arXiv subjects

Kaan Ozkara

Publications and source records attributed to Kaan Ozkara.

13 recordsLinked to original sources

arXiv2026

Compatibility Matters: A Framework for Token-Level Teacher Selection in On-Policy Distillation

On-policy distillation (OPD) has recently been introduced as a promising paradigm for continual learning, where a student policy can be supervised at the token-level. Typically, OPD is performed using a single teacher per prompt rollout (or even per training run). However, this ignores a whole other axis of flexibility that is available due to the on-policy nature - token-level teacher selection during rollouts. Building on this insight, we theoretically explore what makes a teacher and a student compatible for OPD, and leverage our findings to derive several empirical heuristics for teacher selection. In particular, our framework captures several desiderata for OPD: compatible teacher-student reasoning patterns, teacher competence, and induced student diversity. Theoretically, we categorize several types of teacher routing schemes, and we prove that under different scenarios, different routing schemes are likely to be beneficial for optimization and student diversity. We back up our findings with extensive experimental results in domains such as math, coding, kernel generation, and visual reasoning, where we find upwards of 10 percentage points of improvement on pass@$k$ when compared to vanilla OPD and the teacher experts on certain tasks, indicating both capability improvement and diversity over high-quality responses.

cs.LG↗

arXiv2026

How to Train Your Little Dragon: Teaching a Small Language Model to Construct and Refine GPU Optimization Scripts

Compiler transformations interact, making GPU kernel optimization a search for combinations that preserve the computation while improving performance. We introduce HOW TO TRAIN YOUR LITTLE DRAGON, a training method that teaches a small language model both to construct complete optimization scripts and to improve existing ones. Instead of ranking candidates or generating kernel code, our model generates optimization scripts. We devise a compact, lossless representation whose deterministic decoding reconstructs the exact compiler trace, preserving its transformation parameters and dependencies. We use a compiler framework TVM MetaSchedule to build training data on 54,116 distinct workloads, and construct 108,594 examples in two training sets: 60,236 teach the model to generate an optimized script from an unoptimized kernel, while 48,358 teach it to produce a better script given the kernel and a somewhat optimized script. Supervised fine-tuning teaches the model to construct and improve optimization scripts from these search-derived examples. We then add reinforcement learning with a shaped reward that combines correctness with measured performance, awarding a latency-based bonus only to numerically correct kernels. We apply this training method to a model with 8 billion parameters. After supervised fine-tuning and reinforcement learning, the model achieves per-attempt correctness of 91.27% for construction and 92.01% for refinement, while reinforcement learning produces faster kernels than supervised training on 88 of 102 construction tasks and 145 of 170 refinement prompts. With only 8B parameters, our LITTLE DRAGON achieves higher per-attempt correctness and better kernel performance than six frontier LLMs: GPT-6 Astra, Opus 5, Kimi-K3, and GLM-5.3 among them, each with hundreds of billions to trillions of parameters, for which task-specific training is unavailable or expensive.

cs.LG↗

arXiv2026

Optimizing Large Language Models with Chained LMOs

Muon has motivated a growing family of optimizers that compose multiple matrix normalizations, but these methods remain fragmented and lack a unified perspective. We introduce chained linear minimization oracles (chained LMOs), which cast these methods as compositions of LMOs. Despite their empirical success, many chains fall outside the standard LMO framework and can diverge on smooth convex objectives. To explain why composition can nevertheless help, we turn to linear associative memory and show that chaining can improve over Muon under anisotropic embeddings. Empirically, we propose TensorChain, a novel optimizer within the framework that stacks compatible weight matrices across different layers and normalizes the 3d tensor across its axes. In Qwen3 0.6B and 1.7B pretraining, TensorChain outperforms all chained baselines in average token efficiency, with average token savings of 9.6% over Muon at matched validation loss.

cs.LG↗

arXiv2026

Directional Alignment Mitigates Reward Hacking in Reinforcement Learning for Language Models

Reward hacking arises when a model improves a proxy reward by exploiting shortcuts rather than solving the intended task. We study this failure mode through the geometry of reinforcement learning updates in language models and argue that hacking emerges when optimization drifts away from a stable low-dimensional learning trajectory. We analyze this drift through dominant singular directions of parameter updates and show that reward-hacking runs exhibit substantially larger directional change than clean runs. Motivated by this observation, we introduce trusted-direction projection, which constrains gradients to remain within a clean reference subspace. Across reward-hacking experiments on mathematical reasoning, the proposed approach delays shortcut exploitation and better preserves task performance.

cs.LG↗

arXiv2025

MuonBP: Faster Muon via Block-Periodic Orthogonalization

Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Jordan, Jin, et al., 2024) combines gradient orthogonalization with first-order momentum and achieves significant improvement in data efficiency over Adam/AdamW (Loshchilov and Hutter, 2019) for language model training. However, when using model parallelism, gradient orthogonalization introduces additional overhead compared to coordinate-wise optimizers (such as AdamW) due to additional gather and scatter operations on gradient matrix shards from different devices. This additional communication can amount to a throughput hit of 5%-10% compared to Adam/AdamW. To remedy this, we propose Muon with Block-Periodic Orthogonalization (MuonBP), which applies orthogonalization independently to matrix shards on each device and periodically performs full orthogonalization to maintain training stability at scale. We show how to adjust the learning rate from the baseline to MuonBP and give convergence guarantees for this algorithm. Crucially, our theory dictates that we use two stepsizes: one for the blockwise orthogonalization steps, and one for the full orthogonalization steps. Our method is simple, requires minimal hyperparameter adjustments, and achieves competitive iteration complexity compared with baseline Muon while providing per-iteration throughput comparable to coordinate-wise methods such as AdamW. When training an 8B model with eight-way tensor parallelism and ZeRO optimizer state sharding, MuonBP achieves 8% throughput increase compared to Muon with no degradation in performance.

cs.LG↗

arXiv2025

MEL: Multi-level Ensemble Learning for Resource-Constrained Environments

AI inference at the edge is becoming increasingly common for low-latency services. However, edge environments are power- and resource-constrained, and susceptible to failures. Conventional failure resilience approaches, such as cloud failover or compressed backups, often compromise latency or accuracy, limiting their effectiveness for critical edge inference services. In this paper, we propose Multi-Level Ensemble Learning (MEL), a new framework for resilient edge inference that simultaneously trains multiple lightweight backup models capable of operating collaboratively, refining each other when multiple servers are available, and independently under failures while maintaining good accuracy. Specifically, we formulate our approach as a multi-objective optimization problem with a loss formulation that inherently encourages diversity among individual models to promote mutually refining representations, while ensuring each model maintains good standalone performance. Empirical evaluations across vision, language, and audio datasets show that MEL provides performance comparable to original architectures while also providing fault tolerance and deployment flexibility across edge platforms. Our results show that our ensemble model, sized at 40\% of the original model, achieves similar performance, while preserving 95.6\% of ensemble accuracy in the case of failures when trained using MEL.

cs.LG↗

arXiv2025

SPIRE: Conditional Personalization for Federated Diffusion Generative Models

Recent advances in diffusion models have revolutionized generative AI, but their sheer size makes on device personalization, and thus effective federated learning (FL), infeasible. We propose Shared Backbone Personal Identity Representation Embeddings (SPIRE), a framework that casts per client diffusion based generation as conditional generation in FL. SPIRE factorizes the network into (i) a high capacity global backbone that learns a population level score function and (ii) lightweight, learnable client embeddings that encode local data statistics. This separation enables parameter efficient finetuning that touches $\leq 0.01\%$ of weights. We provide the first theoretical bridge between conditional diffusion training and maximum likelihood estimation in Gaussian mixture models. For a two component mixture we prove that gradient descent on the DDPM with respect to mixing weights loss recovers the optimal mixing weights and enjoys dimension free error bounds. Our analysis also hints at how client embeddings act as biases that steer a shared score network toward personalized distributions. Empirically, SPIRE matches or surpasses strong baselines during collaborative pretraining, and vastly outperforms them when adapting to unseen clients, reducing Kernel Inception Distance while updating only hundreds of parameters. SPIRE further mitigates catastrophic forgetting and remains robust across finetuning learning rate and epoch choices.

cs.LG↗

arXiv2025

Stochastic Rounding for LLM Training: Theory and Practice

As the parameters of Large Language Models (LLMs) have scaled to hundreds of billions, the demand for efficient training methods -- balancing faster computation and reduced memory usage without sacrificing accuracy -- has become more critical than ever. In recent years, various mixed precision strategies, which involve different precision levels for optimization components, have been proposed to increase training speed with minimal accuracy degradation. However, these strategies often require manual adjustments and lack theoretical justification. In this work, we leverage stochastic rounding (SR) to address numerical errors of training with low-precision representation. We provide theoretical analyses of implicit regularization and convergence under the Adam optimizer when SR is utilized. With the insights from these analyses, we extend previous BF16 + SR strategy to be used in distributed settings, enhancing the stability and performance for large scale training. Empirical results from pre-training models with up to 6.7B parameters, for the first time, demonstrate that our BF16 with SR strategy outperforms (BF16, FP32) mixed precision strategies, achieving better validation perplexity, up to $1.54\times$ higher throughput, and $30\%$ less memory usage.

cs.LG↗

arXiv2025

ADEPT: Hierarchical Bayes Approach to Personalized Federated Unsupervised Learning

Statistical heterogeneity of clients' local data is an important characteristic in federated learning, motivating personalized algorithms tailored to the local data statistics. Though there has been a plethora of algorithms proposed for personalized supervised learning, discovering the structure of local data through personalized unsupervised learning is less explored. We initiate a systematic study of such personalized unsupervised learning by developing algorithms based on optimization criteria inspired by a hierarchical Bayesian statistical framework. We develop adaptive algorithms that discover the balance between using limited local data and collaborative information. We do this in the context of two unsupervised learning tasks: personalized dimensionality reduction and personalized diffusion models. We develop convergence analyses for our adaptive algorithms which illustrate the dependence on problem parameters (e.g., heterogeneity, local sample size). We also develop a theoretical framework for personalized diffusion models, which shows the benefits of collaboration even under heterogeneity. We finally evaluate our proposed algorithms using synthetic and real data, demonstrating the effective sample amplification for personalized tasks, induced through collaboration, despite data heterogeneity.

cs.LG↗

arXiv2024

MADA: Meta-Adaptive Optimizers through hyper-gradient Descent

Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce Meta-Adaptive Optimizers (MADA), a unified optimizer framework that can generalize several known optimizers and dynamically learn the most suitable one during training. The key idea in MADA is to parameterize the space of optimizers and dynamically search through it using hyper-gradient descent during training. We empirically compare MADA to other popular optimizers on vision and language tasks, and find that MADA consistently outperforms Adam and other popular optimizers, and is robust against sub-optimally tuned hyper-parameters. MADA achieves a greater validation performance improvement over Adam compared to other popular optimizers during GPT-2 training and fine-tuning. We also propose AVGrad, a modification of AMSGrad that replaces the maximum operator with averaging, which is more suitable for hyper-gradient optimization. Finally, we provide a convergence analysis to show that parameterized interpolations of optimizers can improve their error bounds (up to constants), hinting at an advantage for meta-optimizers.

cs.LG↗

arXiv2022

QuPeD: Quantized Personalization via Distillation with Applications to Federated Learning

Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with {\em diverse resources}. In this work, we introduce a \textit{quantized} and \textit{personalized} FL algorithm QuPeD that facilitates collective (personalized model compression) training via \textit{knowledge distillation} (KD) among clients who have access to heterogeneous data and resources. For personalization, we allow clients to learn \textit{compressed personalized models} with different quantization parameters and model dimensions/structures. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements for the compressed model (both in model dimension and precision), we formulate a compressed personalization framework by introducing knowledge distillation loss for local client objectives collaborating through a global model. We develop an alternating proximal gradient update for solving this compressed personalization problem, and analyze its convergence properties. Numerically, we validate that QuPeD outperforms competing personalized FL methods, FedAvg, and local training of clients in various heterogeneous settings.

cs.LG↗

arXiv2022

A Generative Framework for Personalized Learning and Estimation: Theory, Algorithms, and Privacy

A distinguishing characteristic of federated learning is that the (local) client data could have statistical heterogeneity. This heterogeneity has motivated the design of personalized learning, where individual (personalized) models are trained, through collaboration. There have been various personalization methods proposed in literature, with seemingly very different forms and methods ranging from use of a single global model for local regularization and model interpolation, to use of multiple global models for personalized clustering, etc. In this work, we begin with a generative framework that could potentially unify several different algorithms as well as suggest new algorithms. We apply our generative framework to personalized estimation, and connect it to the classical empirical Bayes' methodology. We develop private personalized estimation under this framework. We then use our generative framework for learning, which unifies several known personalized FL algorithms and also suggests new ones; we propose and study a new algorithm AdaPeD based on a Knowledge Distillation, which numerically outperforms several known algorithms. We also develop privacy for personalized learning methods with guarantees for user-level privacy and composition. We numerically evaluate the performance as well as the privacy for both the estimation and learning problems, demonstrating the advantages of our proposed methods.

cs.LG↗

arXiv2021

QuPeL: Quantized Personalization with Applications to Federated Learning

Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with {\em diverse resources}. In this work, we introduce a \textit{quantized} and \textit{personalized} FL algorithm QuPeL that facilitates collective training with heterogeneous clients while respecting resource diversity. For personalization, we allow clients to learn \textit{compressed personalized models} with different quantization parameters depending on their resources. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements of the quantized model (both in value and precision), we formulate a quantized personalization framework by introducing a penalty term for local client objectives against a globally trained model to encourage collaboration. We develop an alternating proximal gradient update for solving this quantized personalization problem, and we analyze its convergence properties. Numerically, we show that optimizing over the quantization levels increases the performance and we validate that QuPeL outperforms both FedAvg and local training of clients in a heterogeneous setting.

cs.LG↗