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Experimenting with hypersurface-constrained dynamic weight updating [P]

Our take

Explore a novel approach to reducing the computational burden of large language models with "Experimenting with hypersurface-constrained dynamic weight updating [P]." This project investigates a looped architecture, inspired by the Universal Transformer, where a single decoder block iteratively processes input while dynamically updating its weights via learned hypersurfaces. Initial results demonstrate a significant reduction in parameter count—approximately 16% of a baseline model—while achieving performance gains over unrolled baselines. See "The KV Cache Tax" for further insights into memory optimization in LLMs.
Experimenting with hypersurface-constrained dynamic weight updating [P]

The ongoing quest for efficient language models continues to yield fascinating experimentation, as evidenced by this recent Reddit post detailing a novel approach to parameter reduction. The core concept—dynamically updating weights within a looped decoder block using learned hypersurfaces—represents a thoughtful departure from traditional architectures. This work builds upon the Universal Transformer concept, aiming to minimize VRAM usage, a significant bottleneck in training. It’s particularly relevant given the rising demands of larger models and the need for accessible experimentation, a point previously highlighted in "What’s So Good About ChatGPT Work? Here’s What I Found" [What’s So Good About ChatGPT Work? Here’s What I Found], where the underlying models' efficacy was examined, and the challenges of resource limitations were discussed. The exploration of hypersurface representations, particularly with triangular wave functions, offers a compelling alternative to simply scaling up model size, a strategy that increasingly strains hardware resources.

The author’s methodical approach, including a clear description of the experimental setup, baselines, and results, strengthens the value of this contribution. The comparative training loss data, showing the "Triangular Surface + Context" model outperforming the unrolled baseline while drastically reducing parameter count, is particularly encouraging. This aligns with broader trends in the field focused on architectural innovation to improve efficiency, as explored in "The KV Cache Tax: Why Inference Servers Run Out of Memory Before Compute" [The KV Cache Tax: Why Inference Servers Run Out of Memory Before Compute], which details the memory challenges inherent in large language model inference and presents optimization strategies. The author’s candid acknowledgment of the need for further experimentation—particularly regarding the size of the triangular wave function set, context vector, and initialization strategies—demonstrates a commitment to rigorous investigation, and the planned expansion to the full FineWeb-Edu dataset is a logical next step. While the author rightly notes that the approach isn’t yet intended to surpass full-parameter models, the demonstrated gains in efficiency while maintaining reasonable performance are significant.

The significance of this work lies in its potential to democratize access to language model development. The ability to achieve comparable performance with significantly fewer parameters opens doors for researchers and practitioners with limited hardware resources. It also suggests a potential pathway toward more sustainable AI development, reducing the environmental impact associated with training massive models. The use of Gated Linear Attention to modulate the hypersurface geometry based on the input sequence adds a layer of sophistication, allowing the model to adapt its weight updates dynamically. This sequence-awareness is a crucial factor in achieving good performance, and the author’s exploration of different initialization strategies suggests a deep understanding of the complexities involved in training such architectures. Furthermore, the choice of using a pre-trained, frozen embedding layer from GPT-2 is a clever optimization, allowing the experiment to focus on the novel hypersurface-based weight update mechanism.

Looking ahead, it will be crucial to see how this approach scales with larger datasets and more complex tasks. The author’s observation about the potentially different convergence dynamics of hypersurface representations is a key point to consider. The ongoing exploration of functional basis size and context vector dimensions will undoubtedly shape the trajectory of this research. Could this represent a foundational step towards a new paradigm in language model design—one that prioritizes efficiency and adaptability over sheer size? As discussed in "Article: Your Next DSL Author Is a Language Model" [Article: Your Next DSL Author Is a Language Model], the ability to create specialized models tailored to specific domains holds immense potential, and this parameter-efficient architecture could be a key enabler of that vision. The question remains: how far can this approach be pushed, and will it ultimately offer a viable alternative to the relentless pursuit of ever-larger models?

Experimenting with hypersurface-constrained dynamic weight updating [P]

Hey everyone!

I want to share the results of a small language model architecture experiment I’ve been running as a side project. The ultimate goal is to test an approach to reduce the number of the model's training parameters, since the main bottleneck in training is VRAM.

The core idea is very similar to Universal Transformer. Let's take just a single decoder block and iteratively pass the input through it L times in a loop. But instead of updating the input with the loop iteration depth information, my model dynamically updates the weights of the base layer.

How is it implemented?

The model uses a set of learned hypersurfaces to generate weight deltas (𝛥Wl) from the hypersurfaces' cross-sections. So a given weight matrix at layer l is constructed as Wl = W0 + 𝛥Wl.

The hypersurfaces are defined by a series of periodic functions. The best results I've got so far are from using a triangular wave. The model learns the amplitudes, frequencies, and phases of these waves across the coordinate dimensions. Given the size of this set E this gives a total of 3*E*dim parameters.

Initially, I tried generating the full weights purely from hypersurfaces, but it was too restrictive and failed to converge. Thus, I moved to my current approach where the model has a base decoder layer that is being updated.

I also added a state vector that is calculated from the input sequence using Gated Linear Attention. It is used to modulate the hypersurface geometry during the forward pass, making the generated weight deltas 𝛥Wl sequence-aware.

Pre-training results

I ran the pre-training experiments on a 10B-token sample from the FineWeb-Edu dataset. I wanted to keep the training parameter count minimal, so I used a pre-trained, frozen embedding layer from GPT-2. I also do not use any positional encoding, following the NoPE approach. The sequence length was 1024 tokens, the batch size was 16, and I ran the training for 10,000 steps.

I used 3 baselines:

  • A simple 1-layer decoder-only transformer
  • A single-layer transformer unrolled across 24 loop iterations
  • A standard 24-layer decoder-only transformer

The experimental models:

  • A single loop block using sinusoidal surface deltas, no context modulation
  • A single loop block using triangular wave surface deltas with context modulation
  • A model that uses three stacked loop blocks, each utilizing triangular wave surface deltas and context modulation

Here's a training loss chart:

Training results

Model parameter count

A standard 24-layer decoder-only transformer: 169,906,944

3 loop blocks + triangular wave + context modulation: 27,162,624 (~16% of the baseline model's size)

Key Takeaways:

While the classic decoder-only architecture still produces the best absolute loss, the Triangular Surface + Context model shows a real performance boost over a standard unrolled baseline.

This model introduces a whole new set of parameters and hyperparameters. I am currently experimenting with the size of the triangular wave function set and the size of the context vector. I am also trying different initialization strategies for the hypersurface parameters. The (very vague) goal isn't necessarily to beat a full-parameter model, but to find a configuration that is "good enough" in terms of loss while remaining drastically lighter on hardware resources.

Another possibility is that hypersurface representations have different convergence dynamics and require more steps and more tokens to converge. So my next step is to train a model with 3 loop blocks and a larger context vector, and an expanded functional basis on the whole 10B-token sample from the FineWeb-Edu dataset.

GitHub repo: https://github.com/morgengramlich/LoopSLM

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