Steering Directions Are Explanations, Not Handles
A direction can be interpretable, causal, and predictive (and still a bad handle for intervention)TLDR: In modern interpretability, we find “directions” inside a language model that seem to encode meaningful concepts. One such example is “This is about food.” A common next step is to steer the model in that direction, in the hopes it produces more of that concept. I show that even when a direction passes the tests we have for whether it “really” means something, the range over which the idea of “more pushing = more concept” remains valid is smaller than is often made explicit in steering work. I derive a closed-form, local Taylor formula that gives a radius within which the quadratic and cubic corrections are bounded relative to the linear term. Empirically, this radius predicts where steering stops behaving linearly across the models I tested. At mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="true"] mjx-math { padding: 0; } mjx-container[jax="CHTML"][justify="left"] { text-align: left; } mjx-container[jax="CHTML"][justify="right"] { text-align: right; } mjx-mi { display: inline-block; text-align: left; } mjx-c { display: inline-block; } mjx-utext { display: inline-block; padding: .75em 0 .2em 0; } mjx-mo { display: inline-block; text-align: left; } mjx-stretchy-h { display: inline-table; width: 100%; } mjx-stretchy-h > * { display: table-cell; width: 0; } mjx-stretchy-h > * > mjx-c { display: inline-block; transform: scalex(1.0000001); } mjx-stretchy-h > * > mjx-c::before { display: inline-block; w