The first two permit using subgradients andstochastic gradients, andareshowntoensureaO(1/ t) convergencerate.

Fine-tuning pre-trained language models for downstream tasks has achieved impressive results in NLP. However, fine-tuning all parameters becomes impractical due to the rapidly increasing size of model parameters. To address this, Parameter Efficient Fine-Tuning (PEFT) methods update only a subset of parameters. Most PEFT methods, such as LoRA, use incremental updates, which involve adding learned weight matrix increments to the original parameters. Although effective, these methods face limitations in capturing complex parameter dynamics and do not maintain a strong correlation between the original and updated parameters. To overcome these challenges, we propose the direct Updated Transformation (UT) paradigm, which constructs a transformation directly from the original to the updated parameters. This approach ensures that the correlation between the original and updated parameters is preserved, leveraging the semantic features learned during pre-training. Building on this paradigm, we present the Hadamard Updated Transformation (HUT) method. HUT efficiently updates the original weight matrix using the Hadamard transformation with two low-rank matrices, offering a more expressive and flexible update mechanism. This allows HUT to capture richer parameter features through functional transformations, reducing computational complexity while maintaining or improving model quality. Theoretical analysis and extensive experiments on RoBERTa and GPT-2 validate the effectiveness of HUT. Results show that HUT performs on par with or better than other PEFT methods in terms of model quality, while significantly reducing computational complexity.

It's hard to love a swamp. Mountains have majesty, deserts have mystery, but what do wetlands have? I imagine some Joe on the street would boil it down to something like "muck, malaria, and mosquitoes." Even so, Famia Mercius, an antiquarian who's a great admirer of the Elder Scrolls series' lizard-like Argonians, is trying to get me to love the surrounding marsh as she does. She slaps a gnat off her neck while in the middle of a giddy introduction, and her stone house suggests she retains some reservations about living like the locals.

In this system data, information or knowledge which is more'uncertain' or more difficult to obtain should attract the highest ENT value as its information content is highest. On the other hand, data which is commonplace, known or easily obtainable has a lower information content and hence less ENT value.

The story of how the Colossus computer at Bletchley Park aided the allied code-cracking effort during World War II is becoming well known. Its claim to be a forerunner of modern-day computers is also well established. What is much less well known is the tale of how Colossus's story came to be told in the first place. It is a tale of how one man's dogged efforts overcame official secrets and official indifference to rewrite computer history. Computer scientist Brian Randell was the man who started uncovering the history of Colossus.