Adapter Modules for Foundation Models

As discussed in the chapter introduction, adapting billion-parameter foundation models presents substantial computational challenges, especially in few-shot scenarios where data is scarce. Full fine-tuning is often infeasible due to memory constraints and the risk of catastrophic forgetting. Parameter-Efficient Fine-Tuning (PEFT) methods offer a solution by modifying only a small fraction of the model's parameters. Among the earliest and most influential PEFT techniques are Adapter Modules.

The core idea behind adapters is elegantly simple: instead of modifying the existing weights of the large pre-trained model, insert small, trainable neural network modules between the layers of the frozen foundation model. During adaptation, only the parameters of these newly added adapter modules are updated, while the original foundation model weights remain untouched.

Adapter Architecture and Insertion

An adapter module typically consists of a sequence of operations designed to project the input activation to a lower-dimensional space (the bottleneck), apply a non-linearity, and then project it back to the original dimension. A common architecture is:

1. Down-Projection: A linear layer ($W_{down}$) maps the input activation $h$ (from the preceding layer) to a smaller dimension $m$.
2. Non-Linearity: An activation function $\sigma$ (e.g., ReLU, GeLU) is applied.
3. Up-Projection: Another linear layer ($W_{up}$) maps the result back to the original dimension of $h$.
4. Residual Connection: The output of the adapter is added back to the original input activation $h$.

Mathematically, the transformation applied by an adapter module to an intermediate activation $h \in \mathbb{R}^d$ can be expressed as:

$$\text{Adapter}(h) = W_{up}(\sigma(W_{down}(h)))$$

Where $W_{down} \in \mathbb{R}^{m \times d}$ and $W_{up} \in \mathbb{R}^{d \times m}$. The dimension $m$ is the adapter's bottleneck dimension, a critical hyperparameter typically chosen such that $m \ll d$. This bottleneck is the source of the parameter efficiency. The final output $h'$ of the layer incorporating the adapter is:

$$h' = h + \text{Adapter}(h)$$

The residual connection is important. It allows the adapter to learn modifications to the layer's function. If the adapter learns to output zero (which can be encouraged through initialization), the adapted layer behaves identically to the original pre-trained layer.

Adapters can be inserted at various locations within a Transformer block. Common strategies include placing them sequentially after the multi-head self-attention (MHSA) sublayer and the feed-forward network (FFN) sublayer.

Insertion points for Adapter Modules within a standard Transformer block. Adapters are typically placed after the main sublayers (MHSA, FFN) and integrated via residual connections. The original Transformer block parameters remain frozen.

Training Adapters

During adaptation for a new task, the parameters of the foundation model ($\theta_{FM}$) are frozen. Only the parameters of the inserted adapter modules ($\theta_{adapter}$, specifically $W_{down}$ and $W_{up}$ in all adapters) are trainable. The training process involves minimizing a task-specific loss function $\mathcal{L}_{task}$ (e.g., cross-entropy for classification) with respect to $\theta_{adapter}$:

$$\min_{\theta_{adapter}} \mathcal{L}_{task}(\text{Model}(X; \theta_{FM}, \theta_{adapter}), Y)$$

Where $(X, Y)$ represents the few-shot training data for the target task.

A common initialization strategy is to initialize $W_{down}$ randomly (e.g., using Xavier or He initialization) and initialize $W_{up}$ to near-zero values. This ensures that at the beginning of training, the adapter modules have minimal impact ($\text{Adapter}(h) \approx 0$), and the model behaves like the original pre-trained foundation model, providing a stable starting point for optimization.

Advantages and Considerations

Adapters offer several compelling advantages for few-shot adaptation:

• High Parameter Efficiency: The number of trainable parameters introduced by adapters is typically very small compared to the total number of parameters in the foundation model (often less than 5%, tunable via the bottleneck dimension $m$). This drastically reduces the memory required for storing optimizer states and gradients during training.
• Reduced Computational Cost: Training is faster because gradients only need to be computed for the small set of adapter parameters. Backpropagation through the frozen foundation model is still required, but the optimizer step is much cheaper.
• Modularity: Since the base model is unchanged, adapters trained for different tasks can be stored independently. For inference on a specific task, the corresponding adapter module can be loaded alongside the base model. This avoids the need to store multiple copies of the large foundation model and prevents catastrophic forgetting when learning sequential tasks. One base model can serve many tasks by simply swapping adapters.

However, there are also considerations:

• Inference Latency: Adding adapter modules introduces extra computational steps during inference compared to the original model or methods like LoRA (which can often merge its modifications into the original weights). While each adapter's computation is relatively small, the cumulative effect across many layers can slightly increase latency. Techniques like adapter fusion aim to mitigate this by combining sequential adapters.
• Potential Performance Limits: While highly effective, especially in low-data regimes, adapters might sometimes underperform full fine-tuning if sufficient data for the downstream task is available. The representational power is limited by the bottleneck dimension and the fixed nature of the base model.
• Hyperparameter Sensitivity: Performance can depend on the choice of bottleneck dimension $m$, the specific non-linearity $\sigma$, the insertion strategy (after MHSA, FFN, or both), and the learning rate used for adapter training.

Adapters represent a foundational technique in PEFT. They demonstrate the viability of adapting large models by introducing and training only a small number of new parameters, creating a path for other methods like LoRA and prompt tuning, which examine different ways to achieve parameter efficiency, as we will see in the following sections.