ZTFlynn/LFM2.5-2.6B-Cascadia-ternary3

LiquidAI/LFM2.5-2.6B compressed to 1.77 GB with Cascadia — a spline manifold plus per-band lookup tables at 0.60 bytes per weight — and executable on CPU by a C runtime whose entire dependency list is libc, libm and libgomp.

Base model	LiquidAI/LFM2.5-2.6B
Parameters	30 layers, hidden 2048
Checkpoint → package	5.14 GB → 1.77 GB (3.05x)
Bits per weight	5.25
Tensors compressed	30
Architecture	30 blocks, GQA 32q/8kv, gated short convolutions

Quality

	perplexity
LiquidAI/LFM2.5-2.6B (bf16)	26.15
This package (ternary-3)	25.45
Result	-2.65% (95% CI [0.9634x, 0.9829x], t = -5.35)

65,408 paired tokens of FineWeb-Edu in 127 independent 512-token windows. Both models score identical tokens and are compared per token, which cuts the standard error 6.2x 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.

Perplexity came out below the uncompressed checkpoint, and at 127 windows the difference resolves. This is not a claim that the package is a better model: a compressed copy cannot acquire capability its source lacked.

What it shows is that perplexity on this corpus is not a measure of how faithful a copy is. The corpus is general web text, and a small perturbation of the weights can move a model's likelihood on out-of-domain text in either direction — here it moved down. Reconstruction fidelity below puts this package in the same band as every other model in the family, which is the fact about the compression.

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.

Relative L2 error vs the bf16 checkpoint	0.0544
Systematic gain (1.0000 is faithful)	0.9993
Measured over	167 of 167 tensors, 100% of parameters

By tensor class:

class	rel L2	share of model
linear	0.0578	2,435M params
embedding	0.0238	262M params

The tied embedding, the tensor whose error reaches the logits undamped, reconstructs at 0.0238.

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:

tensor	codebook	rel L2
tied embedding, 27 entries	27	0.078
tied embedding, 81 entries	81	0.027
a typical linear (32 bands x 27)	864	0.057

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/LFM2.5-2.6B-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.

Python

from transformers import AutoModelForCausalLM
from cascadia import load_compressed

model = AutoModelForCausalLM.from_pretrained("LiquidAI/LFM2.5-2.6B", dtype="bfloat16")
model, stats = load_compressed(model, "./pkg", model_id="LiquidAI/LFM2.5-2.6B")

Sample output

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

Greedy, generated to natural completion.

Package contents

file	size
weights.bin	1.77 GB
manifest.json	per-tensor geometry and offsets
aux.bin	RMSNorm scales, conv kernels, architecture constants
tokenizer.bin	vocabulary, merges, Unicode tables

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}
}