Project: 057_The_Geometry_of_Categorical_and_Hierarchical_Conce | Function: get_g (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Implements the canonical representation transformation that creates the causal inner product space by whitening the unembedding matrix. This is a core geometric transformation that enables linear representations of concepts.

**KEY TERMS:** {
  "gamma": "unembedding_vectors",
  "Cov_gamma": "covariance_matrix",
  "inv_sqrt_Cov_gamma": "whitening_matrix",
  "g": "canonical_representation"
}

**CONTEXT CODE:** import torch
import numpy as np
from transformers import AutoTokenizer, AutoModelForCausalLM
from tqdm import tqdm

def get_gamma(MODEL_NAME, device):
    model = AutoModelForCausalLM.from_pretrained(MODEL_NAME,
                                                 torch_dtype=torch.float32,
                                                 device_map=device)

    gamma = model.get_output_embeddings().weight.detach()
    
    return gamma

def get_g(MODEL_NAME, device):
    raise NotImplementedError("Function implementation has been masked for testing")

def get_vocab(MODEL_NAME):
    tokenizer = AutoTokenizer.from_pretrained(MODEL_NAME)
    vocab_dict = tokenizer.get_vocab()
    vocab_list = [None] * (max(vocab_dict.values()) + 1)
    for word, index in vocab_dict.items():
        vocab_list[index] = word

    return vocab_dict, vocab_list


def compute_lambdas(texts, MODEL_NAME, device):
    tokenizer = AutoTokenizer.from_pretrained(MODEL_NAME)
    model = AutoModelForCausalLM.from_pretrained(MODEL_NAME,
                                                 torch_dtype=torch.float32,
                                                 device_map="auto")

    assert tokenizer.padding_side == "left", "The tokenizer padding side must be 'left'."

    
    with torch.no_grad():
        inputs = tokenizer(texts, return_tensors="pt", padding=True).to(device)
        outputs = model(**inputs, output_hidden_states=True)
        lambdas = outputs.hidden_states[-1][:, -1, :]

    return lambdas


Complete the function implementation replacing "raise NotImplementedError".