Got it! If your dataset consists of independent samples where each sample is either a positive (correct next token) or negative (incorrect next token) example, you can still leverage these negative samples effectively in training your model. Here’s how you can handle this scenario:
1. Binary Classification Approach:
Since each sample is either positive or negative, you can treat the problem as a binary classification task for next-token prediction. Here’s how:
- Positive Sample: These are your standard next-token prediction examples, where the goal is to predict the correct next token.
- Negative Sample: These are incorrect next tokens. In the binary setup, the model will predict a low probability for these tokens.
The loss function would be adjusted accordingly to handle this binary classification setting:
- For positive samples, you compute the standard cross-entropy loss, encouraging the model to predict the correct token.
- For negative samples, you compute a loss that encourages the model to assign a low probability to the incorrect token (e.g., via binary cross-entropy).
The total loss can be written as:
\[\begin{equation} L = -\sum_{i\in Positive samples} \log P(positive\ token|x_i) - \alpha \sum_{j\in Negative samples} \log(1 - P(negative\ token|x_j)) \end{equation}\]where:
-
$P(positive token∣x_i)P(\text{positive token} x_i) $is the predicted probability of the correct next token for input xix_i, -
P(negative token∣xj)P(\text{negative token} x_j) is the predicted probability of the incorrect next token for input xjx_j.
2. Sampling Strategy:
-
If you have an unequal distribution of positive and negative samples (e.g., many more negative samples), you may need to
balance
the samples during training. You could:
- Undersample the negative samples.
- Oversample the positive samples.
- Use class weights in the loss function to give more importance to positive samples.
3. Negative Sample Weighting:
In some cases, you might want to weight negative samples less than positive ones, especially if there is an imbalance. This would ensure that the model does not overly focus on minimizing the probability for negative tokens. You can introduce a weight for negative samples:
\[\begin{equation} L=−∑i∈Positive sampleslogP(positive token∣xi)−α∑j∈Negative sampleslog(1−P(negative token∣xj))\mathcal{L} = - \sum_{i \in \text{Positive samples}} \log P(\text{positive token} | x_i) - \alpha \sum_{j \in \text{Negative samples}} \log(1 - P(\text{negative token} | x_j)) \end{equation}\]where α\alpha is a hyperparameter that controls how much the negative samples influence the loss.
4. Noise Contrastive Estimation (NCE):
If your dataset is large and contains a lot of negative samples, you could use Noise Contrastive Estimation (NCE) to distinguish between positive and negative samples. NCE is a technique where the model is trained to classify each sample as either “real” (positive) or “noise” (negative). This method can help handle large vocabularies and inefficient computation, as it only focuses on distinguishing between positive and negative samples.
In this case, the model learns to maximize the probability of correctly identifying positive samples and minimizing the probability of incorrectly identifying negative samples. The NCE loss can be framed as:
| LNCE=−∑i∈Positive sampleslogP(positive token∣xi)+∑j∈Negative sampleslogP(negative token∣xj)\mathcal{L}{NCE} = - \sum{i \in \text{Positive samples}} \log P(\text{positive token} | x_i) + \sum_{j \in \text{Negative samples}} \log P(\text{negative token} | x_j) |
The objective is to increase the probability for positive samples and decrease the probability for negative samples.
5. Training Procedure:
- Step 1: For each training step, randomly sample both positive and negative examples (depending on your sample distribution).
- Step 2: Compute the loss for both positive and negative samples.
- Step 3: Update the model parameters based on the total loss.
If using a batching strategy, you can treat each batch as a mix of positive and negative samples. The model will then learn to predict the next token as a binary classification task (correct vs. incorrect).
Example Workflow:
- Input: Sequence of tokens x=[x1,x2,…,xn]x = [x_1, x_2, \dots, x_n].
- Positive Sample: (xn,xn+1)(x_n, x_{n+1}) where xn+1x_{n+1} is the correct next token.
- Negative Sample: (xn,xk)(x_n, x_k) where xkx_k is a random incorrect token.
- Loss: Compute the binary cross-entropy for both the positive and negative pairs.
By training with positive and negative samples, the model learns not only to predict the correct token but also to avoid predicting the incorrect ones.