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Nikhil Ghosh

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8 papers

2 author rows

JMLR Journal 2025 Journal Article

The Effect of SGD Batch Size on Autoencoder Learning: Sparsity, Sharpness, and Feature Learning

Nikhil Ghosh
Spencer Frei
Wooseok Ha
Bin Yu

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD with a constant step size successfully finds a global minimum for any batch size choice. However, the particular global minimum found depends upon the batch size. In the full-batch setting, we show that the solution is dense (i.e., not sparse) and is highly aligned with its initialized direction, showing that relatively little feature learning occurs. On the other hand, for any batch size strictly smaller than the number of samples, SGD finds a global minimum that is sparse and nearly orthogonal to its initialization, showing that the randomness of stochastic gradients induces a qualitatively different type of "feature selection" in this setting. Moreover, if we measure the sharpness of the minimum by the trace of the Hessian, the minima found with full-batch gradient descent are flatter than those found with strictly smaller batch sizes, in contrast to previous works which suggest that large batches lead to sharper minima. To prove convergence of SGD with a constant step size, we introduce a powerful tool from the theory of non-homogeneous random walks which may be of independent interest. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

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ICML Conference 2024 Conference Paper

LoRA+: Efficient Low Rank Adaptation of Large Models

Soufiane Hayou
Nikhil Ghosh
Bin Yu 0001

In this paper, we show that Low Rank Adaptation (LoRA) as originally introduced in (Hu et al. , 2021) leads to suboptimal finetuning of models with large width. This is due to the fact that adapter matrices A and B in LoRA are updated with the same learning rate in ADAM. Using scaling arguments for large width networks, we demonstrate that the same learning rate does not allow efficient feature learning. We then show that this suboptimality of LoRA can be corrected simply by setting different learning rates for the LoRA adapter matrices A and B with a well-chosen fixed ratio. We call this proposed algorithm LoRA+. In our extensive experiments, LoRA+ improves finetuning speed (up to ∼ 2X SpeedUp) and performance (1% − 2% improvements), at the same computational cost as LoRA. The code is available at https: //github. com/nikhil-ghosh-berkeley/loraplus

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ICLR Conference 2024 Conference Paper

More is Better: when Infinite Overparameterization is Optimal and Overfitting is Obligatory

James B. Simon
Dhruva Karkada
Nikhil Ghosh
Mikhail Belkin

In our era of enormous neural networks, empirical progress has been driven by the philosophy that *more is better.* Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) optimizing to near-interpolation improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is *obligatory:* near-optimal performance can *only* be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization and overfitting in random feature models.

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NeurIPS Conference 2024 Conference Paper

The Impact of Initialization on LoRA Finetuning Dynamics

Soufiane Hayou
Nikhil Ghosh
Bin Yu

In this paper, we study the role of initialization in Low Rank Adaptation (LoRA) as originally introduced in Hu et al. (2021). Essentially, to start from the pretrained model, one can either initialize $B$ to zero and $A$ to random, or vice-versa. In both cases, the product $BA$ is equal to zero at initialization, which makes finetuning starts from the pretrained model. These two initialization schemes are seemingly similar. They should in-principle yield the same performance and share the same optimal learning rate. We demonstrate that this is an *incorrect intuition* and that the first scheme (of initializing $B$ to zero and $A$ to random) on average in our experiments yields better performance compared to the other scheme. Our theoretical analysis shows that the reason behind this might be that the first initialization allows the use of larger learning rates (without causing output instability) compared to the second initialization, resulting in more efficient learning of the first scheme. We validate our results with extensive experiments on LLMs.

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NeurIPS Conference 2023 Conference Paper

Alternating Updates for Efficient Transformers

Cenk Baykal
Dylan Cutler
Nishanth Dikkala
Nikhil Ghosh
Rina Panigrahy
Xin Wang

It has been well established that increasing scale in deep transformer networks leads to improved quality and performance. However, this increase in scale often comes with prohibitive increases in compute cost and inference latency. We introduce Alternating Updates (AltUp), a simple-to-implement method to increase a model's capacity without the computational burden. AltUp enables the widening of the learned representation, i. e. , the token embedding, while only incurring a negligible increase in latency. AltUp achieves this by working on a subblock of the widened representation at each layer and using a predict-and-correct mechanism to update the inactivated blocks. We present extensions of AltUp, such as its applicability to the sequence dimension, and demonstrate how AltUp can be synergistically combined with existing approaches, such as Sparse Mixture-of-Experts models, to obtain efficient models with even higher capacity. Our experiments on benchmark transformer models and language tasks demonstrate the consistent effectiveness of AltUp on a diverse set of scenarios. Notably, on SuperGLUE and SQuAD benchmarks, AltUp enables up to $87\%$ speedup relative to the dense baselines at the same accuracy.

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ICLR Conference 2023 Conference Paper

Deconstructing Distributions: A Pointwise Framework of Learning

Gal Kaplun
Nikhil Ghosh
Saurabh Garg
Boaz Barak
Preetum Nakkiran

In machine learning, we traditionally evaluate the performance of a single model, averaged over a collection of test inputs. In this work, we propose a new approach: we measure the performance of a collection of models when evaluated at *single input point*. Specifically, we study a point's *profile*: the relationship between models' average performance on the test distribution and their pointwise performance on this individual point. We find that profiles can yield new insights into the structure of both models and data---in and out-of-distribution. For example, we empirically show that real data distributions consist of points with qualitatively different profiles. On one hand, there are ``compatible'' points with strong correlation between the pointwise and average performance. On the other hand, there are points with weak and even *negative* correlation: cases where improving overall model accuracy actually *hurts* performance on these inputs. As an application, we use profiles to construct a dataset we call CIFAR-10-NEG: a subset of CINIC-10 such that for standard models, accuracy on CIFAR-10-NEG is *negatively correlated* with CIFAR-10 accuracy. Illustrating for the first time an OOD dataset that completely inverts ``accuracy-on-the-line'' (Miller et al., 2021).

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ICLR Conference 2022 Conference Paper

The Three Stages of Learning Dynamics in High-dimensional Kernel Methods

Nikhil Ghosh
Song Mei
Bin Yu 0001

To understand how deep learning works, it is crucial to understand the training dynamics of neural networks. Several interesting hypotheses about these dynamics have been made based on empirically observed phenomena, but there exists a limited theoretical understanding of when and why such phenomena occur. In this paper, we consider the training dynamics of gradient flow on kernel least-squares objectives, which is a limiting dynamics of SGD trained neural networks. Using precise high-dimensional asymptotics, we characterize the dynamics of the fitted model in two “worlds”: in the Oracle World the model is trained on the population distribution and in the Empirical World the model is trained on an i.i.d finite dataset. We show that under mild conditions on the kernel and $L^2$ target regression function the training dynamics have three stages that are based on the behaviors of the models in the two worlds. Our theoretical results also mathematically formalize some interesting deep learning phenomena. Specifically, in our setting we show that SGD progressively learns more complex functions and that there is a "deep bootstrap" phenomenon: during the second stage, the test error of both worlds remain close despite the empirical training error being much smaller. Finally, we give a concrete example comparing the dynamics of two different kernels which shows that faster training is not necessary for better generalization.

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NeurIPS Conference 2019 Conference Paper

Landmark Ordinal Embedding

Nikhil Ghosh
Yuxin Chen
Yisong Yue

In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form “item j is closer to item i than item k”. Existing approaches for this “ordinal embedding” problem require expensive optimization procedures, which cannot scale to handle increasingly larger datasets. To address this issue, we propose a landmark-based strategy, which we call Landmark Ordinal Embedding (LOE). Our approach trades off statistical efficiency for computational efficiency by exploiting the low-dimensionality of the latent embedding. We derive bounds establishing the statistical consistency of LOE under the popular Bradley- Terry-Luce noise model. Through a rigorous analysis of the computational complexity, we show that LOE is significantly more efficient than conventional ordinal embedding approaches as the number of items grows. We validate these characterizations empirically on both synthetic and real datasets. We also present a practical approach that achieves the “best of both worlds”, by using LOE to warm-start existing methods that are more statistically efficient but computationally expensive.

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