Memory-Efficient Training

Biosignals exhibit substantial cross-subject and cross-session variability, inducing severe domain shifts that degrade post-deployment performance for small, edge-oriented AI models. On-device adaptation is therefore essential to both preserve user privacy and ensure system reliability. However, existing sub-100 mW MCU-based wearable platforms can only support shallow or sparse adaptation schemes due to the prohibitive memory footprint and computational cost of full backpropagation (BP). In this paper, we propose BioTrain, a framework enabling full-network fine-tuning of state-of-the-art biosignal models under milliwatt-scale power and sub-megabyte memory constraints. We validate BioTrain using both offline and on-device benchmarks on EEG and EOG datasets, covering Day-1 new-subject calibration and longitudinal adaptation to signal drift. Experimental results show that full-network fine-tuning achieves accuracy improvements of up to 35% over non-adapted baselines and outperforms last-layer updates by approximately 7% during new-subject calibration. On the GAP9 MCU platform, BioTrain enables efficient on-device training throughput of 17 samples/s for EEG and 85 samples/s for EOG models within a power envelope below 50 mW. In addition, BioTrain's efficient memory allocator and network topology optimization enable the use of a large batch size, reducing peak memory usage. For fully on-chip BP on GAP9, BioTrain reduces the memory footprint by 8.1x, from 5.4 MB to 0.67 MB, compared to conventional full-network fine-tuning using batch normalization with batch size 8.

Asymmetric Tensor PCA (ATPCA) is a prototypical model for studying the trade-offs between sample complexity, computation, and memory. Existing algorithms for this problem typically require at least $d^{\left\lceil\overline{k}/2\right\rceil}$ state memory cost to recover the signal, where $d$ is the vector dimension and $\overline{k}$ is the tensor order. We focus on the setting where $\overline{k} \geq 4$ is even and consider (stochastic) gradient descent-based algorithms under a limited memory budget, which permits only mild over-parameterization of the model. We propose a matrix-parameterized method (in $d^{2}$ state memory cost) using a novel three-phase alternating-update algorithm to address the problem and demonstrate how mild over-parameterization facilitates learning in two key aspects: (i) it improves sample efficiency, allowing our method to achieve near-optimal $d^{\overline{k}-2}$ sample complexity in our limited memory setting; and (ii) it enhances adaptivity to problem structure, a previously unrecognized phenomenon, where the required sample size naturally decreases as consecutive vectors become more aligned, and in the symmetric limit attains $d^{\overline{k}/2}$, matching the best known polynomial-time complexity. To our knowledge, this is the first tractable algorithm for ATPCA with $d^{\overline{k}}$-independent memory costs.

Training large language models (LLMs) is constrained by memory requirements, with activations accounting for a substantial fraction of the total footprint. Existing approaches reduce memory using low-rank weight parameterizations or low-rank gradient subspaces for optimizer states, while activation memory is addressed through architectural modifications or compression schemes based on periodically updated projections. We propose OASIS, an online activation subspace learning algorithm for memory-efficient training that tracks and continuously updates a low-dimensional activation subspace during training. Intermediate activations are projected onto this evolving subspace, reducing memory without modifying forward-pass computations. The evolving activation subspace induces low-rank gradient representations, enabling both gradients and optimizer states to be maintained directly in this subspace, while a projection-aware optimizer consistently transports optimizer states across subspace updates for stable training. Across various finetuning and pretraining tasks, OASIS achieves up to $2\times$ lower peak memory than full fine-tuning while matching its performance and outperforming prior low-rank methods.

Continual learning (CL) on edge devices requires not only high accuracy but also training-time efficiency to support on-device adaptation under strict memory and computational constraints. While prompt-based continual learning (PCL) is parameter-efficient and achieves competitive accuracy, prior work has focused mainly on accuracy or inference-time performance, often overlooking the memory and computational costs of on-device training. In this paper, we propose CPS-Prompt, a critical patch-aware sparse prompting framework that explicitly targets training-time memory usage and computational cost by integrating critical patch sampling (CPS) for task-aware token reduction and decoupled prompt and classifier training (DPCT) to reduce backpropagation overhead. Experiments on three public benchmarks and real edge hardware show that CPS-Prompt improves peak memory, training time, and energy efficiency by about 1.6x over the balanced CODA-Prompt baseline, while maintaining accuracy within 2% of the state-of-the-art C-Prompt on average and remaining competitive with CODA-Prompt in accuracy. The code is available at https://github.com/laymond1/cps-prompt.

Quantization is an effective way to reduce the memory cost of large-scale model training. However, most existing methods adopt fixed-precision policies, which ignore the fact that optimizer-state distributions vary significantly across layers and training steps. Such uniform designs often introduce noticeable accuracy degradation. To move beyond fixed quantization, we propose STQuant, a distributed training framework that reduces the memory footprint of optimizer states via dynamic precision allocation across layers, state variables, and training steps, while maintaining model quality. Naively applying dynamic quantization during training is challenging for two reasons. First, optimizer states are numerically sensitive, and quantization noise can destabilize quality. Second, jointly considering multiple states and layers induces a large combinatorial search space. STQuant addresses these challenges with two key techniques: 1) a provably near-optimal factor selection strategy that accurately identifies the most influential factors for precision adaptation. 2) a dynamic transition decision algorithm that reduces the search cost from exponential to linear complexity. Experiments on GPT-2 and ViT show that STQuant reduces optimizer-state memory by 84.4%, achieving an average bit-width of as low as 5.1 bits, compared with existing solutions. Moreover, STQuant incurs only O(N/K) computational overhead and requires O(1) extra space.

We present MegaTrain, a memory-centric system that efficiently trains 100B+ parameter large language models at full precision on a single GPU. Unlike traditional GPU-centric systems, MegaTrain stores parameters and optimizer states in host memory (CPU memory) and treats GPUs as transient compute engines. For each layer, we stream parameters in and compute gradients out, minimizing persistent device state. To battle the CPU-GPU bandwidth bottleneck, we adopt two key optimizations. 1) We introduce a pipelined double-buffered execution engine that overlaps parameter prefetching, computation, and gradient offloading across multiple CUDA streams, enabling continuous GPU execution. 2) We replace persistent autograd graphs with stateless layer templates, binding weights dynamically as they stream in, eliminating persistent graph metadata while providing flexibility in scheduling. On a single H200 GPU with 1.5TB host memory, MegaTrain reliably trains models up to 120B parameters. It also achieves 1.84$\times$ the training throughput of DeepSpeed ZeRO-3 with CPU offloading when training 14B models. MegaTrain also enables 7B model training with 512k token context on a single GH200.

Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is essential. However, many uncertainty quantification (UQ) methods remain difficult to apply due to their substantial computational cost. Sampling-based Bayesian learning approaches, such as Bayesian neural networks (BNNs), are particularly expensive since drawing and evaluating multiple parameter samples rapidly exhausts memory and compute resources. These constraints have limited the accessibility and exploration of Bayesian techniques thus far. To address these challenges, we introduce sampling parallelism, a simple yet powerful parallelization strategy that targets the primary bottleneck of sampling-based Bayesian learning: the samples themselves. By distributing sample evaluations across multiple GPUs, our method reduces memory pressure and training time without requiring architectural changes or extensive hyperparameter tuning. We detail the methodology and evaluate its performance on a few example tasks and architectures, comparing against distributed data parallelism (DDP) as a baseline. We further demonstrate that sampling parallelism is complementary to existing strategies by implementing a hybrid approach that combines sample and data parallelism. Our experiments show near-perfect scaling when the sample number is scaled proportionally to the computational resources, confirming that sample evaluations parallelize cleanly. Although DDP achieves better raw speedups under scaling with constant workload, sampling parallelism has a notable advantage: by applying independent stochastic augmentations to the same batch on each GPU, it increases augmentation diversity and thus reduces the number of epochs required for convergence.

We introduce Fact-Hash, a novel parameter-encoding method for training on-device neural radiance fields. Neural Radiance Fields (NeRF) have proven pivotal in 3D representations, but their applications are limited due to large computational resources. On-device training can open large application fields, providing strength in communication limitations, privacy concerns, and fast adaptation to a frequently changing scene. However, challenges such as limited resources (GPU memory, storage, and power) impede their deployment. To handle this, we introduce Fact-Hash, a novel parameter-encoding merging Tensor Factorization and Hash-encoding techniques. This integration offers two benefits: the use of rich high-resolution features and the few-shot robustness. In Fact-Hash, we project 3D coordinates into multiple lower-dimensional forms (2D or 1D) before applying the hash function and then aggregate them into a single feature. Comparative evaluations against state-of-the-art methods demonstrate Fact-Hash's superior memory efficiency, preserving quality and rendering speed. Fact-Hash saves memory usage by over one-third while maintaining the PSNR values compared to previous encoding methods. The on-device experiment validates the superiority of Fact-Hash compared to alternative positional encoding methods in computational efficiency and energy consumption. These findings highlight Fact-Hash as a promising solution to improve feature grid representation, address memory constraints, and improve quality in various applications. Project page: https://facthash.github.io/

The scale of biological datasets now routinely exceeds system memory, making data access rather than model computation the primary bottleneck in training machine-learning models. This bottleneck is particularly acute in biology, where widely used community data formats must support heterogeneous metadata, sparse and dense assays, and downstream analysis within established computational ecosystems. Here we present annbatch, a mini-batch loader native to anndata that enables out-of-core training directly on disk-backed datasets. Across single-cell transcriptomics, microscopy and whole-genome sequencing benchmarks, annbatch increases loading throughput by up to an order of magnitude and shortens training from days to hours, while remaining fully compatible with the scverse ecosystem. Annbatch establishes a practical data-loading infrastructure for scalable biological AI, allowing increasingly large and diverse datasets to be used without abandoning standard biological data formats. Github: https://github.com/scverse/annbatch

The memory wall remains the primary bottleneck for training large language models on consumer hardware. We introduce Spectral Compact Training (SCT), a method that replaces dense weight matrices with permanent truncated SVD factors W = U diag(s) V^T, where the full dense matrix is never materialized during training or inference. Gradients flow through the compact spectral factors via standard backpropagation, and U, V are retracted to the Stiefel manifold via QR decomposition after each optimizer step. SCT achieves up to 199x memory reduction per MLP layer at rank 32, enabling full training steps of 70B-parameter architectures on a Steam Deck handheld (7.2 GB peak memory vs. 1,245 GB for dense FP32 training with Adam). Rank-sweep experiments on SmolLM2-1.7B (ranks 32-256, 2000 steps, NVIDIA A100) show that all tested ranks converge to the same loss floor (~4.2-4.5), identifying the learning rate schedule -- not MLP rank -- as the primary bottleneck. Rank 128 emerges as the efficiency sweet spot at 11.7x MLP compression with the lowest perplexity. GPU memory drops 46% at rank 32 while training throughput doubles.

Graph Neural Networks (GNNs) show strong promise for circuit analysis, but scaling to modern large-scale circuit graphs is limited by GPU memory and training cost, especially for deep models. We revisit deep GNNs for circuit graphs and show that, when trainable, they significantly outperform shallow architectures, motivating an efficient, domain-specific training framework. We propose Grouped-Sparse-Reversible GNN (GSR-GNN), which enables training GNNs with up to hundreds of layers while reducing both compute and memory overhead. GSR-GNN integrates reversible residual modules with a group-wise sparse nonlinear operator that compresses node embeddings without sacrificing task-relevant information, and employs an optimized execution pipeline to eliminate fragmented activation storage and reduce data movement. On sampled circuit graphs, GSR-GNN achieves up to 87.2% peak memory reduction and over 30$\times$ training speedup with negligible degradation in correlation-based quality metrics, making deep GNNs practical for large-scale EDA workloads.

The development of large-scale foundation models, particularly Large Language Models (LLMs), is constrained by significant computational and memory bottlenecks. These challenges elevate throughput optimization from a mere engineering task to a critical strategic lever, directly influencing training time, operational cost, and the feasible scale of next-generation models. This paper synthesizes evidence from recent academic and industry innovations to analyze key advancements in training efficiency. We examine architectural solutions to dataloader bottlenecks, such as the OVERLORD framework, which has demonstrated a 4.5% improvement in end-to-end training throughput. We investigate memory optimization techniques designed to overcome the GPU memory wall, including CPU offloading strategies like DeepSpeed's ZeRO-Offload, which enable the training of models far exceeding single-accelerator capacity. Furthermore, we explore the growing importance of compiler-centric optimizations, exemplified by Triton-distributed, which enables the joint optimization of computation, memory, and communication for substantial performance gains. The analysis is contextualized by advanced profiling tools and hardware characterization studies that identify and mitigate previously overlooked overheads like Dynamic Voltage and Frequency Scaling (DVFS). Findings indicate that a holistic, system-level approach, integrating innovations across data pipelines, memory management, network fabrics, and compiler technologies, is essential for accelerating AI development, managing costs, and pushing the boundaries of model scale.

Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively low-rank during training, we present an unbiased, memory-efficient, low-rank matrix estimator with the lowest variance that is applicable across common stochastic gradient estimation paradigms. The core idea is to project a high-dimensional stochastic gradient estimator onto a random low-dimensional subspace and lift it back, reducing memory while keeping the estimator unbiased and controlling mean-squared error via an optimally designed projection distribution, including Haar--Stiefel projections. The projection distribution is derived by solving a constrained functional optimization problem, yielding an optimal random projector that guides algorithm design. Empirically, the resulting low-rank gradient estimators deliver both practical memory savings and improved training behavior. In RoBERTa-large fine-tuning, our method attains the lowest peak GPU memory among compared methods (e.g., 3.83GB versus 16.7GB for full BP) while remaining competitive in accuracy; in autoregressive LLM pretraining (LLaMA-20M/60M/100M), our method outperforms the traditional methods, supporting the benefit of the proposed optimal projection strategy.

Quantizing optimizer states is becoming an important ingredient of memory-efficient large-scale pre-training, but the resulting optimizer dynamics remain only partially understood. We study low-precision exponential moving average (EMA) optimizer states and show how quantization can cause many nominal updates to round back to the same stored value, making the state effectively stale and slowing adaptation beyond what the nominal decay would suggest. We then develop a simple predictive model of stalling that estimates one-step stalling probabilities and characterizes how stalling builds up over time after the initialization. This perspective provides a mechanistic explanation for why optimizer-state resets help in low precision: once a quantized EMA becomes effectively stale, resetting it can temporarily restore responsiveness. Motivated by this picture, we derive a simple theory-guided method for choosing useful reset periods, showing that in low precision the key question is not only whether resets help, but when they should be applied. Experiments in controlled simulations and LLM pre-training show that suitable reset schedules recover the performance lost to low-precision state storage while substantially reducing optimizer-state memory.

While hardware-software co-design has significantly improved the efficiency of neural network inference, modeling the training phase remains a critical yet underexplored challenge. Training workloads impose distinct constraints, particularly regarding memory footprint and backpropagation complexity, which existing inference-focused tools fail to capture. This paper introduces MONET, a framework designed to model the training of neural networks on heterogeneous dataflow accelerators. MONET builds upon Stream, an experimentally verified framework that that models the inference of neural networks on heterogeneous dataflow accelerators with layer fusion. Using MONET, we explore the design space of ResNet-18 and a small GPT-2, demonstrating the framework's capability to model training workflows and find better hardware architectures. We then further examine problems that become more complex in neural network training due to the larger design space, such as determining the best layer-fusion configuration. Additionally, we use our framework to find interesting trade-offs in activation checkpointing, with the help of a genetic algorithm. Our findings highlight the importance of a holistic approach to hardware-software co-design for scalable and efficient deep learning deployment.

Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose Hybrid-Order Split Federated Learning (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.

Rehearsal-based continual learning (CL) mitigates catastrophic forgetting by maintaining a subset of samples from previous tasks for replay. Existing studies primarily focus on optimizing memory storage through coreset selection strategies. While these methods are effective, they typically require storing a substantial number of samples per class (SPC), often exceeding 20, to maintain satisfactory performance. In this work, we propose to further compress the memory footprint by synthesizing and storing prototypical exemplars, which can form representative prototypes when passed through the feature extractor. Owing to their representative nature, these exemplars enable the model to retain previous knowledge using only a small number of samples while preserving privacy. Moreover, we introduce a perturbation-based augmentation mechanism that generates synthetic variants of previous data during training, thereby enhancing CL performance. Extensive evaluations on widely used benchmark datasets and settings demonstrate that the proposed algorithm achieves superior performance compared to existing baselines, particularly in scenarios involving large-scale datasets and a high number of tasks.

Scaling Mixture-of-Experts (MoE) training introduces systems challenges absent in dense models. Because each token activates only a subset of experts, this sparsity allows total parameters to grow much faster than per-token computation, creating coupled constraints across memory, communication, and computation. Optimizing one dimension often shifts pressure to another, demanding co-design across the full system stack. We address these challenges for MoE training through integrated optimizations spanning memory (fine-grained recomputation, offloading, etc.), communication (optimized dispatchers, overlapping, etc.), and computation (Grouped GEMM, fusions, CUDA Graphs, etc.). The framework also provides Parallel Folding for flexible multi-dimensional parallelism, low-precision training support for FP8 and NVFP4, and efficient long-context training. On NVIDIA GB300 and GB200, it achieves 1,233/1,048 TFLOPS/GPU for DeepSeek-V3-685B and 974/919 TFLOPS/GPU for Qwen3-235B. As a performant, scalable, and production-ready open-source solution, it has been used across academia and industry for training MoE models ranging from billions to trillions of parameters on clusters scaling up to thousands of GPUs. This report explains how these techniques work, their trade-offs, and their interactions at the systems level, providing practical guidance for scaling MoE models with Megatron Core.

Memory-efficient optimization methods have recently gained increasing attention for scaling full-parameter training of large language models under the GPU-memory bottleneck. Existing approaches either lack clear convergence guarantees, or only achieve the standard ${\mathcal{O}}(ε^{-4})$ iteration complexity in the nonconvex settings. We propose Omni-Masked Gradient Descent (OMGD), an optimization method based on mask traversal for memory efficient training, and provide a nonconvex convergence analysis that establishes a strictly improved iteration complexity of $\tilde{\mathcal{O}}(ε^{-3})$ for finding an $ε$-approximate stationary point. Empirically, OMGD is a lightweight, plug-and-play approach that integrates seamlessly into most mainstream optimizers, yielding consistent improvements over competitive baselines in both fine-tuning and pre-training tasks.

The activation memory required for exact backpropagation scales linearly with network depth, context length, and feature dimensionality, forming an O(L * BN ) spatial bottleneck (where B is the sequence-batch cardinality and N is the feature dimension). This constraint historically throttles the scaling of deep neural networks. While randomized automatic differentiation attempts to mitigate this, it historically suffers from catastrophic variance. In this paper, we introduce BASIS (Balanced Activation Sketching with Invariant Scalars), an efficient backpropagation algorithm that fully decouples activation memory from the batch and sequence dimensions. BASIS propagates the exact error signal (dX) to preserve flawless gradient flow, but computes the weight updates (dW) using massively compressed rank-R tensors. To solve the foundational instability of sketched gradients, we propose two novel mechanisms: Balanced Hashing, which strictly eliminates off-diagonal collision variance, and Invariant Scalars, a principled bias-variance tradeoff that deterministically preserves the exact continuous energy norm of the spatial geometry. Theoretically, BASIS reduces activation memory to O(L * RN ) and heavily decreases the backward pass matrix-multiplication footprint. Empirically, training a GPT architecture for 50,000 steps validates our theoretical guarantees: at R = 32, BASIS achieves parity with (and marginally outperforms) exact backpropagation validation loss (6.575 vs. 6.616), acting as an implicit regularizer. Remarkably, the stabilized magnitude trajectory allows the model to converge smoothly even under extreme spatial compression (R = 1), proving the extreme robustness of the estimator. The code is available at https://github.com/VladimerKhasia/basis

Efficient and stable training of large language models (LLMs) remains a core challenge in modern machine learning systems. To address this challenge, Reparameterized Orthogonal Equivalence Training (POET), a spectrum-preserving framework that optimizes each weight matrix through orthogonal equivalence transformation, has been proposed. Although POET provides strong training stability, its original implementation incurs high memory consumption and computational overhead due to intensive matrix multiplications. To overcome these limitations, we introduce POET-X, a scalable and memory-efficient variant that performs orthogonal equivalence transformations with significantly reduced computational cost. POET-X maintains the generalization and stability benefits of POET while achieving substantial improvements in throughput and memory efficiency. In our experiments, POET-X enables the pretraining of billion-parameter LLMs on a single Nvidia H100 GPU, and in contrast, standard optimizers such as AdamW run out of memory under the same settings.

Modern optimizers like Adam and Muon are central to training large language models, but their reliance on first- and second-order momenta introduces significant memory overhead, which constrains scalability and computational efficiency. In this work, we reframe the exponential moving average (EMA) used in these momenta as the training of a linear regressor via online gradient flow. Building on this equivalence, we introduce LoRA-Pre, a novel low-rank optimizer designed for efficient pre-training. Specifically, LoRA-Pre reduces the optimizer's memory footprint by decomposing the full momentum matrix into a compact low-rank subspace within the online linear learner, thereby maintaining optimization performance while improving memory efficiency. We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family, scaling from 60M to 1B parameters. LoRA-Pre achieves the highest performance across all model sizes. Notably, LoRA-Pre demonstrates remarkable rank efficiency, achieving comparable or superior results using only 1/8 the rank of baseline methods. Beyond pre-training, we evaluate LoRA-Pre's effectiveness in fine-tuning scenarios. With the same rank, LoRA-Pre consistently outperforms all efficient fine-tuning baselines. Specifically, compared to standard LoRA, LoRA-Pre achieves substantial improvements of 3.14 points on Llama-3.1-8B and 6.17 points on Llama-2-7B, validating our approach's effectiveness across both pre-training and fine-tuning paradigms. Our code is publicly available at https://github.com/mrflogs/LoRA-Pre.

Resource-efficient training optimization techniques are becoming increasingly important as the size of large language models (LLMs) continues to grow. In particular, batch packing is commonly used in pre-training and supervised fine-tuning to achieve resource-efficient training. We propose preference packing, a method to enhance resource efficiency in training techniques that use data with different responses for the same input prompt, such as reward models or Direct Preference Optimization (DPO). Preference packing improves resource efficiency by reducing the attention operations for duplicate input prompts and decreasing KV cache memory usage. We conducted experiments on text-only datasets and image-included datasets and achieved at least 37% reduction in training time. Notably, this method can be applied alongside existing optimization techniques such as batch sorting, resulting in a 3.22x speedup.

Machine learning models deployed in real-world settings must operate under evolving data distributions and constrained computational resources. This challenge is particularly acute in non-stationary domains such as energy time series, weather monitoring, and environmental sensing. To remain effective, models must support adaptability, continuous learning, and long-term knowledge retention. This paper introduces a oblivious tree-based model with Hoeffding bound controlling its growth. It seamlessly integrates rapid learning and inference with efficient memory management and robust knowledge preservation, thus allowing for online learning. Extensive experiments across energy and environmental sensing time-series benchmarks demonstrate that the proposed framework achieves performance competitive with, and in several cases surpassing, existing online and batch learning methods, while maintaining superior computational efficiency. Collectively, these results demonstrate that the proposed approach fulfills the core objectives of adaptability, continual updating, and efficient retraining without full model retraining. The framework provides a scalable and resource-aware foundation for deployment in real-world non-stationary environments where resources are constrained and sustained adaptation is essential.

Standard mixed-precision training of neural networks requires many bytes of accelerator memory for each model parameter. These bytes reflect not just the parameter itself, but also its gradient and one or more optimizer state variables. With each of these values typically requiring 4 bytes, training even a 7 billion parameter model can be impractical for researchers with less than 100GB of accelerator memory. We introduce FlashOptim, a suite of optimizations that reduces per-parameter memory by over 50% while preserving model quality and API compatibility. Our approach introduces two key techniques. First, we improve master weight splitting by finding and exploiting a tight bound on its quantization error. Second, we design companding functions that greatly reduce the error in 8-bit optimizer state quantization. Together with 16-bit gradients, these techniques reduce AdamW memory from 16 bytes to 7 bytes per parameter, or 5 bytes with gradient release. They also cut model checkpoint sizes by more than half. Experiments with FlashOptim applied to SGD, AdamW, and Lion show no measurable quality degradation on any task from a collection of standard vision and language benchmarks, including Llama-3.1-8B finetuning.

Activations have become the primary memory bottleneck in large-batch LLM training. However, existing compression methods fail to exploit the spectral structure of activations, resulting in slow convergence or limited compression. To address this, we bridge the relationship between the algorithm's fast convergence and the requirements for subspace projection, and show that an effective compression should yield an unbiased estimate of the original activation with low variance. We propose Principal-Random Subspace for LLM Activation Compression (PRAC), which novelly decomposes activations into two components: a principal subspace captured via SVD to retain dominant information, and a random subspace sampled from the orthogonal complement to approximate the tail. By introducing a precise scaling factor, we prove that PRAC yields an unbiased gradient estimator with minimum variance under certain conditions. Extensive experiments on pre-training and fine-tuning tasks demonstrate that PRAC achieves up to 36% total memory reduction with negligible performance degradation and minimal computational cost.

We study efficiency as a first-class objective in Neural Combinatorial Optimization (NCO) and present ECO, an efficient learning framework that combines batched preference optimization with a Mamba backbone. Instead of tightly interleaving every policy update with on-policy rollouts, ECO decouples trajectory generation from gradient updates through two stages: supervised warm-up on pre-computed solutions and iterative Direct Preference Optimization (DPO) on batched candidate sets generated by the current policy. We pair this learning pipeline with a mixed Mamba encoder-decoder that reduces memory growth on long sequences and improves hardware utilization. A local-search-guided bootstrapping strategy is further used during training to widen preference margins and stabilize iterative improvement. Importantly, local search is only used to construct stronger preference pairs during training and is never invoked at inference time. On TSP and CVRP, ECO achieves the strongest overall performance among the compared neural baselines while also delivering clear advantages in memory usage and throughput. We provide additional analysis on memory scaling, throughput, and the contribution of each design component.

Deploying continual object detection on microcontrollers (MCUs) with under 100KB memory requires efficient feature compression that can adapt to evolving task distributions. Existing approaches rely on fixed compression strategies (e.g., FiLM conditioning) that cannot adapt to heterogeneous task characteristics, leading to suboptimal memory utilization and catastrophic forgetting. We introduce Adaptive Hierarchical Compression (AHC), a meta-learning framework featuring three key innovations: (1) true MAML-based compression that adapts via gradient descent to each new task in just 5 inner-loop steps, (2) hierarchical multi-scale compression with scale-aware ratios (8:1 for P3, 6.4:1 for P4, 4:1 for P5) matching FPN redundancy patterns, and (3) a dual-memory architecture combining short-term and long-term banks with importance-based consolidation under a hard 100KB budget. We provide formal theoretical guarantees bounding catastrophic forgetting as O(ε{sq.root(T)} + 1/{sq.root(M)}) where ε is compression error, T is task count, and M is memory size. Experiments on CORe50, TiROD, and PASCAL VOC benchmarks with three standard baselines (Fine-tuning,EWC, iCaRL) demonstrate that AHC enables practical continual detection within a 100KB replay budget, achieving competitive accuracy through mean-pooled compressed feature replay combined with EWC regularization and feature distillation.

In this work we introduce methods to reduce the computational and memory costs of training deep neural networks. Our approach consists in replacing exact vector-jacobian products by randomized, unbiased approximations thereof during backpropagation. We provide a theoretical analysis of the trade-off between the number of epochs needed to achieve a target precision and the cost reduction for each epoch. We then identify specific unbiased estimates of vector-jacobian products for which we establish desirable optimality properties of minimal variance under sparsity constraints. Finally we provide in-depth experiments on multi-layer perceptrons, BagNets and Visual Transfomers architectures. These validate our theoretical results, and confirm the potential of our proposed unbiased randomized backpropagation approach for reducing the cost of deep learning.

Fine-tuning large language models (LLMs) often exceeds GPU memory limits, prompting systems to offload model states to CPU memory. However, existing offloaded training frameworks like ZeRO-Offload treat all parameters equally and update the full model on the CPU, causing severe GPU stalls, where fast, expensive GPUs sit idle, waiting for slow CPU updates and limited-bandwidth PCIe transfers. We present ZenFlow, a new offloaded training framework that decouples updates between GPU and CPU by prioritizing important gradients. ZenFlow performs in-place updates of important gradients on GPU while offloading and accumulating less important ones on CPU without blocking training iterations, fully overlapping CPU work with GPU computation. To make this importance-aware design scalable, ZenFlow leverages a novel spatio-temporal locality of important gradients, concentrated in specific positions that remain stable across iterations, to make important gradient identification efficient and lightweight while preserving fidelity. Evaluation shows that ZenFlow achieves up to 5x end-to-end speedup, 2x lower PCIe traffic, 85% less GPU stalls, and up to 72% lower cloud GPU cost, all while preserving accuracy.