Spiking neural networks (SNNs) offer a path to energy-efficient language modeling through sparse encoding and event-driven computation, but training capable spiking language models from scratch remains difficult. A practical alternative is ANN-to-SNN migration through knowledge distillation (KD), where a pretrained artificial neural network (ANN) teacher supervises an SNN student. Existing migration approaches distill on fixed corpus prefixes, whereas autoregressive inference conditions on self-generated prefixes, creating prefix-source mismatch. It manifests as output-policy mismatch with the ANN teacher and internal spiking-dynamics drift between self-generated and matched corpus prefixes. On-policy distillation (OPD) offers a natural way to mitigate both manifestations by continuing teacher supervision on self-generated prefixes. We evaluate a teacher-only full-KL variant, Vanilla OPD, via a controlled stress test and observe it may suffer from delayed rollout-feedback collapse. This result shows that on-policy coverage alone does not ensure stable adaptation. Motivated by these findings, we propose SpikeOPD, a stable on-policy distillation framework for autoregressive SNNs that learns from self-generated prefixes while maintaining rollout stability. It applies full-KL teacher correction to reduce output-policy mismatch, while matched-prefix policy anchoring constrains policy departure from the frozen reference SNN on the same prefixes. Layerwise spike regularization further limits firing-rate deviations during on-policy adaptation. Across three model scales, SpikeOPD improves average accuracy over the corresponding KD SNNs by 0.8, 1.7, and 2.9 points at 0.125B, 0.35B, and 1.3B, respectively, while preserving their sparse-compute profiles.
Modern sequence models, from Transformers to State Space Models, have enabled powerful generative modeling across diverse domains, yet they are typically trained to predict what happens while treating when it happens as a secondary concern. In data-mining settings where events are associated with explicit timing information, this separation can limit temporal reasoning, anomaly detection, and faithful reconstruction of event chronology. A common strategy is to treat timing as an auxiliary signal, training a separate timing model using representations learned solely for event prediction. However, this two-stage approach implicitly assumes that representations optimized for event prediction already contain sufficient temporal structure. We introduce ChronoSSM, an autoregressive State Space Model (SSM) that jointly models events and timestamps with a shared backbone trained using combined token and temporal generation objectives. We compare the joint regime, where temporal supervision updates the backbone, with the two-stage regime, where timing is learned only using the frozen event representations. Across four domains spanning dense and partial timestamp supervision, joint training consistently makes inter-arrival information more recoverable from frozen representations without any systematic degradation in content-generation quality overall. Our results show that temporal supervision can produce more temporally informative representations without materially degrading autoregressive event modeling.
Large autoregressive language models exhibit a self-correction blind spot: they reliably fix identical errors when attributed to an external source yet fail to fix the same errors in their own outputs. Prior work has documented this phenomenon empirically, through controlled error injection, error-depth decompositions, RL-based verifier-corrector training, and intrinsic self-verification, but offers no formal model of why generating a token suppresses the ability to detect its error, no quantitative activation condition for correction markers, and no convergence guarantee for reinforcement-learning-based self-correction. We close these gaps with SPARC, a spectral-algebraic theory of self-correction in autoregressive generation. We define the error-propagation operator as the product of per-step attention Jacobians on the residual stream and prove that the blind spot arises if and only if the spectral radius of this operator is at least one. We derive a sharp activation threshold, given as a function of the spectral radius, that a correction marker must exceed, recovering the 89.3\% blind-spot reduction observed with a simple ``Wait'' marker. We further prove that RL-based verifier-corrector training converges at a rate proportional to the squared coupling strength over the square root of the number of samples if and only if the verifier-corrector coupling matrix has spectral norm below one, and that this criterion is invariant across residual-stream autoregressive modalities, unifying text LLMs and autoregressive image and video generation. Experiments across four backbones and a visual autoregressive probe validate every theorem, with spectral predictions matching measured blind-spot rates within 3.2\% RMSE.