Scale appears to be the winning recipe in today's leaderboards. And yet, extreme-scale neural models are still brittle and make errors that are nonsensical or even counterintuitive. In this talk, I will discuss how smaller models developed in academia can still have an edge over larger industry-scale models, if powered with grounding and searching. First, I will present MERLOT (and RESERVE) that can learn neural script knowledge from complex multimodal data and achieve new SOTA over a dozen multimodal benchmarks. Next, I will discuss NeuralLogic (and NeuralLogic A*) search algorithms that can integrate logic constraints to language model decoding so that smaller unsupervised models can win over larger supervised models for various constrained generation tasks.