Author name cluster

Boris Hanin

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

15 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Don't be lazy: CompleteP enables compute-efficient deep transformers

Nolan Dey
Bin Zhang
Lorenzo Noci
Mufan Li
Blake Bordelon
Shane Bergsma
Cengiz Pehlevan
Boris Hanin

We study compute efficiency of LLM training when using different parameterizations, i. e. , rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as learning rate) across changes in model depth, requiring practitioners to either re-tune these HPs as they scale up (expensive), or accept sub-optimal training when re-tuning is prohibitive. Even when they achieve HP transfer, we develop theory to show parameterizations may still exist in the lazy learning regime where layers learn only features close to their linearization, preventing effective use of depth and nonlinearity. Finally, we identify and adopt the parameterization we call CompleteP that achieves both depth-wise HP transfer and non-lazy learning in all layers. CompleteP enables a wider range of model width/depth ratios to remain compute-efficient, unlocking shapes better suited for different hardware settings and operational contexts. Moreover, CompleteP enables 12-34% compute efficiency improvements over the prior state-of-the-art. All experiments were run on Cerebras CS-3 systems. A minimal implementation is available at https: //github. com/EleutherAI/nanoGPT-mup/tree/completep.

PDF Details

ICLR Conference 2025 Conference Paper

Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization

Noam Razin
Sadhika Malladi
Adithya Bhaskar
Danqi Chen 0001
Sanjeev Arora
Boris Hanin

Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the likelihood of preferred responses often decreases during training. The current work sheds light on the causes and implications of this counterintuitive phenomenon, which we term *likelihood displacement*. We demonstrate that likelihood displacement can be *catastrophic*, shifting probability mass from preferred responses to responses with an opposite meaning. As a simple example, training a model to prefer $\texttt{No}$ over $\texttt{Never}$ can sharply increase the probability of $\texttt{Yes}$. Moreover, when aligning the model to refuse unsafe prompts, we show that such displacement can *unintentionally lead to unalignment*, by shifting probability mass from preferred refusal responses to harmful responses (e.g., reducing the refusal rate of Llama-3-8B-Instruct from 74.4% to 33.4%). We theoretically characterize that likelihood displacement is driven by preferences that induce similar embeddings, as measured by a *centered hidden embedding similarity (CHES)* score. Empirically, the CHES score enables identifying which training samples contribute most to likelihood displacement in a given dataset. Filtering out these samples effectively mitigated unintentional unalignment in our experiments. More broadly, our results highlight the importance of curating data with sufficiently distinct preferences, for which we believe the CHES score may prove valuable.

Details

NeurIPS Conference 2024 Conference Paper

Are More LLM Calls All You Need? Towards the Scaling Properties of Compound AI Systems

Lingjiao Chen
Jared Davis
Boris Hanin
Peter Bailis
Ion Stoica
Matei Zaharia
James Zou

Many recent state-of-the-art results in language tasks were achieved using compound systems that perform multiple Language Model (LM) calls and aggregate their responses. However, there is little understanding of how the number of LM calls -- e. g. , when asking the LM to answer each question multiple times and taking a majority vote -- affects such a compound system's performance. In this paper, we initiate the study of scaling properties of compound inference systems. We analyze, theoretically and empirically, how the number of LM calls affects the performance of Vote and Filter-Vote, two of the simplest compound system designs, which aggregate LM responses via majority voting, optionally applying LM filters. We find, surprisingly, that across multiple language tasks, the performance of both Vote and Filter-Vote can first increase but then decrease as a function of the number of LM calls. Our theoretical results suggest that this non-monotonicity is due to the diversity of query difficulties within a task: more LM calls lead to higher performance on "easy" queries, but lower performance on "hard" queries, and non-monotone behavior can emerge when a task contains both types of queries. This insight then allows us to compute, from a small number of samples, the number of LM calls that maximizes system performance, and define an analytical scaling model for both systems. Experiments show that our scaling model can accurately predict the performance of Vote and Filter-Vote systems and thus find the optimal number of LM calls to make.

PDF Details DOI

ICLR Conference 2024 Conference Paper

Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit

Blake Bordelon
Lorenzo Noci
Mufan Bill Li
Boris Hanin
Cengiz Pehlevan

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses $\mu$P parameterized networks, where the optimal hyperparameters for small width networks *transfer* to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of $1/\sqrt{\text{depth}}$ in combination with the $\mu$P parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and vision transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

Details

ICLR Conference 2024 Conference Paper

Principled Architecture-aware Scaling of Hyperparameters

Wuyang Chen 0001
Junru Wu
Zhangyang Wang
Boris Hanin

Training a high-quality deep neural network requires choosing suitable hyperparameters, which is a non-trivial and expensive process. Current works try to automatically optimize or design principles of hyperparameters, such that they can generalize to diverse unseen scenarios. However, most designs of principles or optimization methods are agnostic to the choice of network structures, and thus largely ignore the impact of neural architectures on hyperparameters. In this work, we precisely characterize the dependence of initializations and maximal learning rates on the network architecture, which includes the network depth, width, convolutional kernel size, and connectivity patterns. By pursuing every parameter to be maximally updated with the same mean squared change in pre-activations, we can generalize our initialization and learning rates across MLPs (multi-layer perception) and CNNs (convolutional neural network) with sophisticated graph topologies. We verify our principles with comprehensive experiments. More importantly, our strategy further sheds light on advancing current benchmarks for architecture design. A fair comparison of AutoML algorithms requires accurate network rankings. However, we demonstrate that network rankings can be easily changed by better training networks in benchmarks with our architecture-aware learning rates and initialization.

Details

JMLR Journal 2024 Journal Article

Random Fully Connected Neural Networks as Perturbatively Solvable Hierarchies

Boris Hanin

We study the distribution of fully connected neural networks with Gaussian random weights/biases and L hidden layers, each of width proportional to a large parameter n. For polynomially bounded non-linearities we give sharp estimates in powers of 1/n for the joint cumulants of the network output and its derivatives. We further show that network cumulants form a perturbatively solvable hierarchy in powers of 1/n. That is, the k-th order cumulants in each layer are determined to leading order in 1/n by cumulants of order at most k computed at the previous layer. By explicitly deriving and then solving several such recursions, we find that the depth-to-width ratio L/n plays the role of an effective network depth, controlling both the distance to Gaussianity and the size of inter-neuron correlations. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

PDF Details

ICML Conference 2023 Conference Paper

Maximal Initial Learning Rates in Deep ReLU Networks

Gaurav Iyer
Boris Hanin
David Rolnick

Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning rate can be, most prior work focuses only on late-stage training. In this work, we introduce the maximal initial learning rate $\eta^{\ast}$ - the largest learning rate at which a randomly initialized neural network can successfully begin training and achieve (at least) a given threshold accuracy. Using a simple approach to estimate $\eta^{\ast}$, we observe that in constant-width fully-connected ReLU networks, $\eta^{\ast}$ behaves differently from the maximum learning rate later in training. Specifically, we find that $\eta^{\ast}$ is well predicted as a power of depth $\times$ width, provided that (i) the width of the network is sufficiently large compared to the depth, and (ii) the input layer is trained at a relatively small learning rate. We further analyze the relationship between $\eta^{\ast}$ and the sharpness $\lambda_{1}$ of the network at initialization, indicating they are closely though not inversely related. We formally prove bounds for $\lambda_{1}$ in terms of depth $\times$ width that align with our empirical results.

Details

NeurIPS Conference 2022 Conference Paper

Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis

Wuyang Chen
Wei Huang
Xinyu Gong
Boris Hanin
Zhangyang Wang

Advanced deep neural networks (DNNs), designed by either human or AutoML algorithms, are growing increasingly complex. Diverse operations are connected by complicated connectivity patterns, e. g. , various types of skip connections. Those topological compositions are empirically effective and observed to smooth the loss landscape and facilitate the gradient flow in general. However, it remains elusive to derive any principled understanding of their effects on the DNN capacity or trainability, and to understand why or in which aspect one specific connectivity pattern is better than another. In this work, we theoretically characterize the impact of connectivity patterns on the convergence of DNNs under gradient descent training in fine granularity. By analyzing a wide network's Neural Network Gaussian Process (NNGP), we are able to depict how the spectrum of an NNGP kernel propagates through a particular connectivity pattern, and how that affects the bound of convergence rates. As one practical implication of our results, we show that by a simple filtration of "unpromising" connectivity patterns, we can trim down the number of models to evaluate, and significantly accelerate the large-scale neural architecture search without any overhead.

PDF Details

ICLR Conference 2022 Conference Paper

Deep ReLU Networks Preserve Expected Length

Boris Hanin
Ryan S. Jeong
David Rolnick

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.

Details

NeurIPS Conference 2021 Conference Paper

How Data Augmentation affects Optimization for Linear Regression

Boris Hanin
Yi Sun

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate is nascent. In the spirit of classical convex optimization and recent work on implicit bias, the present work analyzes the effect of augmentation on optimization in the simple convex setting of linear regression with MSE loss. We find joint schedules for learning rate and data augmentation scheme under which augmented gradient descent provably converges and characterize the resulting minimum. Our results apply to arbitrary augmentation schemes, revealing complex interactions between learning rates and augmentations even in the convex setting. Our approach interprets augmented (S)GD as a stochastic optimization method for a time-varying sequence of proxy losses. This gives a unified way to analyze learning rate, batch size, and augmentations ranging from additive noise to random projections. From this perspective, our results, which also give rates of convergence, can be viewed as Monro-Robbins type conditions for augmented (S)GD.

PDF Details

ICLR Conference 2020 Conference Paper

Finite Depth and Width Corrections to the Neural Tangent Kernel

Boris Hanin
Mihai Nica

We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation is exponential in the ratio of network depth to width. Thus, even in the limit of infinite overparameterization, the NTK is not deterministic if depth and width simultaneously tend to infinity. Moreover, we prove that for such deep and wide networks, the NTK has a non-trivial evolution during training by showing that the mean of its first SGD update is also exponential in the ratio of network depth to width. This is sharp contrast to the regime where depth is fixed and network width is very large. Our results suggest that, unlike relatively shallow and wide networks, deep and wide ReLU networks are capable of learning data-dependent features even in the so-called lazy training regime.

Details

ICML Conference 2019 Conference Paper

Complexity of Linear Regions in Deep Networks

Boris Hanin
David Rolnick

It is well-known that the expressivity of a neural network depends on its architecture, with deeper networks expressing more complex functions. In the case of networks that compute piecewise linear functions, such as those with ReLU activation, the number of distinct linear regions is a natural measure of expressivity. It is possible to construct networks with merely a single region, or for which the number of linear regions grows exponentially with depth; it is not clear where within this range most networks fall in practice, either before or after training. In this paper, we provide a mathematical framework to count the number of linear regions of a piecewise linear network and measure the volume of the boundaries between these regions. In particular, we prove that for networks at initialization, the average number of regions along any one-dimensional subspace grows linearly in the total number of neurons, far below the exponential upper bound. We also find that the average distance to the nearest region boundary at initialization scales like the inverse of the number of neurons. Our theory suggests that, even after training, the number of linear regions is far below exponential, an intuition that matches our empirical observations. We conclude that the practical expressivity of neural networks is likely far below that of the theoretical maximum, and that this gap can be quantified.

Details

NeurIPS Conference 2019 Conference Paper

Deep ReLU Networks Have Surprisingly Few Activation Patterns

Boris Hanin
David Rolnick

The success of deep networks has been attributed in part to their expressivity: per parameter, deep networks can approximate a richer class of functions than shallow networks. In ReLU networks, the number of activation patterns is one measure of expressivity; and the maximum number of patterns grows exponentially with the depth. However, recent work has showed that the practical expressivity of deep networks - the functions they can learn rather than express - is often far from the theoretical maximum. In this paper, we show that the average number of activation patterns for ReLU networks at initialization is bounded by the total number of neurons raised to the input dimension. We show empirically that this bound, which is independent of the depth, is tight both at initialization and during training, even on memorization tasks that should maximize the number of activation patterns. Our work suggests that realizing the full expressivity of deep networks may not be possible in practice, at least with current methods.

PDF Details

NeurIPS Conference 2018 Conference Paper

How to Start Training: The Effect of Initialization and Architecture

Boris Hanin
David Rolnick

We identify and study two common failure modes for early training in deep ReLU nets. For each, we give a rigorous proof of when it occurs and how to avoid it, for fully connected, convolutional, and residual architectures. We show that the first failure mode, exploding or vanishing mean activation length, can be avoided by initializing weights from a symmetric distribution with variance 2/fan-in and, for ResNets, by correctly scaling the residual modules. We prove that the second failure mode, exponentially large variance of activation length, never occurs in residual nets once the first failure mode is avoided. In contrast, for fully connected nets, we prove that this failure mode can happen and is avoided by keeping constant the sum of the reciprocals of layer widths. We demonstrate empirically the effectiveness of our theoretical results in predicting when networks are able to start training. In particular, we note that many popular initializations fail our criteria, whereas correct initialization and architecture allows much deeper networks to be trained.

PDF Details

NeurIPS Conference 2018 Conference Paper

Which Neural Net Architectures Give Rise to Exploding and Vanishing Gradients?

Boris Hanin

We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network N with ReLU activations. Our results show that the empirical variance of the squares of the entries in the input-output Jacobian of N is exponential in a simple architecture-dependent constant beta, given by the sum of the reciprocals of the hidden layer widths. When beta is large, the gradients computed by N at initialization vary wildly. Our approach complements the mean field theory analysis of random networks. From this point of view, we rigorously compute finite width corrections to the statistics of gradients at the edge of chaos.

PDF Details