The goal of this paper is to accelerate the training of machine learning models, a critical challenge since the training of large-scale deep neural models can be computationally expensive. Stochastic gradient descent (SGD) and its variants are widely used to train deep neural networks. In contrast to traditional approaches that focus on tuning the learning rate, we propose a novel adaptive batch size SGD algorithm, DiveBatch, that dynamically adjusts the batch size. Adapting the batch size is challenging: using large batch sizes is more efficient due to parallel computation, but small-batch training often converges in fewer epochs and generalizes better. To address this challenge, we introduce a data-driven adaptation based on gradient diversity, enabling DiveBatch to maintain the generalization performance of small-batch training while improving convergence speed and computational efficiency. Gradient diversity has a strong theoretical justification: it emerges from the convergence analysis of SGD. Evaluations of DiveBatch on synthetic and CiFar-10, CiFar-100, and Tiny-ImageNet demonstrate that DiveBatch converges significantly faster than standard SGD and AdaBatch (1.06 -- 5.0x), with a slight trade-off in performance.

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine learning models. To address these limitations, we develop a novel decentralized stochastic bilevel optimization algorithm for the nonconvex bilevel optimization problem under heavy-tailed noises. Specifically, we develop a normalized stochastic variance-reduced bilevel gradient descent algorithm, which does not rely on any clipping operation. Moreover, we establish its convergence rate by innovatively bounding interdependent gradient sequences under heavy-tailed noises for nonconvex decentralized bilevel optimization problems. As far as we know, this is the first decentralized bilevel optimization algorithm with rigorous theoretical guarantees under heavy-tailed noises. The extensive experimental results confirm the effectiveness of our algorithm in handling heavy-tailed noises.

Thermodynamic computing offers a potential route to energy-efficient computation. Unlike digital or quantum computing, which must at considerable energetic cost overpower or suppress thermal noise, thermodynamic computing is designed to use thermal noise as a source of energy. Physical devices whose states evolve under Langevin dynamics can be engineered to perform computations as they relax toward thermal equilibrium. Because these computations are carried out by the natural dynamics of the system, such devices can in principle operate with very low energy overhead, approaching fundamental thermodynamic limits [1-6]. A key challenge for thermodynamic computing is to identify algorithms that make efficient use of thermodynamic hardware and that reproduce the algebraic and machine-learning operations done digitally. Recent work has shown that thermodynamic computers can solve linear algebra problems, such as matrix inversion, in thermodynamic equilibrium [4, 5]. The advantage of equilibrium operation is that the computer's degrees of freedom obey the Boltzmann distribution, which depends in a precise way on the computer's potential energy. By choosing this potential energy appropriately, therefore, we can specify the desired computation.

Supervised fine-tuning (SFT) is a pivotal approach to adapting large language models (LLMs) for downstream tasks; however, performance often suffers from the ``seesaw phenomenon'', where indiscriminate parameter updates yield progress on certain tasks at the expense of others. To address this challenge, we propose a novel \emph{Core Parameter Isolation Fine-Tuning} (CPI-FT) framework. Specifically, we first independently fine-tune the LLM on each task to identify its core parameter regions by quantifying parameter update magnitudes. Tasks with similar core regions are then grouped based on region overlap, forming clusters for joint modeling. We further introduce a parameter fusion technique: for each task, core parameters from its individually fine-tuned model are directly transplanted into a unified backbone, while non-core parameters from different tasks are smoothly integrated via Spherical Linear Interpolation (SLERP), mitigating destructive interference. A lightweight, pipelined SFT training phase using mixed-task data is subsequently employed, while freezing core regions from prior tasks to prevent catastrophic forgetting. Extensive experiments on multiple public benchmarks demonstrate that our approach significantly alleviates task interference and forgetting, consistently outperforming vanilla multi-task and multi-stage fine-tuning baselines.

Momentum methods were originally introduced for their superiority to stochastic gradient descent (SGD) in deterministic settings with convex objective functions. However, despite their widespread application to deep neural networks -- a representative case of stochastic nonconvex optimization -- the theoretical justification for their effectiveness in such settings remains limited. Quasi-hyperbolic momentum (QHM) is an algorithm that generalizes various momentum methods and has been studied to better understand the class of momentum-based algorithms as a whole. In this paper, we provide both asymptotic and non-asymptotic convergence results for mini-batch QHM with an increasing batch size. We show that achieving asymptotic convergence requires either a decaying learning rate or an increasing batch size. Since a decaying learning rate adversely affects non-asymptotic convergence, we demonstrate that using mini-batch QHM with an increasing batch size -- without decaying the learning rate -- can be a more effective strategy. Our experiments show that even a finite increase in batch size can provide benefits for training neural networks. The code is available at https://anonymous.4open.science/r/qhm_public.

We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter tuning. The method comes from a theoretically-grounded adaptation of the Adaptive Gradient Descent Without Descent method to the stochastic setting. We prove the convergence of stochastic gradient descent with our step-size under various assumptions, and we show that it empirically competes against tuned baselines.

Wearable exoskeletons can augment human strength and reduce muscle fatigue during specific tasks. However, developing personalized and task-generalizable assistance algorithms remains a critical challenge. To address this, a meta-imitation learning approach is proposed. This approach leverages a task-specific neural network to predict human elbow joint movements, enabling effective assistance while enhancing generalization to new scenarios. To accelerate data collection, full-body keypoint motions are extracted from publicly available RGB video and motion-capture datasets across multiple tasks, and subsequently retargeted in simulation. Elbow flexion trajectories generated in simulation are then used to train the task-specific neural network within the model-agnostic meta-learning (MAML) framework, which allows the network to rapidly adapt to novel tasks and unseen users with only a few gradient updates. The adapted network outputs personalized references tracked by a gravity-compensated PD controller to ensure stable assistance. Experimental results demonstrate that the exoskeleton significantly reduces both muscle activation and metabolic cost for new users performing untrained tasks, compared to performing without exoskeleton assistance. These findings suggest that the proposed framework effectively improves task generalization and user adaptability for wearable exoskeleton systems.

The fairness-accuracy trade-off is a key challenge in NLP tasks. Current work focuses on finding a single "optimal" solution to balance the two objectives, which is limited considering the diverse solutions on the Pareto front. This work intends to provide controllable trade-offs according to the user's preference of the two objectives, which is defined as a reference vector. To achieve this goal, we apply multi-objective optimization (MOO), which can find solutions from various regions of the Pareto front. However, it is challenging to precisely control the trade-off due to the stochasticity of the training process and the high dimentional gradient vectors. Thus, we propose Controllable Pareto Trade-off (CPT) that can effectively train models to perform different trade-offs according to users' preferences. CPT 1) stabilizes the fairness update with a moving average of stochastic gradients to determine the update direction, and 2) prunes the gradients by only keeping the gradients of the critical parameters. We evaluate CPT on hate speech detection and occupation classification tasks. Experiments show that CPT can achieve a higher-quality set of solutions on the Pareto front than the baseline methods. It also exhibits better controllability and can precisely follow the human-defined reference vectors.

We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. The progress metric is the Pareto stationarity gap $\mathcal{G}(x)$ (the norm of an optimal convex combination of gradients). Our contributions are fourfold. (i) For strongly convex objectives, any span first-order method (iterates lie in the span of past gradients) exhibits linear convergence no faster than $\exp(-Θ(T/\sqrtκ))$ after $T$ oracle calls, where $κ$ is the condition number, implying $Θ(\sqrtκ\log(1/\varepsilon))$ iterations; this matches classical accelerated upper bounds. (ii) For convex problems and oblivious one-step methods (a fixed scalarization with pre-scheduled step sizes), we prove a lower bound of order $1/T$ on the best gradient norm among the first $T$ iterates. (iii) Although accelerated gradient descent is outside this restricted class, it is an oblivious span method and attains the same $1/T$ upper rate on a fixed scalarization. (iv) For convex problems and general span methods with adaptive scalarizations, we establish a universal lower bound of order $1/T^{2}$ on the gradient norm of the final iterate after $T$ steps, highlighting a gap between known upper bounds and worst-case guarantees. All bounds hold on non-degenerate instances with distinct objectives and non-singleton Pareto fronts; rates are stated up to universal constants and natural problem scaling.

This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the gradient descent iterate concentrates around a deterministic vector called the `Gaussian theoretical gradient descent', whose dynamics can be tracked by a state evolution system of two recursive equations for two scalars. Our concentration guarantees hold universally for a broad class of design matrices and remain valid over long time horizons until algorithmic convergence or divergence occurs. Moreover, our approach reveals that gradient descent iterates are in general approximately independent of the data and strongly incoherent with the feature vectors, a phenomenon previously known as the `implicit regularization' effect of gradient descent in specific models under Gaussian data. As an illustration of the utility of our general theory, we present two applications of different natures in the regression setting. In the first, we prove global convergence of nonconvex gradient descent with general independent initialization for a broad class of structured link functions, and establish universality of randomly initialized gradient descent in phase retrieval for large aspect ratios. In the second, we develop a data-free iterative algorithm for estimating state evolution parameters along the entire gradient descent trajectory, thereby providing a low-cost yet statistically valid tool for practical tasks such as hyperparameter tuning and runtime determination. As a by-product of our analysis, we show that in the large aspect ratio regime, the Gaussian theoretical gradient descent coincides with a recent line of dynamical mean-field theory for gradient descent over the constant-time horizon.