# SLAP: The Semantic Least Action Principle for Variational Video-Language Modeling

arXiv: https://arxiv.org/abs/2605.30750 · HTML: https://mlsanity.com/paper/2605.30750/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 86 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Video-LLaMA: An Instruction-tuned Audio-Visual Language Model for Video Understanding](https://mlsanity.com/paper/2306.02858/) (2023)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Frozen in Time: A Joint Video and Image Encoder for End-to-End Retrieval](https://mlsanity.com/paper/2104.00650/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [LLaVA-Video: Video Instruction Tuning With Synthetic Data](https://mlsanity.com/paper/2410.02713/) (2024)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Instant3D: Instant Text-to-3D Generation](https://mlsanity.com/paper/2311.08403/) (2023)
- [Multi-Modal Cross-Domain Alignment Network for Video Moment Retrieval](https://mlsanity.com/paper/2209.11572/) (2022)
- [You Can Ground Earlier than See: An Effective and Efficient Pipeline for Temporal Sentence Grounding in Compressed Videos](https://mlsanity.com/paper/2303.07863/) (2023)
- [Hierarchical Local-Global Transformer for Temporal Sentence Grounding](https://mlsanity.com/paper/2208.14882/) (2022)
- [Exploring Optical-Flow-Guided Motion and Detection-Based Appearance for Temporal Sentence Grounding](https://mlsanity.com/paper/2203.02966/) (2022)
- [Unbalanced Incomplete Multi-view Clustering via the Scheme of View Evolution: Weak Views are Meat; Strong Views do Eat](https://mlsanity.com/paper/2011.10254/) (2020)
- [ANIMC: A Soft Framework for Auto-weighted Noisy and Incomplete Multi-view Clustering](https://mlsanity.com/paper/2011.10331/) (2020)
- [STPrivacy: Spatio-Temporal Privacy-Preserving Action Recognition](https://mlsanity.com/paper/2301.03046/) (2023)
- [Self-supervised Geometric Features Discovery via Interpretable Attention for Vehicle Re-Identification and Beyond](https://mlsanity.com/paper/2010.09221/) (2020)

## Built on by (most cited first, 2 of 2)

- [Hierarchical Semantic-Augmented Navigation: Optimal Transport and Graph-Driven Reasoning for Vision-Language Navigation](https://mlsanity.com/paper/2606.01565/) (2026)
- [Turing Patterns for Multimedia: Reaction-Diffusion Multi-Modal Fusion for Language-Guided Video Moment Retrieval](https://mlsanity.com/paper/2606.01615/) (2026)

## Abstract (arXiv)

In the era of Large Video-Language Models (LVLMs), the computational necessity of sparse frame sampling creates a fundamental ``temporal gap'', rendering models blind to critical causal transitions. Existing solutions relying on generative hallucination (e.g., latent diffusion) or autoregressive extrapolation often fail to maintain semantic consistency over long horizons, suffering from object vanishing and energetic instability. We propose a paradigm shift from probabilistic generation to variational mechanics with the Semantic Least Action Principle (SLAP). Drawing a rigorous isomorphism between classical mechanics and semantic dynamics, we model the latent video trajectory as a path on a Riemannian manifold governed by a Semantic Lagrangian. By formulating the interpolation task as a Boundary Value Problem (BVP) solved via the discrete Euler-Lagrange equations, SLAP naturally enforces object persistence without pixel-level rendering. Extensive experiments show the effectiveness of our proposed SLAP.