Model Card for Qemma-Q14B

Gap Envelope Integral

• My mathematical formulation to utilize space projections to "measure" the Jump between points of discontinuity found in Non-Differentialable Functions.

Redux

• This Model underwent an additional merge between Qemma-redux and Qwen3-14B, in addition to adding Rope Scaling.

Additionally

• Fusion Logic was updated to aid per layer fusion and post fusion embedding alignment.
• Qemma is a HuggingFace-native hybrid model that merges Gemma-3 (1B) and Qwen-3 (14B) at the weight level (no adapters).
• Design: Gemma MLP/body + Qwen attention/head, projected and aligned to Gemma’s hidden size. The model is then SFT-tuned for stepwise reasoning.
• This variant uses Yarn based Rope Scaling with 1:* Ratio from max_position_embeddings = 524288

Quick start

from transformers import AutoTokenizer, AutoModelForCausalLM
import torch

model_id = "reaperdoesntknow/Qemma-Q14B"
tokenizer = AutoTokenizer.from_pretrained(model_id, use_fast=True)
model = AutoModelForCausalLM.from_pretrained(model_id, torch_dtype=torch.bfloat16).eval()

text = (
    "<|user|>"
    "What makes the sky blue?."
    "<|assistant|>"
    "<think><reasoning_step>"
)

inputs = tokenizer(text, return_tensors="pt", max_length=64, padding='max_length', truncation=True)
inputs = {k: v.to(model.device) for k, v in inputs.items()}

with torch.no_grad():
    model.eval()
    outputs = model.generate(**inputs, max_new_tokens=256, do_sample=True, min_length=32)
print(tokenizer.decode(outputs[0], skip_special_tokens=True))

What’s inside

• Architecture:
• Gemma-3 backbone (26 layers, hidden 1152, MLP 6912)
• Qwen-style attention regrouped to Gemma’s 4×256 heads. (head_dim=128, hidden=5120, intermediate_size=17408, num_attn_heads=40, KV heads=8, num_hidd_layers=40)
• Tokenizer: Gemma-3 tokenizer and chat template (see chat_template.jinja).
• Training: SFT for instruction following and stepwise reasoning.

Intended use & limitations

Use: research, instruction following, code/help, analysis, further SFT/RLHF. Limits: may hallucinate; not for safety-critical, medical, legal, or financial decisions. Follow dataset/model licenses.

Training procedure

• ~512 warm-start steps (HuggingFaceH4/ultrachat_200k) ~ A small post fussion training round was done (8 steps): to encourage embedding realignment.
• ~256 SFT steps with (TIGER-Lab/MathInstruct + HuggingFaceH4/ultrachat_200k)

Framework versions

• TRL: 0.25.0
• Transformers: 4.57.1
• Pytorch: 2.8.0+cpu
• Datasets: 4.4.1
• Tokenizers: 0.22.1

Mathematical Foundations: Discrepancy Calculus (DISC)

Qemma's cross-architecture fusion is built on the Gap Envelope Integral (GEI) — Chapter 7 of the DISC monograph. The discrepancy operator:

$$Df(x)=\underset{\epsilon \downarrow 0}{\lim }\frac{1}{\epsilon }{\int }_x^{x+\epsilon }\frac{\mathrm{\mid }f(t)-f(x)\mathrm{\mid }}{\mathrm{\mid }t-x\mathrm{\mid }}dtDf(x)\; =\; \backslash lim\_\{\backslash varepsilon\; \backslash downarrow\; 0\}\; \backslash frac\{1\}\{\backslash varepsilon\}\; \backslash int\_x^\{x+\backslash varepsilon\}\; \backslash frac\{|f(t)\; -\; f(x)|\}\{|t\; -\; x|\}\backslash ,\; dt$$

When two architectures (Gemma, Qwen) are fused at the weight level, the resulting function is not smooth — it has jump discontinuities at layer boundaries where the two architectures' representations meet. The Mesh Fundamental Identity decomposes this:

$$f(b)-f(a)={\int }_a^b{f}^{\mathrm{\prime }}(x)dx+\sum _{x\in J_f}\mathrm{\Delta }f(x)+D^{c}f(I)f(b)\; -\; f(a)\; =\; \backslash int\_a^b\; f\text{'}(x)\backslash ,dx\; +\; \backslash sum\_\{x\; \backslash in\; J\_f\}\; \backslash Delta\; f(x)\; +\; D^c\; f(I)$$

The GEI specifically measures the jump component $\sum |\Delta f(x)|$ — the total mismatch at fusion boundaries. The model name (GEI) references this directly: the Gap Envelope Integral is the mathematical tool for quantifying what happens when two different weight geometries are projected into a shared space.

Full theory: "On the Formal Analysis of Discrepancy Calculus" (Colca, 2026; Convergent Intelligence LLC: Research Division).

Citations

Cite TRL as:

@misc{vonwerra2022trl,
    title        = {{TRL: Transformer Reinforcement Learning}},
    author       = {Leandro von Werra and Younes Belkada and Lewis Tunstall and Edward Beeching and Tristan Thrush and Nathan Lambert and Shengyi Huang and Kashif Rasul and Quentin Gallou{\'e}dec},
    year         = 2020,
    journal      = {GitHub repository},
    publisher    = {GitHub},
    howpublished = {\url{https://github.com/huggingface/trl}}
}

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By Convergent Intelligence LLC: Research Division

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