StyleGAN-V: A Continuous Video Generator with the Price, Image Quality and Perks of StyleGAN2 (2112.14683v4)

Abstract: Videos show continuous events, yet most $-$ if not all $-$ video synthesis frameworks treat them discretely in time. In this work, we think of videos of what they should be $-$ time-continuous signals, and extend the paradigm of neural representations to build a continuous-time video generator. For this, we first design continuous motion representations through the lens of positional embeddings. Then, we explore the question of training on very sparse videos and demonstrate that a good generator can be learned by using as few as 2 frames per clip. After that, we rethink the traditional image + video discriminators pair and design a holistic discriminator that aggregates temporal information by simply concatenating frames' features. This decreases the training cost and provides richer learning signal to the generator, making it possible to train directly on 1024$^2$ videos for the first time. We build our model on top of StyleGAN2 and it is just ${\approx}5\%$ more expensive to train at the same resolution while achieving almost the same image quality. Moreover, our latent space features similar properties, enabling spatial manipulations that our method can propagate in time. We can generate arbitrarily long videos at arbitrary high frame rate, while prior work struggles to generate even 64 frames at a fixed rate. Our model is tested on four modern 256$^2$ and one 1024$^2$-resolution video synthesis benchmarks. In terms of sheer metrics, it performs on average ${\approx}30\%$ better than the closest runner-up. Project website: https://universome.github.io.

Analysis of Temporal Vector Transformations in Computation

The paper in question presents a paper focused on the mathematical representation and transformation of variables over time, illustrating the evolution of certain temporal vectors. It delineates the progressive stages of these transformations through symbolic representations, characterized by the progression from $t^{'}$ to $t^{''}$ and ultimately $t^{'''}$. This sequential portrayal underscores a potentially iterative or dynamic process that is mathematically modeled for analysis within computational contexts.

The authors introduce vectors $\bm{v}_{t^{'}}$, $\bm{v}_{t^{''}}$, and $\bm{v}_{t^{'''}}$, signifying variance or alteration in states across these temporal markers. Following a similar progression, vectors $\bm{x}_{t^{'}}$, $\bm{x}_{t^{''}}$, and $\bm{x}_{t^{'''}}$ are also defined, likely reflecting spatial or state-related attributes evolving through time. This dual vectorial approach may indicate a dual perspective on state evolutions, capturing both inherent changes (perhaps in velocity or momentum) and externally influenced transformations (potentially in position or configuration).

The primary implication of this paper lies in its potential applicability across domains requiring precise mathematical articulation of dynamic systems. It could be particularly salient in fields such as physics-based simulations, real-time system modeling, or AI systems that necessitate keeping track of evolving states or conditions over time. The specific delineation of the vector progression has profound implications for how such systems are calibrated, measured, or predicted.

Of particular interest would be the numerical significance attached to these vector transformations. The marked transitions from $t^{'}$ to $t^{'''}$ suggest not just mathematical abstraction but also indicate a measure of the system's evolution, which could be interpreted as a model for quantitative analysis and calibration in temporal datasets.

Theoretical exploration might delve into the broader mathematical underpinnings of this paradigm, examining the robustness of these vector transformations under various conditions or constraints. Practically, this framework could be applied to system optimization tasks, temporal analysis in datasets, or enhancing predictive model accuracy with respect to time.

Future investigations might involve the exploration of these transformations in multi-dimensional spaces or their extension to stochastic or non-linear dynamics. Examining the scalability of these principles within machine learning algorithms or real-time feedback systems could also yield significant contributions to computational science.

Thus, this paper contributes foundational insights into the temporal transformation of vectors, offering a springboard for further academic inquiry and potential technological advancement.