Learn Your Own Thoughts: Abstract Token Curriculum

While long, explicit chains-of-thought (CoT) have proven effective on complex reasoning tasks, they are costly to generate during inference. Non-verbal reasoning methods have emerged with shorter generation lengths by leveraging continuous representations, yet their performance lags behind verbalized CoT. We propose $\textbf{Abstract Chain-of-Thought}$, a discrete latent reasoning post-training mechanism in which the language model produces a short sequence of tokens from a reserved vocabulary in lieu of a natural language CoT, before generating a response. To make previously unseen ''abstract'' tokens useful, we introduce a policy iteration-style warm-up loop that alternates between (i.) bottlenecking from a verbal CoT via masking and performing supervised fine-tuning, and (ii.) self-distillation by training the model to generate abstract tokens from the prompt alone via constrained decoding with the codebook. After warm-up, we optimize the generation of abstract sequences with warm-started reinforcement learning under constrained decoding. Abstract-CoT achieves up to $11.6\times$ fewer reasoning tokens while demonstrating comparable performance across mathematical reasoning, instruction-following, and multi-hop reasoning, and generalizes across language model families. We also find an emergent power law distribution over the abstract vocabulary, akin to those seen in natural language, that evolves across the training phases. Our findings highlight the potential for post-training latent reasoning mechanisms that enable efficient inference through a learned abstract reasoning language.

Continuous Chain-of-Thought methods replace verbose reasoning traces with a short sequence of dense latent representations. Earlier continuous CoT methods indirectly supervise the latent representations such that its final state match that of verbose reasoning traces, requiring autoregressive, slow generation during training. We introduce C-MTP, a simpler, faster direct supervision approach that models each latent as an average of the embeddings in the CoT traces to be compressed. Our approach outperforms a prior direct supervision method that approximates the distribution of compressed tokens, and performs competitively to slower indirect supervision approaches in existing evaluation setup with simplified CoT traces (less than 100 tokens). Lastly, we extend the evaluation of Continuous CoT methods to complex tasks with longer reasoning traces ($\ge$ few hundreds reasoning tokens). We find both direct and indirect supervision training methods perform poorly (roughly 65% performance drop) in this setting, revealing the limitations of current continuous CoT methods. The code and checkpoints are released at https://github.com/Varun221/cmtp_research

Large language models (LLMs) have demonstrated remarkable reasoning abilities on mathematical and multi-hop planning tasks. The CoCoNuT (Chain of Continuous Thought) paradigm~\cite{hao2024coconut} extends this by enabling models to reason in latent space, exploring multiple reasoning paths simultaneously rather than committing to a single chain early on. However, we identify a limitation we term the \textbf{concept bottleneck}. At each reasoning pass, intermediate hidden states are overwritten, causing the model to lose critical facts computed in earlier steps as reasoning depth increases. We observe this empirically. On HotpotQA, vanilla CoCoNuT (10.4% EM) fails to improve over the CoT baseline (11.0% EM), and performance degrades with curriculum depth on GSM8K. To address this, we propose \textbf{AGCLR} (Adaptive Gated Continuous Latent Reasoning), which augments CoCoNuT with a \textit{Gated Concept Stream}. A persistent residual memory maintained across all reasoning passes, controlled by three learned gates: a \textit{write} gate that commits intermediate facts to memory, a \textit{read} gate that retrieves relevant prior states, and a \textit{forget} gate that prunes irrelevant context. Evaluated on GSM8K, HotpotQA, and ProsQA using GPT-2 as our base model, AGCLR achieves consistent improvements across all types of datasets. With the performance gap compounding as curriculum depth increases, directly resolving the concept bottleneck. Code available at https://anonymous.4open.science/r/JJJJ/README.md