Zeroth-order (ZO) optimization estimates gradients using only forward-pass evaluations, making it suitable for fine-tuning non-differentiable, event-driven spiking neural networks (SNNs). However, its deployment on in-memory computing (IMC) accelerators is constrained by the repeated read-modify-write (RMW) operations arising from explicit weight perturbation and the prohibitive hardware footprint of random number generators (RNGs) for statistically independent per-weight perturbations. To address these challenges, we propose an implicit-perturbation ZO (IPZO) architecture in which perturbation sums computed by an event-triggered perturbation generation unit (PGU) are combined with the weighted sums produced by the IMC array, eliminating perturbation-induced RMW operations while preserving weight-stationary execution of IMC. By exploiting spike sparsity, the PGU generates and accumulates perturbation contributions only for spike-activated weight rows, reducing the required row dimension of the RNG array. An address-driven XOR recombination scheme (PGU-XOR) is further introduced to mitigate the spatial correlations caused by direct RNG reuse (PGU-Reuse). The results show that (1) PGU-XOR matches software RNGs in accuracy on Spikingformer/CIFAR-10 (76.41% vs. 76.53%) and perplexity (PPL) on SpikeGPT/WikiText-2 (54.20 vs. 53.23), whereas PGU-Reuse degrades accuracy by 9.56 percentage points and increases PPL by 11.8; (2) implemented in a TSMC 16-nm CMOS technology, PGU-XOR incurs 40.3%-46.0% area and 15.2%-48.9% energy overhead per matrix-vector multiplication relative to PGU-Reuse, yet its faster convergence reduces the total perturbation energy to 0.51x that of PGU-Reuse at iso-accuracy; (3) IPZO reduces the perturbation energy to 0.46x-0.83x that of conventional explicit weight perturbation for a batch size of B=64 and T=4 time steps, with the advantage growing as BT decreases.
Zeroth-order (ZO) optimization enables backpropagation-free fine-tuning of large language models, but existing ZO methods suffer from high-variance gradient estimators, making convergence unstable and highly sensitive to learning rates. We propose SubZero+, an improved SubZero framework that improves stability in three complementary ways: (i) multi-query gradient estimation within layer-specific low-rank subspaces to reduce variance without exhibiting the multi-query paradox; (ii) a subspace Adam optimizer that performs adaptive updates using in-subspace multi-query gradient statistics; and (iii) a sign correction for QR-based subspace construction to ensure Haar-distributed projection matrices, eliminating implementation-dependent orientation ambiguity. Experiments on models from 1.3B to 32B across SuperGLUE, under both full-parameter tuning and LoRA, show that SubZero+ consistently outperforms prior ZO baselines, enlarges the stable learning-rate range, and narrows the gap to first-order methods with minimal extra memory overhead.
Test-time adaptation (TTA) aims to enhance the cross-domain performance of pre-trained models by adapting to unlabeled test data. While most existing TTA methods rely on backpropagation (BP) for finetuning, BP-free methods such as zeroth-order (ZO) methods are more desired in practical on-device scenarios. ZO methods rely only on forward computation, which can largely reduce the complexity and memory overhead of on-device deployment. However, ZO methods suffer from much higher variance compared with first-order methods in estimating the gradient. To address this, we propose an improved ZO method to substantially boost the performance of ZO optimization based TTA. First, we provide an observation to reveal the persistent low-rank Hessian structure of the loss during the adaptation process. Based on this insight, we then propose a loss-landscape curvature-aware zeroth-order (CAZO) method, which leverages a sliding-average estimation of the diagonal Hessian to construct a covariance matrix for anisotropic perturbation sampling. CAZO operates by freezing pretrained weights and optimizing minimal adapter parameters via forward-only passes based gradient estimation, which can substantially reduce the memory overhead compared to BP-based methods. Extensive experiments demonstrate that CAZO significantly outperforms existing TTA methods, achieving state-of-the-art performance while maintaining an excellent balance between accuracy and memory efficiency. Code is available at https://github.com/Hollyming/CAZO.
Fine-tuning vision-language models such as CLIP typically requires backpropagation (BP) through the full model, which is infeasible when only forward-pass access is available, as is common for memory-constrained edge devices and proprietary model deployments. Prior BP-free, zeroth-order prompt-tuning methods avoid this requirement but often tune prompts in a single modality or optimize over a search space large enough that convergence requires thousands of forward passes, which is impractical under realistic query budgets. We propose ZOMP (Zeroth-Order Multimodal Prompt tuning), a query-efficient, fully forward-only method that tunes deep prompts in both the vision and text branches of a frozen CLIP model using simultaneous perturbation stochastic approximation. ZOMP combines three ingredients: a cross-modal low-rank reparameterization that ties the two branches through a shared factor and keeps the effective search dimensionality small, a gradient-correction momentum term that stabilizes the noisy zeroth-order estimate, and a budget-indexed rank schedule that unlocks capacity as the query budget is spent. Across 13 vision-language benchmarks under a matched 5,000-query budget, ZOMP consistently outperforms prior BP-free prompt-tuning methods in both few-shot accuracy and query efficiency, and it generalizes better across base-to-new, cross-dataset transfer, and out-of-distribution settings. Our results show that jointly exploiting multimodality and low-rank structure is an effective route to practical, query-efficient BP-free prompt tuning.
Differentially private zeroth-order optimization (DP-ZO) enables memory-efficient private fine-tuning of large language models using only forward evaluations. Existing aggregation-based DP-ZO methods reconstruct model updates at a fixed scale, ignoring that the strength of useful signals varies throughout training. Consequently, noise-dominated updates may receive excessive weight and degrade model utility. To address this issue, we propose SAGE, a noise-aware shrinkage method that adaptively attenuates privatized estimates according to their estimated signal quality. SAGE subtracts the known Gaussian noise variance from the observed second moment to estimate the underlying signal energy, stabilizes this estimate through temporal tracking, and compares its current signal-to-noise level with a warm-up reference to derive a bounded shrinkage factor. As pure post-processing, SAGE requires neither additional privacy budget nor model queries and introduces only constant additional state. Our theoretical analysis shows that shrinkage reduces the quadratic update-risk term faster than the linear descent term, preserving useful descent while limiting the influence of noise-dominated updates. Experiments on RoBERTa-large, OPT-1.3B, and OPT-6.7B demonstrate that SAGE outperforms existing baselines in most settings under the same privacy budgets while preserving the forward-only memory efficiency of DP-ZO.
While skill optimization for autonomous agents has gained traction, existing methods rely on complex pipelines. This leaves a fundamental question unaddressed: What constitutes a minimal viable pipeline for skill optimization, where every component is justified by theory or empirical necessity? We formalize skill optimization via Zeroth-Order (ZO) optimization, mapping classical counterparts (central difference, trust regions) to recent literature. Noting that unlike blind numerical perturbations in classical ZO, skill trajectories serve as interpretable debugging feedback. Grounded in Claude Code philosophy and PAC learning, we establish three principles for convergence and generalization: file-system-based trajectory exploration, consensus attribute mining, and independent validation gating. Eliminating redundancies, we propose SkillOpt-Lite. It accelerates convergence and outperforms full SkillOpt: improving LiveMath by +8.8 points on GPT-5.5 and +25.4 points on GPT-5.4-nano, allowing the nano model to surpass standard GPT-5.4 optimized by SkillOpt. Finally, we integrate our framework into production coding agents like VSCode Copilot, enabling developers to evolve agent skills via one line of vibe. Because our framework treats all agent components simply as standard editable code, this minimal pipeline naturally generalizes to full harness optimization (HarnessOpt). On SpreadsheetBench, HarnessOpt enables GPT-5.4-nano to achieve 0.7758 accuracy, outperforming the larger GPT-5.5 running standard pipelines (0.7620). Code is available at https://github.com/EvolvingLMMs-Lab/SkillOpt-Lite.
Fine-tuning large language models (LLMs) has become a central application of modern optimization, enabling pretrained models to adapt to diverse downstream tasks and domain-specific data. A major obstacle in large-scale fine-tuning is the memory overhead of backpropagation, which requires storing activations, gradients, and optimizer states. Zeroth-order (ZO) optimization offers a memory-efficient alternative, but its performance is highly sensitive to the stepsize and smoothing parameter, often requiring costly task-specific tuning. Parameter-free (PF) optimization addresses this issue by adapting algorithmic parameters without prior knowledge of problem-dependent constants. Moreover, large-scale fine-tuning can benefit from geometry-aware updates that account for the heterogeneous structure of parameter blocks, which can be modeled through methods that exploit linear minimization oracle (LMO). In this work, we study PF adaptation for LMO-based ZO optimization and introduce $\texttt{AdaNAGED}$, a method that unifies gradient-free training, adaptive tuning, and non-Euclidean update geometry. We establish convergence guarantees and validate the method on large-scale LLM fine-tuning task with $\texttt{OPT}-1.3\mathrm{B}$ model.
Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation. We propose GRZO, a Group-Relative Zeroth-Order optimizer that draws one pseudo-independent perturbation per mini-batch example and aggregates the per-example losses through group-relative normalization, raising the effective gradient-direction count from one to the batch size at no additional forward cost while preserving inference-level memory. We prove that GRZO is directionally unbiased with variance shrinking proportionally to the batch size, yielding a tighter nonconvex convergence bound than MeZO. Across RoBERTa-large, Llama3-8B, and OPT-13B over multiple tasks, GRZO improves average accuracy on Llama3-8B by $+3.0$ over MeZO at $23\%$ lower peak GPU memory; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by $+6.0$ on average.
Amir Ali Farzin, Philipp Braun, Iman Shamesmath.OC cs.LG eess.SY math.NA
While it is generally understood that zeroth-order (ZO) algorithms have an extra dependency on their number of iterations for any choice of parameters, compared to their first-order (FO) counterparts, in this work, we show that under several conditions, in expectation, ZO methods do not suffer from extra dimension dependencies in their convergence rates with respect to their FO counterparts. We look at optimisation algorithms from the dynamical systems perspective and analyse the conditions under which one can formulate the average of a ZO algorithm as the average of its FO counterpart with bounded perturbations with values dependent on design parameters. Then, using input-to-state stability properties, we show ZO methods follow the same decay rate as their FO counterparts and converge to a neighbourhood of the fixed point of FO methods, where its radius depends on the bound of the norm of the perturbations, which can be made arbitrarily small. The theoretical findings are illustrated via numerical examples.