Autoregressive Language Modeling

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning state $z$ and the predicted output $y$. Naturally, such refinement is of interest for any predictor; it is therefore natural to wonder whether the TRM mechanism could be effectively re-adopted in autoregressive models. However, TRMs cannot be simply compared to standard models because they lack causal predictive structures and contain persistent latent states that make it difficult to isolate specific performance gains. In this paper, we propose the Autoregressive TRM and evaluate it on small autoregressive tasks. To understand its efficacy, we propose a suite of models that gradually transform a standard Transformer to a Tiny Autoregressive Recursive Model in a controlled setting that fixes the block design, token stream, and next-token objective. Across compute-matched experiments on character-level algorithmic tasks, we surprisingly find that there are some two-level refinement baselines that show strong performance. Contrary to expectations, we find no reliable performance gains from the full Autoregressive TRM architecture. These results offer potential promise for two-step refinement mechanisms more broadly but caution against investing in the autoregressive TRM-specific model as a fruitful research direction.

Autoregressive (AR) language models build representations incrementally via left-to-right prediction, while diffusion language models (dLLMs) are trained through full-sequence denoising. Although recent dLLMs match AR performance, whether diffusion objectives fundamentally reshape internal representations remains unclear. We perform the first layer- and token-wise representational analysis comparing native dLLMs (LLaDA), native AR models (Qwen2.5), and AR-initialized dLLMs (Dream-7B), using cosine similarity across layers and tokens alongside static inference-time layer-skipping as an analytical probe of redundancy. We find that diffusion objectives produce more global representations with substantial early-layer redundancy and reduced recency bias, while AR objectives yield tightly coupled, locally structured representations. AR-initialized dLLMs retain AR-like dynamics despite diffusion training, revealing persistent initialization bias. Leveraging this redundancy, native dLLMs absorb up to 18.75% FLOPs reduction while retaining over 90% performance on math-reasoning and coding benchmarks, whereas AR models collapse under identical skipping, revealing that diffusion objectives, rather than architecture alone, induce depth redundancy that enables principled compression.

Large language models show that simple autoregressive training can yield scalable and coherent generation, but extending this paradigm to speech remains challenging due to the entanglement of semantic and acoustic information. Most existing speech language models rely on text supervision, hierarchical token streams, or complex hybrid architectures, departing from the single-stream generative pretraining paradigm that has proven effective in text. In this work, we introduce WavSLM, a speech language model trained by quantizing and distilling self-supervised WavLM representations into a single codebook and optimizing an autoregressive next-chunk prediction objective. WavSLM jointly models semantic and acoustic information within a single token stream without text supervision or text pretraining. Despite its simplicity, it achieves competitive performance on consistency benchmarks and speech generation while using fewer parameters, less training data, and supporting streaming inference.

Autoregressive language models trained with next-token prediction generate text by sampling one discrete token at a time. Although very scalable, this objective forces the model to commit at every step, preventing it from exploring or reflecting upon multiple plausible continuations. Furthermore, the compute allocation across tokens is uniform; every token is formed based on a single forward-pass, potentially limiting the model's expressiveness in cases where difficult tokens require inherently more compute. Towards addressing these limitations, we introduce latent lookahead, a training strategy that enables models to "think" before generating: at selected positions in the sequence, before committing to the next token, the model performs a multi-step lookahead in latent space. More precisely, instead of sampling future tokens, we leverage the network's latent space by recursively feeding its hidden states back into the context for $τ$ steps, investing more compute on predicting that token. This produces $τ$ latent predictions that are supervised against the next $τ$ ground-truth tokens, encouraging the model to "lookahead" and refine its prediction. We show that latent lookahead substantially outperforms both autoregressive and non-autoregressive baselines on planning tasks such as maze solving, Sudoku, and ProsQA, where foresight is essential.

The Stop-Think-AutoRegress Language Diffusion Model (STAR-LDM) integrates latent diffusion planning with autoregressive generation. Unlike conventional autoregressive language models limited to token-by-token decisions, STAR-LDM incorporates a "thinking" phase that pauses generation to refine a semantic plan through diffusion before continuing. This enables global planning in continuous space prior to committing to discrete tokens. Evaluations show STAR-LDM significantly outperforms similar-sized models on language understanding benchmarks and achieves $>70\%$ win rates in LLM-as-judge comparisons for narrative coherence and commonsense reasoning. The architecture also allows straightforward control through lightweight classifiers, enabling fine-grained steering of attributes without model retraining while maintaining better fluency-control trade-offs than specialized approaches.

While Autoregressive (AR) Transformer-based Generative Language Models are frequently employed for lookahead tasks, recent research suggests a potential discrepancy in their ability to perform planning tasks that require multi-step lookahead. In this work, we investigate the distinct emergent mechanisms that arise when training AR versus Non-Autoregressive (NAR) models, such as Discrete Diffusion Models (dLLMs), on lookahead tasks. By requiring the models to plan ahead to reach the correct conclusion, we analyze how these two paradigms fundamentally differ in their approach to the problem. We identify a critical asymmetry in planning problems: while forward generation requires complex lookahead at branching junctions, reverse generation is often deterministic. This asymmetry creates an opportunity for NAR models. Through mechanistic analysis of training and inference dynamics, we demonstrate that NAR models learn to solve planning tasks by utilizing future tokens to decode backwards, avoiding the need to learn complex traversal mechanisms entirely. Consequently, we report that both AR and NAR models are able to achieve perfect accuracy on the lookahead task. However, NAR models require exponentially fewer training examples and shallower architectures compared to AR models, which often fail to converge without specific curriculum adjustments.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) provides an efficient route to diffusion language modeling, but it remains unclear whether the resulting models reuse inherited autoregressive computation or reorganize it for non-autoregressive generation. We compare two 7B ARM-MDM families across four controlled diagnostic tasks and find a task-dependent mechanism shift. On prefix-dominant tasks, MDMs largely preserve inherited high-attribution pathways or exhibit only modest changes in where computation occurs. On globally constrained tasks, the reorganization is substantially stronger, with task-relevant computation shifting toward earlier layers. This depth-wise pattern persists across prompt resampling, circuit budgets, and tested inference budgets, while targeted ablations support the functional importance of the identified structures under the tested intervention protocols. At the component level, diagnostic probes suggest that ARMs rely more strongly on sharply specialized components, whereas MDMs exhibit weaker single-component specialization and more diffuse output-space alignment. Together, these results suggest that diffusion post-training selectively preserves or reorganizes inherited computation according to task structure, rather than uniformly replacing autoregressive mechanisms.

In decoder-only (causal) transformers, the computation graph created by causal masking routes information through both direct-path attention and indirect paths formed by intermediate tokens. We denote these indirect paths between token pairs as their runways. We argue that certain failure modes of causal transformers as observed by a growing body of recent works are likely exacerbated by a misalignment between these two information propagation modes. We formalize runway cascade as a phenomenon whereby this misalignment results in redundancies and irrelevant information cascading to token representations despite adequately learned attention patterns. As a solution, we propose runway-aware rewiring as a more explicit way of incorporating runway context directly into each token's direct-path attention. This mechanism re-wires the attention pattern for each token based on a summary of its runway landscape, enabling awareness of accumulating representational influences and allowing for more balanced information propagation. Our proposed methodology introduces no additional parameters and can seamlessly be integrated into standard attention mechanism. Empirically, our rewired transformer results in steady improvements in general language modeling as well as noticeably stronger information retrieval and extrapolation abilities compared to standard transformers.

We study whether a transformer network can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $\mathbb{N}\mathscr{T}$ defines an arithmetic text with measurable statistical structure. A transformer network (the GPT-2 architecture) is trained from scratch on the first $10^{11}$ elements and evaluated on next-token prediction and masked-token prediction tasks, with a Hidden Markov Model as baseline and a scaling analysis over context window, dataset size, vocabulary size and model size. The model reaches a word accuracy of about $0.4$, well above the baseline, and its performance remains stable on test blocks located at $10^{13}$-$10^{15}$, far beyond the training interval. Moreover, the likelihood assigned by the trained model separates the arithmetic text from two controls: synthetic token sequences that preserve the marginal token frequencies but not their order, with a separation that widens with the context, and sequences containing more than three consecutive square-free integers, a configuration that arithmetic forbids. These results indicate that the transformer captures regularities of the arithmetic text that go beyond its frequency profile.

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (RoPE) encode positions through fixed-angle rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce Selective RoPE, an input-dependent rotary embedding mechanism, that generalizes RoPE, and enables rotation in arbitrary angles for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with Selective RoPE, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

Autoregressive language models are usually trained with next-token prediction under a fixed left-to-right target order. This paper studies target-token organization as a training-time design choice across arithmetic reasoning, multi-label text classification, and text generation. Controlled order studies show that the default NTP order can be far from the best-performing tested organization, while fixed hand-crafted orders such as reverse order do not generalize across tasks. To address this, Max(MI(S;t)) is introduced as a deterministic mutual-information-based heuristic that prioritizes information-rich target tokens. For fixed-length outputs, it constructs task-specific prediction orders; for open-vocabulary text generation, the same principle is applied through lightweight prefix augmentation. Experiments with GPT-style models and pretrained Llama/Qwen variants show that Max(MI(S;t)) often improves over standard NTP and simple baselines such as reverse order, TF-IDF, and conditional-probability selection, without changing model architecture or autoregressive decoding.

We introduce Robust Filter Attention (RFA), a formulation of self-attention as a robust state estimator. Each token is treated as a noisy observation of a latent trajectory governed by a linear stochastic differential equation (SDE), and attention weights are determined by consistency under this model rather than static feature similarity. Under isotropic noise and decay assumptions, RFA matches the computational complexity of standard attention. On language modeling benchmarks, RFA achieves lower perplexity than RoPE within the training window while remaining stable under zero-shot extrapolation to longer contexts. The framework also provides a dynamical interpretation of standard positional mechanisms, connecting rotational embeddings and recency biases to transport and uncertainty propagation induced by stochastic dynamics.

Efficiently scaling Large Language Models (LLMs) necessitates exploring alternatives to dominant autoregressive (AR) methods, with Masked Diffusion Models (MDMs) emerging as candidates. However, comparing AR (typically decoder-only) and MDM (often encoder-only) paradigms is confounded by differing architectures, obscuring true algorithmic and efficiency trade-offs. This research decouples these factors by evaluating MDMs within a decoder-only framework to: (1) Equitably compare MDM (as Any-Order AR) and standard AR paradigms through discrepancies on orders. (2) Investigate MDM architectural impacts on computational efficiency. We show decoder-only MDMs, despite a larger modeling space, can achieve significant inference speedups ($\sim25\times$) and comparable perplexity with techniques like temperature annealing, offering a path to reduced inference compute. This work provides insights for developing more computationally efficient foundation models by disentangling core modeling choices from architectural influences. Code is available at https://github.com/scxue/AO-GPT-MDM.