory consumption. First, to reduce the communication cost, we propose a diagonalization method such that an approximate Newton direction can be obtained without communication between machines. Second, we consider subsampled Gauss-Newton matrices for reducing the running time as well as the communication cost. Third, to reduce the synchronization cost, we terminate the process of finding an approximate Newton direction even though some nodes have not finished their tasks. Details of some implementation issues in distributed environments are thoroughly investigated. Experiments demonstrate that the proposed method is effective for the distributed training of deep neural networks. In compared with stochastic gradient methods, it is more robust and may give better test accuracy.

Dhruv Mahajan, Vivek Gupta, S Sathiya Keerthi et al.

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a given ensemble. The efficient estimation of G is the focus of this paper. The key idea is to approximate the variance of the class scores/probabilities of the base classifiers over the randomness imposed by the training subset by normal/beta distribution at each point x in the input feature space. We estimate the parameters of the distribution using a small set of randomly chosen base classifiers and use those parameters to give efficient estimation schemes for G. We give empirical evidence for the quality of the various estimators. We also demonstrate their usefulness in making design choices such as the number of classifiers in the ensemble and the size of a subset of data used for training that is needed to achieve a certain value of generalization error. Our approach also has great potential for designing distributed ensemble classifiers.

Michał Dereziński, Dhruv Mahajan, S. Sathiya Keerthi et al.

We propose Batch-Expansion Training (BET), a framework for running a batch optimizer on a gradually expanding dataset. As opposed to stochastic approaches, batches do not need to be resampled i.i.d. at every iteration, thus making BET more resource efficient in a distributed setting, and when disk-access is constrained. Moreover, BET can be easily paired with most batch optimizers, does not require any parameter-tuning, and compares favorably to existing stochastic and batch methods. We show that when the batch size grows exponentially with the number of outer iterations, BET achieves optimal $O(1/ε)$ data-access convergence rate for strongly convex objectives. Experiments in parallel and distributed settings show that BET performs better than standard batch and stochastic approaches.

S. Sathiya Keerthi, Tobias Schnabel, Rajiv Khanna

In a recent paper, Levy and Goldberg pointed out an interesting connection between prediction-based word embedding models and count models based on pointwise mutual information. Under certain conditions, they showed that both models end up optimizing equivalent objective functions. This paper explores this connection in more detail and lays out the factors leading to differences between these models. We find that the most relevant differences from an optimization perspective are (i) predict models work in a low dimensional space where embedding vectors can interact heavily; (ii) since predict models have fewer parameters, they are less prone to overfitting. Motivated by the insight of our analysis, we show how count models can be regularized in a principled manner and provide closed-form solutions for L1 and L2 regularization. Finally, we propose a new embedding model with a convex objective and the additional benefit of being intelligible.

Dhruv Mahajan, S. Sathiya Keerthi, S. Sundararajan

Distributed training of $l_1$ regularized classifiers has received great attention recently. Most existing methods approach this problem by taking steps obtained from approximating the objective by a quadratic approximation that is decoupled at the individual variable level. These methods are designed for multicore and MPI platforms where communication costs are low. They are inefficient on systems such as Hadoop running on a cluster of commodity machines where communication costs are substantial. In this paper we design a distributed algorithm for $l_1$ regularization that is much better suited for such systems than existing algorithms. A careful cost analysis is used to support these points and motivate our method. The main idea of our algorithm is to do block optimization of many variables on the actual objective function within each computing node; this increases the computational cost per step that is matched with the communication cost, and decreases the number of outer iterations, thus yielding a faster overall method. Distributed Gauss-Seidel and Gauss-Southwell greedy schemes are used for choosing variables to update in each step. We establish global convergence theory for our algorithm, including Q-linear rate of convergence. Experiments on two benchmark problems show our method to be much faster than existing methods.

Dhruv Mahajan, S. Sathiya Keerthi, S. Sundararajan

This paper concerns the distributed training of nonlinear kernel machines on Map-Reduce. We show that a re-formulation of Nyström approximation based solution which is solved using gradient based techniques is well suited for this, especially when it is necessary to work with a large number of basis points. The main advantages of this approach are: avoidance of computing the pseudo-inverse of the kernel sub-matrix corresponding to the basis points; simplicity and efficiency of the distributed part of the computations; and, friendliness to stage-wise addition of basis points. We implement the method using an AllReduce tree on Hadoop and demonstrate its value on a few large benchmark datasets.

P. Balamurugan, Shirish Shevade, S. Sundararajan et al.

The task of assigning label sequences to a set of observed sequences is common in computational linguistics. Several models for sequence labeling have been proposed over the last few years. Here, we focus on discriminative models for sequence labeling. Many batch and online (updating model parameters after visiting each example) learning algorithms have been proposed in the literature. On large datasets, online algorithms are preferred as batch learning methods are slow. These online algorithms were designed to solve either a primal or a dual problem. However, there has been no systematic comparison of these algorithms in terms of their speed, generalization performance (accuracy/likelihood) and their ability to achieve steady state generalization performance fast. With this aim, we compare different algorithms and make recommendations, useful for a practitioner. We conclude that the selection of an algorithm for sequence labeling depends on the evaluation criterion used and its implementation simplicity.

Vinod Nair, Rahul Kidambi, Sundararajan Sellamanickam et al.

We consider the problem of quantitatively evaluating missing value imputation algorithms. Given a dataset with missing values and a choice of several imputation algorithms to fill them in, there is currently no principled way to rank the algorithms using a quantitative metric. We develop a framework based on treating imputation evaluation as a problem of comparing two distributions and show how it can be used to compute quantitative metrics. We present an efficient procedure for applying this framework to practical datasets, demonstrate several metrics derived from the existing literature on comparing distributions, and propose a new metric called Neighborhood-based Dissimilarity Score which is fast to compute and provides similar results. Results are shown on several datasets, metrics, and imputations algorithms.

Rahul Kidambi, Vinod Nair, Sundararajan Sellamanickam et al.

Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the imputed data, for example on the distribution associated with each variable. None of the existing imputation methods use these constraints. In this paper we propose a structured output approach for missing value imputation that also incorporates domain constraints. We focus on large margin models, but it is easy to extend the ideas to probabilistic models. We deal with the intractable inference step in learning via a piecewise training technique that is simple, efficient, and effective. Comparison with existing state-of-the-art and baseline imputation methods shows that our method gives significantly improved performance on the Hamming loss measure.

Dhruv Mahajan, S. Sathiya Keerthi, S. Sundararajan et al.

This paper proposes a novel parallel stochastic gradient descent (SGD) method that is obtained by applying parallel sets of SGD iterations (each set operating on one node using the data residing in it) for finding the direction in each iteration of a batch descent method. The method has strong convergence properties. Experiments on datasets with high dimensional feature spaces show the value of this method.

Dhruv Mahajan, Nikunj Agrawal, S. Sathiya Keerthi et al.

Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are substantial and algorithms need to be designed suitably considering those costs. In this paper we give a novel approach to the distributed training of linear classifiers (involving smooth losses and L2 regularization) that is designed to reduce the total communication costs. At each iteration, the nodes minimize locally formed approximate objective functions; then the resulting minimizers are combined to form a descent direction to move. Our approach gives a lot of freedom in the formation of the approximate objective function as well as in the choice of methods to solve them. The method is shown to have $O(log(1/ε))$ time convergence. The method can be viewed as an iterative parameter mixing method. A special instantiation yields a parallel stochastic gradient descent method with strong convergence. When communication times between nodes are large, our method is much faster than the Terascale method (Agarwal et al., 2011), which is a state of the art distributed solver based on the statistical query model (Chuet al., 2006) that computes function and gradient values in a distributed fashion. We also evaluate against other recent distributed methods and demonstrate superior performance of our method.