Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict satisfaction of differential-algebraic equations (DAEs) to embed domain knowledge and first-principles in data-driven models is generally challenging. This is because data-driven models consider the original functions to be black-box whose derivatives can only be obtained after evaluating the functions. We introduce DAE-HardNet, a physics-constrained (rather than simply physics-informed) neural network that learns both the functions and their derivatives simultaneously, while enforcing algebraic as well as differential constraints. This is done by projecting model predictions onto the constraint manifold using a differentiable projection layer. We apply DAE-HardNet to several systems and test problems governed by DAEs, including the dynamic Lotka-Volterra predator-prey system and transient heat conduction. We also show the ability of DAE-HardNet to estimate unknown parameters through a parameter estimation problem. Compared to multilayer perceptrons (MLPs) and PINNs, DAE-HardNet achieves orders of magnitude reduction in the physics loss while maintaining the prediction accuracy. It has the added benefits of learning the derivatives which improves the constrained learning of the backbone neural network prior to the projection layer. For specific problems, this suggests that the projection layer can be bypassed for faster inference. The current implementation and codes are available at https://github.com/SOULS-TAMU/DAE-HardNet.

Vision-Language Models (VLMs) excel at reasoning in linguistic space but struggle with perceptual understanding that requires dense visual perception, e.g., spatial reasoning and geometric awareness. This limitation stems from the fact that current VLMs have limited mechanisms to capture dense visual information across spatial dimensions. We introduce Chain-of-Visual-Thought (COVT), a framework that enables VLMs to reason not only in words but also through continuous visual tokens-compact latent representations that encode rich perceptual cues. Within a small budget of roughly 20 tokens, COVT distills knowledge from lightweight vision experts, capturing complementary properties such as 2D appearance, 3D geometry, spatial layout, and edge structure. During training, the VLM with COVT autoregressively predicts these visual tokens to reconstruct dense supervision signals (e.g., depth, segmentation, edges, and DINO features). At inference, the model reasons directly in the continuous visual token space, preserving efficiency while optionally decoding dense predictions for interpretability. Evaluated across more than ten diverse perception benchmarks, including CV-Bench, MMVP, RealWorldQA, MMStar, WorldMedQA, and HRBench, integrating COVT into strong VLMs such as Qwen2.5-VL and LLaVA consistently improves performance by 3% to 16% and demonstrates that compact continuous visual thinking enables more precise, grounded, and interpretable multimodal intelligence.

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems are dissipative and ergodic, motivating data-driven models that aim to learn invariant statistical properties over long time horizons. While recent models have shown empirical success in preserving invariant statistics, they are prone to generating unbounded predictions, which prevent meaningful statistics evaluation. To overcome this, we introduce the Energy-Constrained Operator (ECO) that simultaneously learns the system dynamics while enforcing boundedness in predictions. We leverage concepts from control theory to develop algebraic conditions based on a learnable energy function, ensuring the learned dynamics is dissipative. ECO enforces these algebraic conditions through an efficient closed-form quadratic projection layer, which provides provable trajectory boundedness. To our knowledge, this is the first work establishing such formal guarantees for data-driven chaotic dynamics models. Additionally, the learned invariant level set provides an outer estimate for the strange attractor, a complex structure that is computationally intractable to characterize. We demonstrate empirical success in ECO's ability to generate stable long-horizon forecasts, capturing invariant statistics on systems governed by chaotic PDEs, including the Kuramoto--Sivashinsky and the Navier--Stokes equations.

Part of this work was carried out while the author was at CSIRO's Data61.

Most existing CL techniques usually encourage learning such feature embeddings in the high-dimensional space to maximize the instance discrimination.

We demonstrate the effectiveness of our method for model training in two domains - image classification, and automatic speech recognition.

Vision-Language-Action (VLA) models often fail to generalize to novel camera viewpoints, a limitation stemming from their difficulty in inferring robust 3D geometry from 2D images. We introduce GeoAware-VLA, a simple yet effective approach that enhances viewpoint invariance by integrating strong geometric priors into the vision backbone. Instead of training a visual encoder or relying on explicit 3D data, we leverage a frozen, pretrained geometric vision model as a feature extractor. A trainable projection layer then adapts these geometrically-rich features for the policy decoder, relieving it of the burden of learning 3D consistency from scratch. Through extensive evaluations on LIBERO benchmark subsets, we show GeoAware-VLA achieves substantial improvements in zero-shot generalization to novel camera poses, boosting success rates by over 2x in simulation. Crucially, these benefits translate to the physical world; our model shows a significant performance gain on a real robot, especially when evaluated from unseen camera angles. Our approach proves effective across both continuous and discrete action spaces, highlighting that robust geometric grounding is a key component for creating more generalizable robotic agents.

As the large language models (LLMs) grow in size each day, efficient training and fine-tuning has never been as important as nowadays. This resulted in the great interest in parameter efficient fine-tuning (PEFT), and effective methods including low-rank adapters (LoRA) has emerged. Although the various PEFT methods have been studied extensively in the recent years, the greater part of the subject remains unexplored with the huge degree of freedom. In this paper, we propose FLoRA, a family of fused forward-backward adapters (FFBA) for parameter-efficient fine-tuning of LLMs on downstream tasks. The FFBA combine ideas from the popular LoRA and parallel adapters to improve the overall fine-tuning accuracies. At the same time, latencies are minimized by fusing the forward and backward adapters into existing projection layers of the base model. Experimental results show that the proposed FFB adapters perform significantly better than the popularly used LoRA in both accuracy and latency for a similar parameter budget.