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101 papers
The null token is turned into a diagnostic lens on hallucination and motivate evaluating abstention methods by both suppression and deletion costs, rather than by hallucination reduction alone.
Scaling transformer language models creates an inherent tension between expressivity and memory efficiency. While unique weights across layers preserve functional specialization---from input-grounding to abstract refinement---they incur a substantial memory footprint. Conversely, standard depth-sharing enforces uniform transformations that collapse representational diversity and degrade modeling quality. We introduce RecurrentGPT, a recurrent depth transformer where fixed-depth prelude and coda blocks bracket a single shared core iterated R times. Inspired by gated recurrent neural networks, we employ a lightweight projection and an elementwise update gate---conditioned on the hidden state, the fixed prelude output, and noise resampled at every step---to modulate the recurrent update. This allows the model to specialize the input to the same few layers across recurrences, rather than requiring many unique layers to achieve functional diversity. Under an isoFLOPS constraint, a 3-layer RecurrentGPT matches the accuracy of a 12-layer GPT-2 Small baseline with similar training and inference FLOPs, and leads MoR and heavy-tail depth sampling in all nine scale-by-budget cells; at medium and large scale it approaches dense quality at the standard token budget and overtakes it at medium scale once that budget is doubled. Under an isoPARAMS constraint, deeper recurrence achieves a 2.76 validation loss versus 2.84 for a non-recurrent counterpart at matched parameter and data budget. Our results demonstrate that adaptive depth reuse is a principled strategy for trading parameters for quality: at large scale, 63% fewer parameters and 59% less peak decoding memory for a 10% increase in compiled generation latency.
Post-training alignment is often shallow, eroding under fine-tuning. It remains untested as to whether constitutional midtraining interventions can produce durable alignment when cleanly isolated from post-training. We build a 394M-token constitutional corpus from Anthropic's Constitution and apply constitutional midtraining at 120B scale, where principled, values-based content is inserted into midtraining. A 2x2 design (curriculum ordering x deliberative reasoning) was used to produce four constitutionally midtrained conditions, plus a control, which were evaluated on self-generated and established benchmarks including alignment under pressure, value conflict resolution, blackmail, and emergent misalignment. All models were evaluated across three stages: post-midtraining, post-SFT, and post-benign fine-tuning. Constitutionally midtrained models outperformed the control on alignment generalization and durability, notably on blackmail: SFT instilled a blackmail propensity in all models, but constitutional midtraining blunted it, with the advantage surviving benign fine-tuning (-17.5pp). This durability did not extend to settings that required active resistance to in-context pressure or conflict, where the advantage attenuates after SFT. The presence of constitutional content at midtraining also mattered more than its structure, and constitutional midtraining incurred no capability cost, on average, at any stage (MMLU, ARC-Easy, piqa, GSM8K). A modest amount of constitutional content at midtraining could therefore yield broad, persistent alignment gains, offering a cheap, complementary addition to SFT-centered pipelines. Code, data, and models are available.
Reinforcement learning (RL) post-training for large language models (LLMs) follows a efficient paradigm of "rollout then update", which inevitably results in off-policy training data. To resolve this, Importance sampling (IS) is proposed, while the token-level ratios compound over long sequences, causing severe variance exploded. A natural idea is "transferring" these off-policy token into on-policy token, so that the importance scores for correction are unnecessary. Following this idea, we propose Selective Importance Sampling (SIS), which is inspired by rejection sampling. Concretely, SIS implements by viewing off-policy model as proposal distribution, and implement a token-level rejection test: accepted tokens are viewed as on-policy, so that receive unit importance score, while rejected tokens retain the standard IS correction. Our proposed SIS is theoretically proved reducing the gap between token-level and sequence-level off-policy gradient estimators. The SIS acts as a plug-in that only modifies the importance ratio in the policy loss, adding negligible wall-clock overhead, and can be combine with a vast vary of RL post-training algorithms. Experiments on dense and MoE LLMs across math and agent benchmarks show that SIS consistently improves all objectives, while providing substantially stronger robustness under off-policy data.
Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-$T$ spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-$T$. To explain this incongruity, we prove that Fourier domain sparsity is necessary but not sufficient for mod-$T$ geometric separability. Empirically, we investigate when model training yields geometrically separable features, finding that the data, architecture, optimizer, and tokenizer all play key roles. In particular, we identify two different routes through which models can acquire geometrically separable features: they can learn them from complementary co-occurrence signals in general language data, including text-number co-occurrence and cross-number interaction, or from multi-token (but not single-token) addition problems. Overall, our results highlight the phenomenon of convergent evolution in feature learning: A diverse range of models learn similar features from different training signals.
Although LLM context lengths have grown, there is evidence that their ability to integrate information across long-form texts has not kept pace. We evaluate one such understanding task: generating summaries of novels. When human authors of summaries compress a story, they reveal what they consider narratively important. Therefore, by comparing human and LLM-authored summaries, we can assess whether models mirror human patterns of conceptual engagement with texts. To measure conceptual engagement, we align sentences from 150 human-written novel summaries with the specific chapters they reference. We demonstrate the difficulty of this alignment task, which indicates the complexity of summarization as a task. We then generate and align additional summaries by nine state-of-the-art LLMs for each of the 150 reference texts. Comparing the human and model-authored summaries, we find both stylistic differences between the texts and differences in how humans and LLMs distribute their focus throughout a narrative, with models emphasizing the ends of texts. Comparing human narrative engagement with model attention mechanisms suggests explanations for degraded narrative comprehension and targets for future development. We release our dataset to support future research.
Self-distillation has emerged as an effective post-training paradigm for LLMs, often improving performance while shortening reasoning traces. However, in mathematical reasoning, we find that it can reduce response length while degrading performance. We trace this degradation to the suppression of epistemic verbalization - the model's expression of uncertainty during reasoning. Through controlled experiments varying conditioning context richness and task coverage, we show that conditioning the teacher on rich information suppresses uncertainty expression, enabling rapid in-domain optimization with limited task coverage but harming OOD performance, where unseen problems benefit from expressing uncertainty and adjusting accordingly. Across Qwen3-1.7B/8B, DeepSeek-Distill-Qwen-7B, and Olmo3-7B-Instruct, we observe performance drops of up to 40%. Our findings highlight that exposing appropriate levels of uncertainty is crucial for robust reasoning and underscore the importance of optimizing reasoning behavior beyond merely reinforcing correct answer traces.
Large Language Models (LLMs) show promise in generating long-form scientific explanations that synthesize evidence and connect multiple factors. However, in long-form scientific question answering, LLMs often hallucinate, producing unsupported or inconsistent claims. Retrieval-Augmented Generation (RAG) improves trustworthiness by grounding generation in external sources; scientific simulators are valuable because they can validate quantitative hypotheses and capture evolving dynamics. Yet simulation-based RAG is non-trivial due to two challenges: how to retrieve from scientific simulators, and how to efficiently verify and update long-form answers. To overcome these challenges, we propose SimulRAG, a simulator-based RAG framework with a generalized retrieval interface that translates between text and simulator parameters/outputs. SimulRAG further introduces claim-level generation with uncertainty estimation and simulator boundary assessment (UE+SBA) to selectively verify and update claims. Unlike tool-first or holistic answer revision, it first elicits diverse answers without retrieval and then grounds uncertain, simulator-verifiable atomic claims with simulator evidence. We also release a long-form scientific QA benchmark spanning climate science, epidemiology, and urban planning, with ground truth verified by simulations and human annotators. Experiments show SimulRAG improves informativeness by 30.4% and factuality by 16.3% over the strongest adapted RAG baselines, while UE+SBA enhances claim-level efficiency and quality.
Human ratings are the gold standard in NLG evaluation. The standard protocol is to collect ratings of generated text, average across annotators, and rank NLG systems by their average scores. However, little consideration has been given as to whether this approach faithfully captures human preferences. Analyzing this standard protocol through the lens of utility theory in economics, we identify the implicit assumptions it makes about annotators. These assumptions are often violated in practice, in which case annotator ratings cease to reflect their preferences. The most egregious violations come from using Likert scales, which provably reverse the direction of the true preference in certain cases. We suggest improvements to the standard protocol to make it more theoretically sound, but even in its improved form, it cannot be used to evaluate open-ended tasks like story generation. For the latter, we propose a new human evaluation protocol called $\textit{system-level probabilistic assessment}$ (SPA). When human evaluation of stories is done with SPA, we can recover the ordering of GPT-3 models by size, with statistically significant results. However, when human evaluation is done with the standard protocol, less than half of the expected preferences can be recovered (e.g., there is no significant difference between $\texttt{curie}$ and $\texttt{davinci}$, despite using a highly powered test).
Trained transformer models develop privileged bases: coordinate axes whose statistics differ from the rest of the residual stream. But what kind of direction does such a basis select? We investigate the prediction direction, the unembedding direction of the token a model currently predicts, and find that it functions as a content-defined privileged anchor. Measured with respect to this anchor, residual-stream variation is geometrically and behaviorally stratified by proximity to the prediction. The stratification holds in all eighteen models tested (dense and mixture-of-experts, 7B-120B, base and instruction-tuned). A narrow, scale-invariant prediction interface concentrates readout-relevant structure, while the vast prediction-distal complement expands with model scale. Because the prediction direction sits nearly orthogonal to the principal variance axes, variance-based analyses recover this organization only partly, and the shortfall grows with prompt heterogeneity. Anchoring reveals a steep geometric gradient: prediction-proximal regions are highly structured and cluster related prompts, while the complement is flatter and anti-discriminates among prompt groups. The interface is a narrow slice but functionally decisive. Disrupting the variance directions closest to the prediction causes immediate divergence and frequent task-frame shifts; disrupting the next level down delays divergence and preserves framing. The complement is weakly readout-aligned per direction yet causally and temporally load-bearing, and behavior is driven by direction rather than magnitude. These results establish the prediction direction as a privileged anchor distinct from previously described coordinate axes, and give a geometric account of how high-dimensional computation coexists with linear readout.
Activation steering has emerged as a lightweight approach for modifying language model behavior without parameter updates, yet existing methods remain brittle: unstable across layers and prone to disturbing behavior unrelated to the target concept. We trace these failures to a hidden assumption shared by widely-used methods such as CAA, ActAdd, and ITI: that the intermediate activation space is Euclidean. We show this assumption is fundamentally flawed. The metric that actually governs how a hidden-state perturbation changes the output is the Fisher information metric of the softmax layer, pulled back to the intermediate layer through the Jacobian of the intervening layers. From it we derive a closed-form steering direction, applied to a hidden state at an intermediate layer, that reaches a target concept change with the least non-target distortion. The framework is sharpest in the early and middle intermediate layers, where the metric is strongly non-Euclidean and geometric correction matters most. We evaluate it on three verb-morphology concepts: third-person-singular, progressive, and past-tense inflection, following standard counterfactual-concept evaluation. On GPT-2 Small, this non-Euclidean geometry is borne out empirically, and our method lowers off-target KL divergence by median factors of 1.4--6.5x against individual steering baselines. On Llama-3-8B and Qwen3-8B, it lowers off-target KL by median factors of 1.8--3.6x against individual baselines at the early and middle layers. These results show that geometric correction retains its advantage on larger models with more complex internal structure.
Large Language Models (LLMs) have achieved remarkable success, underpinning diverse AI applications. However, they often suffer from performance degradation due to factors such as catastrophic forgetting during Supervised Fine-Tuning (SFT), quantization, and pruning. In this work, we introduce a performance recovery framework based on Self-Distillation Fine-Tuning (SDFT) that effectively restores model capabilities. Complementing this practical contribution, we provide a rigorous theoretical explanation for the underlying recovery mechanism. We posit that an LLM's generative capability fundamentally relies on the high-dimensional manifold constructed by its hidden layers. To investigate this, we employ Centered Kernel Alignment (CKA) to quantify the alignment between student and teacher activation trajectories, leveraging its invariance to orthogonal transformations and scaling. Our experiments demonstrate a strong correlation between performance recovery and manifold alignment, substantiating the claim that self-distillation effectively aligns the student's high-dimensional manifold with the optimal structure represented by the teacher. This study bridges the gap between practical recovery frameworks and geometric representation theory, offering new insights into the internal mechanisms of self-distillation.