LFM2-350M-Math-Cascadia-ternary3

ZTFlynn/LFM2-350M-Math-Cascadia-ternary3

LiquidAI/LFM2-350M-Math compressed to 241 MB with Cascadia — a spline manifold plus per-band lookup tables at 0.675 bytes per weight — and executable on CPU by a C runtime whose entire dependency list is libc, libm and libgomp.

Quality

Running it

Measured on a Jetson AGX Thor: CPU is 12 threads of a 14-core Arm part, GPU is the integrated Blackwell. Decode is the median of five runs; prefill is from a 162-token prompt. Both backends produce byte-identical output.

Load takes 0.51 s on CPU and 0.29 s on GPU, the latter including the host-to-device upload.

16,352 paired tokens of FineWeb-Edu in 31 independent 512-token windows. Both models score identical tokens and are compared per token, which cuts the standard error 2.9x versus two independent means.

The window is the unit of inference, not the token: tokens inside one window share a context, and counting them as independent samples inflates the t-statistic several-fold. Resolving a difference of a few percent takes hundreds of windows.

A measured cost: 2.96x compression for 13.4% higher perplexity on this corpus.

The corpus is general web text (FineWeb-Edu). How much a given model is affected depends on its own sensitivity and on how close that text is to its domain, so this figure is specific to both. Two models in this family compressed to the same 0.055 reconstruction error measured +13.4% and −2.4% here. The fidelity figure below describes the compression itself and does not vary that way.

Reconstruction fidelity

Perplexity measures how good a model is on a corpus, not how faithful a copy is, and the two disagree here: models compressed to identical reconstruction error differ by 16 percentage points of measured perplexity. Fidelity has no sampling uncertainty and no dependence on corpus domain, so it is measured directly and reported alongside.

By tensor class:

The tied embedding, the tensor whose error reaches the logits undamped, reconstructs at 0.0261.

Where the compression cost comes from

The cost is concentrated in one tensor. The tied embedding, which also serves as lm_head, is compressed by a single global codebook — no bands, no spline manifold, no exact outliers — while every linear tensor gets 32 bands, a spline, and 0.5% of its weights kept exact. Its error is the only error in the model that reaches the logits with nothing downstream to absorb it.

Measured on LFM2-350M, relative L2 reconstruction error:

At 27 entries the embedding is the worst-reconstructed tensor in the model. This package uses 81 entries for it, which costs about 6% in size and makes it the best-reconstructed tensor instead.

Usage

Executed by the Cascadia C runtime. This is a compressed package, not a transformers checkpoint.

git clone https://github.com/EntroMorphic/cassie && cd cassie
cmake -S src/c -B build -DCMAKE_BUILD_TYPE=Release && cmake --build build -j

huggingface-cli download ZTFlynn/LFM2-350M-Math-Cascadia-ternary3 --local-dir ./pkg
./build/cascadia_generate ./pkg 512 --chat "Explain gradient descent."

Sampling is --temp / --top-k / --top-p / --seed; the default is greedy and seed-reproducible. Generation stops at <|im_end|>, so max_new is a ceiling.

On an NVIDIA GPU

The same package runs entirely on the GPU, with byte-identical output and roughly 14-16x the throughput. Opt-in, so the default build is unchanged:

cmake -S src/c -B build -DCASCADIA_CUDA=ON -DCMAKE_BUILD_TYPE=Release \
    && cmake --build build -j
./build/cascadia_generate_cuda ./pkg 512 --chat "Explain gradient descent."

Same arguments, same tokens. Needs CUDA and sm_75 or newer.

Python

from transformers import AutoModelForCausalLM
from cascadia import load_compressed

model = AutoModelForCausalLM.from_pretrained("LiquidAI/LFM2-350M-Math", dtype="bfloat16")
model, stats = load_compressed(model, "./pkg", model_id="LiquidAI/LFM2-350M-Math")

Sample output

Prompt: "How many eggs are in a baker's dozen?"

Okay, so I need to figure out how many eggs are in a dozen. Hmm, let's start by recalling what a dozen means. I think a dozen is a unit of measurement, right? Like, how many times something fits into a certain area. But in this case, it's eggs. So, a dozen would be the number of eggs that make up a dozen.

Wait, but how do I calculate that? I remember that there are different types of dozen, like the ones you see in books or in a store. There's the ones you see in a book, which are usually 12, but sometimes you can have more or fewer. But the question is about eggs, so maybe it's a standard on

Greedy, generated to natural completion.

Package contents

Format specified in docs/package_format.md and machine-verified against every package.

How it works

A B-spline surface is fitted to each weight matrix to capture large-scale structure. Each weight is assigned to one of 32 bands by its spline value, and a k-means codebook is learned per band over the residuals. The top 0.5% of errors are kept exactly as f32. Codebook indices pack in base 3, five trits per byte, since 3⁵ = 243 fits a byte.

Reconstruction is W = spline(j,c) + codebook[band][index], evaluated inside the matvec so no dense weight matrix is ever built. Because the spline carries dynamic range, the residual tables need no per-block scale factors.

Limitations

• Runs under the Cascadia C runtime rather than transformers directly.
• The runtime executes ternary-3 packages; other presets convert but are not yet supported by the kernel.
• Batch-1 CPU inference, suited to edge and batch workloads.
• Greedy and sampled decoding; no beam search.

Acknowledgements

Deeply inspired by Magneato/deepseek-r1-qwen-7b-lutc, which demonstrated LUT-cascade compression of a 7B model at 5.45 bits per weight. The Guanaco LUT cascade — no-scale residuals, variable bit rate, and f32 outlier preservation — is the foundation this builds on. Cascadia adds a spline manifold for band selection and a Harmonic Collapse step that removes per-block scale factors entirely. Our thanks to Magneato for publishing both the approach and the weights that made it concrete.

Base model by Liquid AI, used under the LFM Open License.

Citation

@software{cascadia,
  title  = {Cascadia: Spline Manifold LUT Compression for Language Models},
  author = {Josserand-Austin, Tripp},
  year   = {2026},
  url    = {https://github.com/EntroMorphic/cassie}
}