As language-model compute continues to scale, high-quality training data is becoming an increasingly important bottleneck. Conventional next-token prediction supervises what follows a context but leaves the intermediate reasoning behind that continuation implicit. We introduce \textbf{REER-PT}, a scalable framework that extends Reverse-Engineered Reasoning (REER) to raw pre-training data. REER-PT identifies continuations that are difficult to predict but can still be inferred from the preceding context, and inserts concise reasoning annotations that reconstruct the missing connection between context and continuation. Candidate annotations are generated and refined offline, with perplexity serving as the optimization signal. Constraints on length and target leakage filter out unhelpful or trivial annotations. This sparse transformation preserves the source text and remains compatible with standard next-token prediction, avoiding online reasoning rollouts during pre-training. We apply REER-PT to transform a source pre-training corpus into an augmented one. Across augmented-data, original-token, and selected-continuation comparisons, perplexity reductions range from 0.42 to 7.29, and only about 0.05\% of annotation 13-grams appear verbatim in the source text. We then train two 680M-parameter models with the same architecture and training configuration on the source and augmented corpora, respectively. The augmented-data model gains up to 2.07 percentage points on several knowledge and reasoning benchmarks. Together, the perplexity analysis indicates improved continuation predictability, while the controlled pre-training experiments suggest that this augmentation can improve model performance without changing the standard pre-training objective.
Flow-matching language models refine all token positions in parallel and can trade sampling steps for latency, yet generation quality still degrades sharply with few sampling steps. We trace a source of this degradation to a train--inference mismatch in previous-prediction self-conditioning: during training, the self-conditioning input is computed from the current noisy state with no intervening solver step; during sampling, the solver folds the previous prediction into the latent before that same prediction reappears as the explicit self-conditioning input. This coupling, absent during training, creates redundancy that grows with step width. We show that the mismatch degrades both the self-conditioning input and the solver update, and derive a correction for each from the model's own structure. From the frozen projection weights we identify directions along which the self-conditioning input is redundant with the latent and dampen them; from the solver's integration structure we derive that a step-average prediction is needed and approximate it from prediction history, with scale set by offline trajectory statistics. The resulting sampler, Untied Self-Conditioning, requires no retraining and uses one evaluation per step. At 8 sampling steps on LangFlow, it reduces OpenWebText generative perplexity from $531$ to~$62$ ($8.6\times$); under an adapted Arena-Hard-Auto~v2 protocol, its outputs are preferred in $96\%$ of pairwise comparisons. On ELF-B it reduces generative perplexity from $71$ to~$43$. Improvements hold from 8 to 256 sampling steps.
Michael C. Mozer, Shoaib Ahmed Siddiqui, Danny Sawyer +2cs.LG
We describe an inference-time architectural enhancement for off-the-shelf foundation models that markedly reduces perplexity and boosts accuracy across generation and reasoning tasks. Our approach incurs essentially no additional latency during generation, though it requires serial processing in the prefill phase. Motivated by the fundamental limitation that state updates in feedforward transformers are bounded by model depth, our technique, recirculation, introduces a specific form of recurrence that allows the model to act as a dynamical system and track belief states. We distinguish this technique from chain-of-thought computation---which is better reserved for complex inferences rather than basic state tracking---as well as from popular depth-recurrence techniques (looping) and the costly training of recurrent transformers. We also propose and evaluate an adaptive variant of recirculation which requires only light tuning of hyperparameters while freezing the original model weights. Relative to the off-the-shelf baseline, adaptive recirculation achieves remarkable gains on the Gemma3 family, including a 23% reduction in perplexity on a suite of datasets, a 21% increase in accuracy on GSM8k, and reliable improvements in accuracy on other downstream tasks. Our training-free approach succeeds by leveraging the model itself to inform architectural modifications, suggesting a route to architectural evolution guided by a trained network's properties rather than forced, arbitrary design choices.
Franky Kevin Nando Tezoh, Ali Hussaini Umar, Alessandro Laio +2cs.CL
Reconstructing prompts that can elicit a desired answer or behaviour in an LLM is an open and important research topic. Optimisation methods which aim at minimising the perplexity of a given answer, however, consistently yield so-called pseudoprompts, unintelligible strings of tokens which can lack human interpretability. We argue that this is a consequence of the ill-posedness of the prompt optimisation task. By reframing the task as a Bayesian posterior inference over prompts, we propose an efficient algorithm to sample prompts which are both efficient (in terms of perplexity) and human readable. We compare our approach with state of the art alternatives showing on a real data set a marked improvement over a range of metrics.
Aggressive quantization disproportionately harms multilingual capability: in the sub-4B INT3 GPTQ regime, we measure 2-4x larger perplexity degradation on non-English languages than on English. We propose Language-Conditional Dequantization (LCD), a post-hoc method that attaches per-language rank-2 LoRA corrections to the linear layers of an already-quantized model, adding 0.12% parameters per language and training in under 20 minutes on a single GPU. Across Qwen2.5-3B and Llama-3.2-3B, LCD recovers 70-83% of the perplexity gap for non-Latin script languages and 17-28% of the GlobalMMLU accuracy gap, outperforming a language-agnostic correction of equal capacity by 3-9 points on typologically distant languages and a data-free low-rank baseline (LQER) by an order of magnitude. We further identify a perplexity-accuracy disconnect and trace it to where quantization concentrates damage: early-depth errors (Llama) propagate downstream and resist local correction, while late-depth errors (Qwen) do not. A layer-restricted variant of LCD validates this mechanism directly.
Embedded Language Flows (ELF) rely primarily on full non-causal attention for iterative denoising, repeatedly incurring quadratic sequence-mixing cost at each sampling step. Gated Delta Networks (GDNs) provide an efficient recurrent alternative, but their standard causal formulation cannot directly capture the bidirectional context required by ELF. We introduce DeltaFlow, a noise-adaptive bidirectional GDN backbone for continuous language denoising. We study two variants: DeltaFlow-A, which alternates scan directions across layers, and DeltaFlow-P, which performs parallel forward and backward scans within each layer. We further introduce noise-adaptive memory control and scheduled Temporal State Consistency (TSC) to stabilize hidden representations across nearby noise levels. On OpenWebText, using a 32-step stochastic differential equation sampler, DeltaFlow-P reduces generated perplexity from 24.218 for the full-attention ELF baseline to 21.228 while maintaining comparable unigram entropy, with 36B training-token exposure compared with 45B for the baseline. In a denoiser-only benchmark, DeltaFlow-P achieves a 2.72x throughput speedup over the full-attention baseline at a sequence length of 16k. These results show that DeltaFlow is a promising alternative to dense attention for efficient continuous language denoising.
Human language exhibits lawful structure at the level of words (frequency, vocabulary growth) and word pairs (co-occurrence across distance). Here we show that the arrangement of words in sequence -- a central determinant of meaning -- obeys a comparable law. Using large language models as probabilistic probes, we measured the reduction in target perplexity conferred by prior context at distance d beyond that of the same words scrambled; this difference, the contextual persistence function P(d), isolates the influence of arrangement. Across ten corpora spanning six language families and written and spoken modalities, P(d) decayed approximately as 1/d ($P(d) \propto d^{-α}$, mean $α= 1.04$; median $r^2 = 0.96$). The effect vanished in scrambled and synthetic controls, replicated across independent probes, and did not appear in genomic or protein sequences under domain-native models. An exponent near 1 distributes contextual influence approximately uniformly across logarithmic timescales. The results establish a scaling law of contextual persistence in human language.
Möbius RoPE is a rotary positional encoding built on the anti-periodic frequency ladder $θ_i=π(2i+1)/N$: every rotation plane advances by an odd multiple of $π$ across the training context, so the positional holonomy is $-1$ and the two ends of the sequence are deterministically coupled through a closed-form Dirichlet "dipole"; to our knowledge this is the first anti-periodic boundary condition in positional encoding. We verify the theory numerically to $\sim 10^{-6}$ and pretrain 48 models spanning six 160M-class and three 410M-class arms (2B FineWeb-Edu tokens each; the hybrid arm puts Möbius frequencies on 25% of heads). Hybrid perplexity is unchanged (29.66 vs. 29.72), but needle-in-a-haystack retrieval becomes reliable: $90.3\pm5.7\%$ versus $63.3\pm31.4\%$ at context 512 ($n=6$ seeds), observed worst seed 86% versus 14%, robust variance tests $p=0.013$-$0.029$ (unadjusted), recurring at 410M (Levene $p=0.040$). Matched controls isolate the mechanism: an aperiodic ladder in the same frequency band reproduces none of the effect, and a periodic (holonomy $+1$) ladder only a fraction. Swapping trained models' frequency table back to standard RoPE (weights frozen) collapses retrieval, with damage concentrated on far needles: trained models depend on this long-range geometry. A NoPE arm is even more reliable at short context but pays a 13% perplexity tax and extrapolates worst; only the anti-periodic hybrid pairs baseline perplexity with a high reliability floor. The effect is scoped to single-needle retrieval within the training window; a one-line frequency swap thus provides zero-cost insurance against the retrieval seed lottery.
Not all training samples contribute equally to large language model fine-tuning. Selecting informative training samples can reduce the computational cost while preserving downstream performance. Many existing data selection methods rely on indirect heuristics, such as data quality, diversity or reasoning trace length. However, the effectiveness of these fixed criteria is task-dependent and difficult to generalize across diverse downstream tasks. Perplexity-based data selection provides a simple and model-aware solution to estimate the sample difficulty, but existing approaches typically score the entire training sequence and ignore the difference in learning objectives of language modeling and reasoning tasks. In this paper, we propose PPL-Factory, a simple and interpretable data selection framework that combines task-aware perplexity-based scores and data budget-aware selection criteria. Experiments on GSM8K demonstrate that PPL-Factory outperforms other state-of-the-art data selection methods using only $1\%$ of the training set. With $10\%$ of the data, PPL-Factory exceeds full-data fine-tuning accuracy by 0.9 on GSM8K and 4.8 on MATH. Overall, our results demonstrate that task-aware and budget-aware perplexity-based selection provides an effective and applicable approach for efficient fine-tuning.
Autoregressive language models are least accurate at the beginning of a sequence, where little context forces reliance on a generic pretraining prior. We show that this cold-start penalty is domain dependent and reduce it with a domain-conditional position offset: a single learned vector added to the embedding activation at the first sequence positions while all model weights remain frozen. The offset trains in minutes on roughly one hundred documents, switches between domains without added sequence state, and has no measurable latency overhead. Across eight Mamba, GPT-NeoX, and Llama models spanning 410M to 8B parameters, it reduces held-out in-domain perplexity by up to 27%; the effect persists at 70B, and one position captures most of the benefit. A matched, converged direct logit-bias correction reaches at most only 7.9% and leaves later-token loss unchanged, showing that the offset propagates through model state rather than merely recalibrating the output prior. A tuned LoRA reaches lower perplexity but uses two to three orders of magnitude more parameters and an active low-rank weight path, while soft prompts add sequence positions. With wrong-domain controls, offsets improve retrieval reranking and domain classification when decisions depend on early in-domain tokens, For the few-shot reasoning whose signal occurs later, the results maintains unchanged. Position-aware prefill application also help generation tasks, whereas naive application at every cached decoding step causes repetition. The offset is therefore not the strongest adapter, but a lightweight, hot switchable tool for short in-domain scoring and calibration.
The CoTFormer architecture formalizes Chain-of-Thought as a form of recurrent latent computation, preserving intermediate states as attendable representations to mimic explicit reasoning traces. In this work, we evaluate CoTFormer and its structural variants across perplexity and compute efficiency metrics. Furthermore, we extend evaluation to controlled algorithmic settings to determine whether this recurrent framework improves out-of-distribution generalisation on inductive reasoning tasks.
Continuous diffusion language models such as ELF report record-low generative perplexity (Gen-PPL). We find a catch: these models repeat far more than human text, and Gen-PPL rewards rather than penalizes that repetition, so its low scores overstate quality. Strip the repetition and ELF-B's Gen-PPL rises from $19.5$ to $27.7$; the smallest model even posts the best Gen-PPL because it repeats most. We trace the repetition to its source: a contractive attractor along a \emph{single direction} in the self-conditioning feedback loop, the loop that feeds each step's clean estimate into the next. Because the failure is one-dimensional, a one-dimensional fix suffices, and we propose one. \textbf{ACE} (Attractor-Contrast-Escape) subtracts that single, label-free direction from the feedback at each step. Estimated once on the $105$M model, the direction cuts repetition to near the human level while keeping quality competitive, and transfers near-unchanged to the $342$M and $652$M models and across samplers; the same recipe recovers useful directions on other architectures. Since Gen-PPL itself rewards repetition, we instead measure the compute each fix needs to produce human-clean text, where ACE is $1.5$--$5\times$ cheaper.
Reza Bayat, Ali Behrouz, Aaron Courvillecs.LG cs.AI cs.CL
Modern language models, including transformer, recurrent, and memory-based variants, share a common chassis: a stack of identical layers in which parameters are allocated uniformly across depth. This is a default inherited from the original transformer and largely unchanged since, yet a growing body of evidence suggests that layers contribute non-uniformly to the final output, with later layers refining the residual stream rather than transforming it. We ask whether parameter capacity should reflect this asymmetry. Our controlled experiment shows that, under a fixed budget, allocating more capacity to earlier layers and less to later layers improves perplexity over a uniform-width baseline, while the reverse allocation hurts. Building on this result, we introduce Tapered Language Models (TLMs), an architectural principle in which a parameter-bearing component is monotonically tapered across depth under a fixed total budget. MLPs are the natural site for this instantiation: they dominate parameter count across all modern LM families and expose width as a single, clean axis of variation. Across three model scales and four architectures (Transformer, Gated Attention, Hope-attention, and Titans), tapering MLP width via a smooth cosine schedule consistently improves perplexity and downstream benchmark performance over uniform baselines, at no additional parameter or compute cost. These findings establish depth-aware capacity allocation as a simple, architecture-agnostic axis of language model design, a free lever hidden in plain sight.
Mullosharaf K. Arabov, Svetlana S. Khaybullinacs.CL
This paper presents a comparative study of parameter-efficient fine-tuning (PEFT) methods, including LoRA and QLoRA, applied to the task of adapting large language models to the Bashkir language, a low-resource agglutinative language of the Turkic family. Experimental evaluation is conducted on a Bashkir text corpus of 71k documents (46.9M tokens) using models of various architectures: DistilGPT2, GPT-2 (base, medium), Phi-2, Qwen2.5-7B, DeepSeek-7B, and Mistral-7B. To improve the reliability of results, each configuration was trained with three different random seeds. The lowest perplexity on the test set was obtained for GPT-2 medium with full fine-tuning (3.34). Meanwhile, QLoRA applied to Mistral-7B (3.79) and Phi-2 (3.81) achieved comparable quality with over 40 times fewer trainable parameters. However, we also observed cases of significant quality degradation when using PEFT for certain architectures (e.g., DeepSeek-7B with rank 8, perplexity = 129.55), indicating that the outcome depends critically on the choice of the base model and its tokenizer. Additionally, a qualitative analysis of generated texts based on Bashkir prompts revealed that models with the best perplexity do not necessarily produce the most coherent outputs: QLoRA-tuned models generated monolingual Bashkir continuations, whereas the fully fine-tuned model with the lowest perplexity frequently switched to English. The results suggest that QLoRA on 7B-scale models offers an effective compromise between quality and computational cost for Bashkir. To ensure reproducibility, open data, code, and trained adapters will be released upon acceptance.