PNM-Negotiate

A language model based on Paraconsistent Negotiated Mathematics.

Architecture

Standard causal transformer with two extra heads:

• Commitment head: outputs a_t ∈ (0,1) per token
• Denial head: outputs b_t ∈ (0,1) per token

A token with a_t > 0.5 and b_t > 0.5 is a negotiated token — simultaneously asserted and denied. The model does not collapse contradictions; it represents them.

Training

Loss = cross-entropy + λ · mean(a_t · b_t)

The tension term penalizes simultaneous high commitment and denial, but does not forbid it.

Usage

from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained(
    "zeechimp/pnm-negotiate",
    trust_remote_code=True,
)
tokenizer = AutoTokenizer.from_pretrained("zeechimp/pnm-negotiate")

inputs = tokenizer("The truth is", return_tensors="pt")
out = model.generate(**inputs, max_new_tokens=32, return_commitment=True)
print(tokenizer.decode(out[0]))
print("Commitment:", out.commitment[0, -1].max().item())
print("Denial:     ", out.denial[0, -1].max().item())

## Limitations

- The negotiation loss is a soft constraint, not a hard one.
- The model can still collapse to `a ≈ b ≈ 0.5` for all tokens if the tension weight is too high.
- No theoretical guarantee that the fixed point is unique.

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Running It

pip install transformers torch datasets tokenizers huggingface_hub
python train_pnm.py

The training script uses WikiText-2 as a stand-in. Replace with your own corpus. The model pushes to your-username/pnm-negotiate after training.

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What This Model Actually Does

The commitment_head and denial_head are trained to predict, for each token, how much the model asserts it and how much it denies it. The negotiation loss mean(a · b) pushes the model to keep these two quantities from both being high — but does not forbid it. The result is a model that can output a token with a = 0.7, b = 0.4 — asserted and denied simultaneously.

This is the only architectural change from a standard causal LM. Everything else is standard. The PNM structure lives entirely in the two extra heads and the auxiliary loss.

To verify the claim, after training, inspect the commitment/denial values on a contradictory prompt like "This statement is false". If the model has learned the PNM structure, you should see elevated denial alongside commitment — not a collapse to one or the other. If it has not, the heads will have collapsed to a ≈ 1, b ≈ 0 (standard LM behavior) or a ≈ b ≈ 0.5 (tension-dominated collapse). Both are failures of the negotiation, and both are measurable.