Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model is available here: http://ouro-llm.github.io.

We would like to thank all reviewers for their comments and helpful feedback. Simplicity was meant to quantify this. We agree with both of those points. Figure 1 - these steps were the most minimal configuration that produced the best model as determined by our scores. Training for more recurrent steps is possible, but at least on our current set of scores, we see no improvement.

Staircase model, Transformer cores are stacked diagonally, so each step sees one new input chunk.

Here, we propose that extra-synaptic diffusion of local neuromodulators such as neuropeptides may afford an effective mode of back-propagation lying within the bounds of biological plausibility.

Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner, having clear advantages over state-of-the-art methods such as Graph Neural Networks, SATNet, and some neuro-symbolic models. With the ability of Transformer to handle visual input, the proposed Recurrent Transformer can straightforwardly be applied to visual constraint reasoning problems while successfully addressing the symbol grounding problem. We also show how to leverage deductive knowledge of discrete constraints in the Transformer's inductive learning to achieve sampleefficient learning and semi-supervised learning for CSPs. Constraint Satisfaction Problems (CSPs) are about finding values of variables that satisfy given constraints. They have been widely studied in symbolic AI with an emphasis on designing efficient algorithms to deductively find solutions for explicitly stated constraints. In the recent deep learningbased approach, the focus is on inductively learning the constraints and solving them in an end-to-end manner. For example, the Recurrent Relational Network (RRN) (Palm et al., 2018) uses message passing over graph structures to learn logical constraints, achieving high accuracy in textual Sudoku. On the other hand, it uses hand-coded information about Sudoku constraints, namely, which variables are allowed to interact. Moreover, it is limited to textual input. SATNet (Wang et al., 2019) is a differentiable MAXSAT solver that can infer logical rules and can be integrated into DNNs.

We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key feature is that the unknown dynamical system contains system parameters that are completely hidden, in the sense that no information about the parameters is available through either the measurement trajectory data or our prior knowledge of the system. We demonstrate that by training a DNN using the trajectory data with sufficient time history, the resulting DNN model can accurately model the unknown dynamical system. For new initial conditions associated with new, and unknown, system parameters, the DNN model can produce accurate system predictions over longer time.

Modern neural networks obtain information about the problem and calculate the output solely from the input values. We argue that it is not always optimal, and the network's performance can be significantly improved by augmenting it with a query mechanism that allows the network to make several solution trials at run time and get feedback on the loss value on each trial. To demonstrate the capabilities of the query mechanism, we formulate an unsupervised (not dependant on labels) loss function for Boolean Satisfiability Problem (SAT) and theoretically show that it allows the network to extract rich information about the problem. We then propose a neural SAT solver with a query mechanism called QuerySAT and show that it outperforms the neural baseline on a wide range of SAT tasks and the classical baselines on SHA-1 preimage attack and 3-SAT task.