arXiv subjects

Sham Kakade

Publications and source records attributed to Sham Kakade.

At least 55 records · Page 3Linked to original sources

arXiv2025

Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Models

Self-improvement is a mechanism in Large Language Model (LLM) pre-training, post-training and test-time inference. We explore a framework where the model verifies its own outputs, filters or reweights data based on this verification, and distills the filtered data. Despite several empirical successes, a fundamental understanding is still lacking. In this work, we initiate a comprehensive, modular and controlled study on LLM self-improvement. We provide a mathematical formulation for self-improvement, which is largely governed by a quantity which we formalize as the generation-verification gap. Through experiments with various model families and tasks, we discover a scaling phenomenon of self-improvement -- a variant of the generation-verification gap scales monotonically with the model pre-training flops. We also examine when self-improvement is possible, an iterative self-improvement procedure, and ways to improve its performance. Our findings not only advance understanding of LLM self-improvement with practical implications, but also open numerous avenues for future research into its capabilities and boundaries.

cs.CL↗

arXiv2025

Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants

Recent advancements in deep learning optimization have introduced new algorithms, such as Schedule-Free optimizers, AdEMAMix, MARS and Lion which modify traditional momentum mechanisms. In a separate line of work, theoretical acceleration of stochastic gradient descent (SGD) in noise-dominated regime has been achieved by decoupling the momentum coefficient from the current gradient's weight. In this paper, we establish explicit connections between these two lines of work. We substantiate our theoretical findings with preliminary experiments on a 150m language modeling task. We find that AdEMAMix, which most closely resembles accelerated versions of stochastic gradient descent, exhibits superior performance. Building on these insights, we introduce a modification to AdEMAMix, termed Simplified-AdEMAMix, which maintains the same performance as AdEMAMix across both large and small batch-size settings while eliminating the need for two different momentum terms. The code for Simplified-AdEMAMix is available on the repository: https://github.com/DepenM/Simplified-AdEMAMix/.

cs.LG↗

arXiv2025

SOAP: Improving and Stabilizing Shampoo using Adam

There is growing evidence of the effectiveness of Shampoo, a higher-order preconditioning method, over Adam in deep learning optimization tasks. However, Shampoo's drawbacks include additional hyperparameters and computational overhead when compared to Adam, which only updates running averages of first- and second-moment quantities. This work establishes a formal connection between Shampoo (implemented with the 1/2 power) and Adafactor -- a memory-efficient approximation of Adam -- showing that Shampoo is equivalent to running Adafactor in the eigenbasis of Shampoo's preconditioner. This insight leads to the design of a simpler and computationally efficient algorithm: $\textbf{S}$hampo$\textbf{O}$ with $\textbf{A}$dam in the $\textbf{P}$reconditioner's eigenbasis (SOAP). With regards to improving Shampoo's computational efficiency, the most straightforward approach would be to simply compute Shampoo's eigendecomposition less frequently. Unfortunately, as our empirical results show, this leads to performance degradation that worsens with this frequency. SOAP mitigates this degradation by continually updating the running average of the second moment, just as Adam does, but in the current (slowly changing) coordinate basis. Furthermore, since SOAP is equivalent to running Adam in a rotated space, it introduces only one additional hyperparameter (the preconditioning frequency) compared to Adam. We empirically evaluate SOAP on language model pre-training with 360m and 660m sized models. In the large batch regime, SOAP reduces the number of iterations by over 40% and wall clock time by over 35% compared to AdamW, with approximately 20% improvements in both metrics compared to Shampoo. An implementation of SOAP is available at https://github.com/nikhilvyas/SOAP.

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arXiv2024

Scaling Laws for Imitation Learning in Single-Agent Games

Imitation Learning (IL) is one of the most widely used methods in machine learning. Yet, many works find it is often unable to fully recover the underlying expert behavior, even in constrained environments like single-agent games. However, none of these works deeply investigate the role of scaling up the model and data size. Inspired by recent work in Natural Language Processing (NLP) where "scaling up" has resulted in increasingly more capable LLMs, we investigate whether carefully scaling up model and data size can bring similar improvements in the imitation learning setting for single-agent games. We first demonstrate our findings on a variety of Atari games, and thereafter focus on the extremely challenging game of NetHack. In all games, we find that IL loss and mean return scale smoothly with the compute budget (FLOPs) and are strongly correlated, resulting in power laws for training compute-optimal IL agents. Finally, we forecast and train several NetHack agents with IL and find they outperform prior state-of-the-art by 1.5x in all settings. Our work both demonstrates the scaling behavior of imitation learning in a variety of single-agent games, as well as the viability of scaling up current approaches for increasingly capable agents in NetHack, a game that remains elusively hard for current AI systems.

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arXiv2024

MatFormer: Nested Transformer for Elastic Inference

Foundation models are applied in a broad spectrum of settings with different inference constraints, from massive multi-accelerator clusters to resource-constrained standalone mobile devices. However, the substantial costs associated with training these models often limit the number of unique model sizes that can be offered. Consequently, practitioners are compelled to select a model that may not be optimally aligned with their specific latency and cost requirements. We present MatFormer, a novel Transformer architecture designed to provide elastic inference across diverse deployment constraints. MatFormer achieves this by incorporating a nested Feed Forward Network (FFN) block structure within a standard Transformer model. During training, we optimize the parameters of multiple nested FFN blocks with varying sizes, enabling the extraction of hundreds of accurate smaller models without incurring additional computational costs. We empirically validate the efficacy of MatFormer across different model classes (decoders and encoders) and modalities (language and vision), demonstrating its potential for real-world deployment. We show that a 850M decoder-only MatFormer language model (MatLM) allows us to extract multiple smaller models spanning from 582M to 850M parameters, each exhibiting better validation loss and one-shot downstream evaluations than independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can lead to significant reduction in inference latency. Project website: https://devvrit.github.io/matformer/

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arXiv2024

From an Image to a Scene: Learning to Imagine the World from a Million 360 Videos

Three-dimensional (3D) understanding of objects and scenes play a key role in humans' ability to interact with the world and has been an active area of research in computer vision, graphics, and robotics. Large scale synthetic and object-centric 3D datasets have shown to be effective in training models that have 3D understanding of objects. However, applying a similar approach to real-world objects and scenes is difficult due to a lack of large-scale data. Videos are a potential source for real-world 3D data, but finding diverse yet corresponding views of the same content has shown to be difficult at scale. Furthermore, standard videos come with fixed viewpoints, determined at the time of capture. This restricts the ability to access scenes from a variety of more diverse and potentially useful perspectives. We argue that large scale 360 videos can address these limitations to provide: scalable corresponding frames from diverse views. In this paper, we introduce 360-1M, a 360 video dataset, and a process for efficiently finding corresponding frames from diverse viewpoints at scale. We train our diffusion-based model, Odin, on 360-1M. Empowered by the largest real-world, multi-view dataset to date, Odin is able to freely generate novel views of real-world scenes. Unlike previous methods, Odin can move the camera through the environment, enabling the model to infer the geometry and layout of the scene. Additionally, we show improved performance on standard novel view synthesis and 3D reconstruction benchmarks.

cs.CV↗

arXiv2024

LoRA Soups: Merging LoRAs for Practical Skill Composition Tasks

Low-Rank Adaptation (LoRA) is a popular technique for parameter-efficient fine-tuning of Large Language Models (LLMs). We study how different LoRA modules can be merged to achieve skill composition -- testing the performance of the merged model on a target task that involves combining multiple skills, each skill coming from a single LoRA. This setup is favorable when it is difficult to obtain training data for the target task and when it can be decomposed into multiple skills. First, we identify practically occurring use-cases that can be studied under the realm of skill composition, e.g. solving hard math-word problems with code, creating a bot to answer questions on proprietary manuals or about domain-specialized corpora. Our main contribution is to show that concatenation of LoRAs (CAT), which optimally weights LoRAs that were individually trained on different skills, outperforms existing model- and data- merging techniques; for instance on math-word problems, CAT beats these methods by an average of 43% and 12% respectively. Thus, this paper advocates model merging as an efficient way to solve compositional tasks and underscores CAT as a simple, compute-friendly and effective procedure. To our knowledge, this is the first work demonstrating the superiority of model merging over data mixing for binary skill composition tasks. Code and data are available at https://github.com/aksh555/LoRA-Soups

cs.CL↗

arXiv2024

Loss-to-Loss Prediction: Scaling Laws for All Datasets

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

cs.LG↗

arXiv2024

CoLoR-Filter: Conditional Loss Reduction Filtering for Targeted Language Model Pre-training

Selecting high-quality data for pre-training is crucial in shaping the downstream task performance of language models. A major challenge lies in identifying this optimal subset, a problem generally considered intractable, thus necessitating scalable and effective heuristics. In this work, we propose a data selection method, CoLoR-Filter (Conditional Loss Reduction Filtering), which leverages an empirical Bayes-inspired approach to derive a simple and computationally efficient selection criterion based on the relative loss values of two auxiliary models. In addition to the modeling rationale, we evaluate CoLoR-Filter empirically on two language modeling tasks: (1) selecting data from C4 for domain adaptation to evaluation on Books and (2) selecting data from C4 for a suite of downstream multiple-choice question answering tasks. We demonstrate favorable scaling both as we subselect more aggressively and using small auxiliary models to select data for large target models. As one headline result, CoLoR-Filter data selected using a pair of 150m parameter auxiliary models can train a 1.2b parameter target model to match a 1.2b parameter model trained on 25b randomly selected tokens with 25x less data for Books and 11x less data for the downstream tasks. Code: https://github.com/davidbrandfonbrener/color-filter-olmo Filtered data: https://huggingface.co/datasets/davidbrandfonbrener/color-filtered-c4

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arXiv2024

Follow My Instruction and Spill the Beans: Scalable Data Extraction from Retrieval-Augmented Generation Systems

Retrieval-Augmented Generation (RAG) improves pre-trained models by incorporating external knowledge at test time to enable customized adaptation. We study the risk of datastore leakage in Retrieval-In-Context RAG Language Models (LMs). We show that an adversary can exploit LMs' instruction-following capabilities to easily extract text data verbatim from the datastore of RAG systems built with instruction-tuned LMs via prompt injection. The vulnerability exists for a wide range of modern LMs that span Llama2, Mistral/Mixtral, Vicuna, SOLAR, WizardLM, Qwen1.5, and Platypus2, and the exploitability exacerbates as the model size scales up. We also study multiple effects of RAG setup on the extractability of data, indicating that following unexpected instructions to regurgitate data can be an outcome of failure in effectively utilizing contexts for modern LMs, and further show that such vulnerability can be greatly mitigated by position bias elimination strategies. Extending our study to production RAG models GPTs, we design an attack that can cause datastore leakage with a 100% success rate on 25 randomly selected customized GPTs with at most 2 queries, and we extract text data verbatim at a rate of 41% from a book of 77,000 words and 3% from a corpus of 1,569,000 words by prompting the GPTs with only 100 queries generated by themselves.

cs.CL↗

arXiv2024

Neural Coordination and Capacity Control for Inventory Management

This paper addresses the capacitated periodic review inventory control problem, focusing on a retailer managing multiple products with limited shared resources, such as storage or inbound labor at a facility. Specifically, this paper is motivated by the questions of (1) what does it mean to backtest a capacity control mechanism, (2) can we devise and backtest a capacity control mechanism that is compatible with recent advances in deep reinforcement learning for inventory management? First, because we only have a single historic sample path of Amazon's capacity limits, we propose a method that samples from a distribution of possible constraint paths covering a space of real-world scenarios. This novel approach allows for more robust and realistic testing of inventory management strategies. Second, we extend the exo-IDP (Exogenous Decision Process) formulation of Madeka et al. 2022 to capacitated periodic review inventory control problems and show that certain capacitated control problems are no harder than supervised learning. Third, we introduce a `neural coordinator', designed to produce forecasts of capacity prices, guiding the system to adhere to target constraints in place of a traditional model predictive controller. Finally, we apply a modified DirectBackprop algorithm for learning a deep RL buying policy and a training the neural coordinator. Our methodology is evaluated through large-scale backtests, demonstrating RL buying policies with a neural coordinator outperforms classic baselines both in terms of cumulative discounted reward and capacity adherence (we see improvements of up to 50% in some cases).

eess.SY↗

arXiv2024

Universal Length Generalization with Turing Programs

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to achieve length generalization, these proposals typically apply to a limited set of tasks. Building on prior scratchpad and Chain-of-Thought (CoT) techniques, we propose Turing Programs, a novel CoT strategy that decomposes an algorithmic task into steps mimicking the computation of a Turing Machine. This framework is both universal, as it can accommodate any algorithmic task, and simple, requiring only copying text from the context with small modifications. We show that by using Turing Programs, we obtain robust length generalization on a range of algorithmic tasks: addition, multiplication and in-context SGD. We then demonstrate that transformers achieve length generalization on random Turing Programs, suggesting that length generalization is possible for any algorithmic task. Finally, we theoretically prove that transformers can implement Turing Programs, constructing a simple RASP (Weiss et al.) program that simulates an arbitrary Turing machine.

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arXiv2024

Koopman Spectrum Nonlinear Regulators and Efficient Online Learning

Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack predictability. In this work, we present a novel paradigm of controlling nonlinear systems via the minimization of the Koopman spectrum cost: a cost over the Koopman operator of the controlled dynamics. This induces a broader class of dynamical behaviors that evolve over stable manifolds such as nonlinear oscillators, closed loops, and smooth movements. We demonstrate that some dynamics characterizations that are not possible with a cumulative cost are feasible in this paradigm, which generalizes the classical eigenstructure and pole assignments to nonlinear decision making. Moreover, we present a sample efficient online learning algorithm for our problem that enjoys a sub-linear regret bound under some structural assumptions.

cs.LG↗

arXiv2024

A New Perspective on Shampoo's Preconditioner

Shampoo, a second-order optimization algorithm which uses a Kronecker product preconditioner, has recently garnered increasing attention from the machine learning community. The preconditioner used by Shampoo can be viewed either as an approximation of the Gauss--Newton component of the Hessian or the covariance matrix of the gradients maintained by Adagrad. We provide an explicit and novel connection between the $\textit{optimal}$ Kronecker product approximation of these matrices and the approximation made by Shampoo. Our connection highlights a subtle but common misconception about Shampoo's approximation. In particular, the $\textit{square}$ of the approximation used by the Shampoo optimizer is equivalent to a single step of the power iteration algorithm for computing the aforementioned optimal Kronecker product approximation. Across a variety of datasets and architectures we empirically demonstrate that this is close to the optimal Kronecker product approximation. Additionally, for the Hessian approximation viewpoint, we empirically study the impact of various practical tricks to make Shampoo more computationally efficient (such as using the batch gradient and the empirical Fisher) on the quality of Hessian approximation.

cs.LG↗

arXiv2024

Beyond Implicit Bias: The Insignificance of SGD Noise in Online Learning

The success of SGD in deep learning has been ascribed by prior works to the implicit bias induced by finite batch sizes ("SGD noise"). While prior works focused on offline learning (i.e., multiple-epoch training), we study the impact of SGD noise on online (i.e., single epoch) learning. Through an extensive empirical analysis of image and language data, we demonstrate that small batch sizes do not confer any implicit bias advantages in online learning. In contrast to offline learning, the benefits of SGD noise in online learning are strictly computational, facilitating more cost-effective gradient steps. This suggests that SGD in the online regime can be construed as taking noisy steps along the "golden path" of the noiseless gradient descent algorithm. We study this hypothesis and provide supporting evidence in loss and function space. Our findings challenge the prevailing understanding of SGD and offer novel insights into its role in online learning.

cs.LG↗

arXiv2024

Q-Probe: A Lightweight Approach to Reward Maximization for Language Models

We present an approach called Q-probing to adapt a pre-trained language model to maximize a task-specific reward function. At a high level, Q-probing sits between heavier approaches such as finetuning and lighter approaches such as few shot prompting, but can also be combined with either. The idea is to learn a simple linear function on a model's embedding space that can be used to reweight candidate completions. We theoretically show that this sampling procedure is equivalent to a KL-constrained maximization of the Q-probe as the number of samples increases. To train the Q-probes we consider either reward modeling or a class of novel direct policy learning objectives based on importance weighted policy gradients. With this technique, we see gains in domains with ground-truth rewards (code generation) as well as implicit rewards defined by preference data, even outperforming finetuning in data-limited regimes. Moreover, a Q-probe can be trained on top of an API since it only assumes access to sampling and embeddings. Code: https://github.com/likenneth/q_probe .

cs.LG↗

arXiv2024

A Study on the Calibration of In-context Learning

Accurate uncertainty quantification is crucial for the safe deployment of machine learning models, and prior research has demonstrated improvements in the calibration of modern language models (LMs). We study in-context learning (ICL), a prevalent method for adapting static LMs through tailored prompts, and examine the balance between performance and calibration across a broad spectrum of natural language understanding and reasoning tasks. Through comprehensive experiments, we observe that, with an increasing number of ICL examples, models initially exhibit increased miscalibration before achieving better calibration and miscalibration tends to arise in low-shot settings. Moreover, we find that methods aimed at improving usability, such as fine-tuning and chain-of-thought (CoT) prompting, can lead to miscalibration and unreliable natural language explanations. Furthermore, we explore recalibration techniques and find that a scaling-binning calibrator can reduce calibration errors consistently.

cs.CL↗

arXiv2024

Feature emergence via margin maximization: case studies in algebraic tasks

Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks implement specific target functions, this paper explores a complementary question -- why do networks arrive at particular computational strategies? Our inquiry focuses on the algebraic learning tasks of modular addition, sparse parities, and finite group operations. Our primary theoretical findings analytically characterize the features learned by stylized neural networks for these algebraic tasks. Notably, our main technique demonstrates how the principle of margin maximization alone can be used to fully specify the features learned by the network. Specifically, we prove that the trained networks utilize Fourier features to perform modular addition and employ features corresponding to irreducible group-theoretic representations to perform compositions in general groups, aligning closely with the empirical observations of Nanda et al. and Chughtai et al. More generally, we hope our techniques can help to foster a deeper understanding of why neural networks adopt specific computational strategies.

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