No sign of backtracking in latent reasoning: the final answer simply settles in instead

Solving a hard math problem is not linear, it's trial and error. You drop an idea, pick up an earlier one, go back to a computation from another approach, until something clicks. You might scribble on paper, but even if you don't, you still remember the path to get to the result, as well as the other methods you tried before one worked. Do language models do this too? In chain-of-thought reasoning, we can see that they do: the backtracking shows up in the transcript, signaled by tokens such as "wait". But in latent reasoning, models think without writing tokens down, and the intermediate steps are just vectors. Recent work (Cui & Ye) implies that latent models backtrack as well. Do they? Why would it even matter? If a latent model goes back to its earlier thoughts, those thoughts become a trace that we can monitor and potentially steer. On the models we could evaluate (including the one the claim was made on),  nothing resembled a change of mind, and what could seem like backtracking was actually just the final answer settling in. We also show some observations we made along the way, as well as why this question is harder to answer than it may seem at first glance. What could latent backtracking be and how we defined it There are two kinds of reasoning in LMs: Text: the model writes its steps as a sequence of tokens, so the backtracking can be pinpointed (“wait, that’s wrong”, “wait, actually”) and the earlier idea is right there to reconsider Latent: the steps are hidden states. Models such as Coconut and CODI feed each thought back as the next input, so later steps can reference earlier thoughts, while looped models such as Huginn (Geiping et al.) iterate over the same set of layers on a state that gets overwritten, so earlier content is no longer accessible. As latent backtracking cannot be identified as its text counterpart, where you just have to look at the output words, we investigate it by passing each step’s hidden state through the output layers, and analyze the situation of the candidate answers. Backtracking should show up as the top answer changing, as it “drops” the current idea in favour of another one, and this should be reflected in its top choices. We adopt Cui & Ye's interpretation of backtracking, which counts when the top answer changes. Cui & Ye report the winner flips on 32% of Huginn's questions, and it's more likely to get the answer right when it happens. By establishing that backtracking requires a “change of mind”, to determine whether latent models even backtrack, we wanted to analyze each flip (where the order of the top candidates changed) and see if we could figure out whether it is a revisit of an earlier idea, or an override where the state just keeps on moving until it settles on a different answer, without reading anything from early thoughts. However, an answer leaderboard change could be caused by multiple factors: A real reversal: the top candidate switches, and the model’s final output is affected by it Confidence buildup: the same top candidate, but it increasingly distances itself from the other potential outputs Noise: two close candidates alternating by a small margin We can classify only the first one as a genuine change of mind, but before we could investigate the phenomenon, we had to find one. ​ Searching for the phenomenon in classic model architectures We started with a simple graph model: Coconut-style, two layers, trained from scratch on graph reachability, with two possible candidates per question (from now on, when we refer to candidates, we refer to a node in this pair). The model achieves 95% accuracy, and we had two separate trained runs, evaluated on the same 419 test graphs. Throughout the reasoning steps, leaderboard changes occur frequently. The candidate pair’s winner swaps in 29 to 38% of transitions from one reasoning step to another, but a random node pair’s winner flips in 32-42% of the cases as well. On closer look, most last-step flips are the correct answer taking the lead (129/134 and 151/154 for the two trained runs), so this is the final answer settling in, not really a change of mind. Sequences with two or more flips (the natural structure of a true answer reversal) are more frequent for random node pair flips (0.34) than for the candidate pair (0.15). The two training runs only agreed on flips 31% of the time, so they are specific to the training run and not just dependent on the problem. The readout tracks the search frontier across the graph, so a node’s score gets boosted when the search reaches it. This means that the wrong candidate, if it is reached towards the end, will get a late rise too, but it will not be that close to the top. ​What if the model considers both answers from the candidate pair at the same time, but the readout only shows the winner? After checking how strongly the wrong candidate is represented, we found that it is well above the range unrelated nodes fall in. It distances itself late, and by the time