A Little Guide to Causal Abstraction

A Little Guide to Causal Abstraction#

From Interventions to Gaining Interpretability Insights

author:

Zhengxuan Wu

Basic interventions are fun but we cannot make any causal claim systematically. To gain actual interpretability insights, we want to measure the counterfactual behaviors of a model in a data-driven fashion. In other words, if the model responds systematically to your interventions, then you start to associate certain regions in the network with a high-level concept. We also call this alignment search process with model internals.

Understanding Causal Mechanisms with Static Interventions#

Here is a more concrete example,

def add_three_numbers(a, b, c):
    var_x = a + b
    return var_x + c

The function solves a 3-digit sum problem. Let’s say, we trained a neural network to solve this problem perfectly. “Can we find the representation of (a + b) in the neural network?”. We can use this library to answer this question. Specifically, we can do the following,

  • Step 1: Form Interpretability (Alignment) Hypothesis: We hypothesize that a set of neurons N aligns with (a + b).

  • Step 2: Counterfactual Testings: If our hypothesis is correct, then swapping neurons N between examples would give us expected counterfactual behaviors. For instance, the values of N for (1+2)+3, when swapping with N for (2+3)+4, the output should be (2+3)+3 or (1+2)+4 depending on the direction of the swap.

  • Step 3: Reject Sampling of Hypothesis: Running tests multiple times and aggregating statistics in terms of counterfactual behavior matching. Proposing a new hypothesis based on the results.

To translate the above steps into API calls with the library, it will be a single call,

intervenable.eval_alignment(
    train_dataloader=test_dataloader,
    compute_metrics=compute_metrics,
    inputs_collator=inputs_collator
)

where you provide testing data (basically interventional data and the counterfactual behavior you are looking for) along with your metrics functions. The library will try to evaluate the alignment with the intervention you specified in the config.

Understanding Causal Mechanism with Trainable Interventions#

The alignment searching process outlined above can be tedious when your neural network is large. For a single hypothesized alignment, you basically need to set up different intervention configs targeting different layers and positions to verify your hypothesis. Instead of doing this brute-force search process, you can turn it into an optimization problem which also has other benefits such as distributed alignments.

In its crux, we basically want to train an intervention to have our desired counterfactual behaviors in mind. And if we can indeed train such interventions, we claim that causally informative information should live in the intervening representations! Below, we show one type of trainable intervention RotatedSpaceIntervention as,

class RotatedSpaceIntervention(TrainableIntervention):

    """Intervention in the rotated space."""
    def forward(self, base, source):
        rotated_base = self.rotate_layer(base)
        rotated_source = self.rotate_layer(source)
        # interchange
        rotated_base[:self.interchange_dim] = rotated_source[:self.interchange_dim]
        # inverse base
        output = torch.matmul(rotated_base, self.rotate_layer.weight.T)
        return output

Instead of activation swapping in the original representation space, we first rotate them, and then do the swap followed by un-rotating the intervened representation. Additionally, we try to use SGD to learn a rotation that lets us produce expected counterfactual behavior. If we can find such rotation, we claim there is an alignment. If the cost is between X and Y.ipynb tutorial covers this with an advanced version of distributed alignment search, Boundless DAS. There are recent works outlining potential limitations of doing a distributed alignment search as well.

You can now also make a single API call to train your intervention,

intervenable.train_alignment(
    train_dataloader=train_dataloader,
    compute_loss=compute_loss,
    compute_metrics=compute_metrics,
    inputs_collator=inputs_collator
)

where you need to pass in a trainable dataset, and your customized loss and metrics function. The trainable interventions can later be saved on to your disk. You can also use intervenable.evaluate() your interventions in terms of customized objectives.