The choice of optimiser is important in deep learning, as it strongly influences model efficiency and speed of convergence. However, many commonly used optimisers encounter difficulties when applied to imbalanced and sequential datasets, limiting their ability to capture patterns of minority classes. In this study, we propose Dynamic Batch-Sensitive Adam (DBS-Adam), an optimiser that dynamically scales the learning rate using a batch difficulty score derived from exponential moving averages of gradient norms and batch loss. DBS-Adam improves training stability and accelerates convergence by increasing updates for difficult batches and reducing them for easier ones. We evaluate DBS-Adam by integrating it with Bi-Directional LSTM networks for accident injury severity prediction, addressing class imbalance through SMOTE-ENN resampling and Focal Loss. Four experimental configurations compare baseline Bi-LSTM models and alternative architectures to assess optimiser impact. Rigorous comparison against state-of-the-art optimisers (AMSGrad, AdamW, AdaBound) across five random seeds demonstrated DBS-Adam's competitive performance with statistically significant precision improvements (p=0.020). Results indicate that DBS-Adam outperforms standard optimisation approaches, achieving 95.22% test accuracy, 96.11% precision, 95.28% recall, 95.39% F1-score, and a test loss of 0.0086. The proposed framework enables effective real-time accident severity classification for targeted emergency response and road safety interventions, demonstrating the value of DBS-Adam for learning from imbalanced sequential data.
Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients, and second, it has an overshoot phenomenon. To address noisy gradients, Adam was proposed, which remains the most widely used adaptive optimizer. To address the overshoot phenomenon, a control-theory-based PID optimizer was proposed. To tackle both the limitations within a single framework, several variants of Adaptive PID (AdaPID) have recently been proposed. Although AdaPID performs well, it still inherits two critical drawbacks from Adam, namely convergence and stability issues. In this work, we address both these limitations. To fix the convergence issue, we uniquely integrate the idea of using a non-increasing effective learning rate into AdaPID (originally proposed in AMSGrad, an extension of Adam). To fix the stability issue, we innovatively integrate a gradient difference based modulation factor into AdaPID (originally proposed in DiffGrad, another extension of Adam). Combining both these ideas in AdaPID, results in our novel IAdaPID-ADG optimizer. We evaluate our proposed optimizer on multiple datasets, including benchmark datasets (MNIST and CIFAR10) and real-world datasets (IARC and AnnoCerv). The IAdaPID-ADG substantially outperforms all competing optimizers. Additionally, we perform an ablation study on the MNIST dataset to demonstrate the contribution of each added component.
Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an ADMM-Inspired Momentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem determines the acceleration form. Building on AIM, we propose Relativistic Adaptive gradient Descent with Accelerated Residual (RADAR), which combines relativistic adaptive geometry, decoupled residual correction, and second-order momentum filtering to improve the update direction and momentum estimation. We establish stochastic convergence through a variance-perturbed Lyapunov drift analysis. Experiments on supervised vision learning, language modeling, and reinforcement learning show that RADAR achieves consistent improvements over strong adaptive optimizer baselines.
Adaptive optimizers such as Adam and non-adaptive methods like SGD exhibit distinct generalization capabilities across different architectures. Prior tunable optimizers attempt to bridge this gap by strictly interpolating between SGD and Adam, effectively confining adaptivity within the 0-to-1 bound. However, this restricted interpolation is fundamentally insufficient: we reveal that optimal adaptivity often requires extrapolation, such as negative adaptivity for classical CNNs and adaptivity of at least one (γ≥1) for Transformers. Extrapolating adaptivity theoretically violates the strict non-decreasing pre-conditioner assumption, often leading to divergence in existing methods. To break this barrier, we propose Anon, an optimizer that achieves fully continuous adaptivity extrapolation across the entire real-number spectrum. To guarantee provable stability in these out-of-bound regimes, we introduce Incremental Delay Update (IDU), a novel mechanism that bypasses hard max-tracking strategies. We theoretically establish Anon's convergence in both convex and non-convex settings. Empirically, by exploring previously unreachable adaptivity landscapes, Anon demonstrates highly competitive and scalable performance among state-of-the-art element-wise optimizers on representative image classification, diffusion, and large language modeling tasks.