Encoding an LLM in {-1, 0, +1} is not theory only. It is already viable in recent research.
The literature converges on two practical paths: post-training ternarization and
native ternary training. Both can be used today to build lean models with useful quality.
Essential takeaway: a well-calibrated ternary LLM can deliver around
2.4x memory reduction, comparable latency, and competitive perplexity or F1.
Foundational method for learned thresholds/scales in ternary weight quantization.
6) Practical code kit (ready to adapt)
Pick the block that matches your goal: full ternary model, module encoder, post-training quantization, or brain-inspired variant.
import torch
import torch.nn as nn
import torch.nn.functional as F
def ternarize(w, alpha=0.7):
delta = alpha * w.abs().mean()
q = torch.where(w > delta, torch.ones_like(w), torch.zeros_like(w))
q = torch.where(w < -delta, -torch.ones_like(w), q)
# STE: backward uses gradient of w
return (q - w).detach() + w
class TernaryLinear(nn.Module):
def __init__(self, in_f, out_f, bias=False):
super().__init__()
self.weight = nn.Parameter(torch.randn(out_f, in_f) * 0.02)
self.scale = nn.Parameter(torch.tensor(1.0))
self.bias = nn.Parameter(torch.zeros(out_f)) if bias else None
def forward(self, x):
wq = ternarize(self.weight)
return F.linear(x, self.scale * wq, self.bias)
class TernaryMLP(nn.Module):
def __init__(self, d_model, d_ff):
super().__init__()
self.fc1 = TernaryLinear(d_model, d_ff)
self.fc2 = TernaryLinear(d_ff, d_model)
def forward(self, x):
return self.fc2(F.gelu(self.fc1(x)))
class TinyTernaryBlock(nn.Module):
def __init__(self, d_model=512, d_ff=2048):
super().__init__()
self.norm1 = nn.LayerNorm(d_model)
self.norm2 = nn.LayerNorm(d_model)
self.qkv = TernaryLinear(d_model, 3 * d_model)
self.proj = TernaryLinear(d_model, d_model)
self.mlp = TernaryMLP(d_model, d_ff)
def forward(self, x):
qkv = self.qkv(self.norm1(x))
q, k, v = qkv.chunk(3, dim=-1)
attn = (q @ k.transpose(-1, -2)) / (x.size(-1) ** 0.5)
attn = attn.softmax(dim=-1)
x = x + self.proj(attn @ v)
x = x + self.mlp(self.norm2(x))
return x
import torch
def ternary_encode_module(module, alpha=0.7):
"""Convert matrix-like parameters to scaled ternary values."""
with torch.no_grad():
for name, p in module.named_parameters():
if p.dim() >= 2:
delta = alpha * p.abs().mean()
q = torch.where(p > delta, torch.ones_like(p), torch.zeros_like(p))
q = torch.where(p < -delta, -torch.ones_like(p), q)
scale = p.abs().mean() + 1e-8
p.copy_(scale * q)
return module
# Example:
# model = YourModel()
# model.load_state_dict(torch.load("checkpoint.pt"))
# model = ternary_encode_module(model, alpha=0.75)
# torch.save(model.state_dict(), "checkpoint_ternary.pt")
from transformers import AutoModelForCausalLM, AutoTokenizer
import torch
model_id = "gpt2" # swap with LLaMA or Mistral in your environment
model = AutoModelForCausalLM.from_pretrained(model_id, torch_dtype=torch.float16)
tokenizer = AutoTokenizer.from_pretrained(model_id)
def pt2_ternarize_tensor(w, alpha=0.7):
delta = alpha * w.abs().mean()
q = torch.where(w > delta, torch.ones_like(w), torch.zeros_like(w))
q = torch.where(w < -delta, -torch.ones_like(w), q)
# closed-form scale update for fixed q
s = (w * q).sum() / (q.pow(2).sum() + 1e-8)
return s * q
with torch.no_grad():
for n, p in model.named_parameters():
if p.dim() >= 2 and "lm_head" not in n:
p.copy_(pt2_ternarize_tensor(p, alpha=0.7))
prompt = "Ternary quantization can"
inputs = tokenizer(prompt, return_tensors="pt")
out = model.generate(**inputs, max_new_tokens=32)
print(tokenizer.decode(out[0], skip_special_tokens=True))
# Next practical step: run calibration data to optimize alpha and layer scales.
import math
import torch
import torch.nn as nn
class OscillationGate(nn.Module):
def __init__(self, d_model, freq=6.0):
super().__init__()
self.freq = nn.Parameter(torch.tensor(freq))
self.amp = nn.Parameter(torch.tensor(0.2))
self.bias = nn.Parameter(torch.zeros(d_model))
def forward(self, x, t):
phase = 2 * math.pi * self.freq * t
gate = 1.0 + self.amp * torch.sin(torch.tensor(phase, device=x.device))
return x * gate + self.bias
class BrainInspiredTernaryLayer(nn.Module):
def __init__(self, d_model, ternary_linear_cls):
super().__init__()
self.lin = ternary_linear_cls(d_model, d_model)
self.gate = OscillationGate(d_model)
self.norm = nn.LayerNorm(d_model)
def forward(self, x, t):
y = self.lin(x)
y = self.gate(y, t)
return self.norm(x + y)
# Idea: combine ternary sparsity with rhythmic modulation for sequence dynamics.
Production tip: add a short calibration loop and track activation error per layer to tune Delta and scaling robustly.
6) Quick quiz (check your understanding)
Answer all ten questions, then compute your score.