Attractors

Model-Based Reinforcement Learning distinguishes between physical dynamics models operating on proprioceptive inputs and latent dynamics models operating on high-dimensional image observations. A prominent latent approach is the Recurrent State Space Model used in the Dreamer family. While epistemic uncertainty quantification to inform exploration and mitigate model exploitation is well established for physical dynamics models, its transfer to latent dynamics models has received limited scrutiny. We empirically demonstrate that latent transitions are biased toward well-represented regions of latent space, exhibiting an attractor behavior that can deviate from true environment dynamics. As a result, discrepancies in environment dynamics may not manifest in latent space, undermining the reliability of epistemic uncertainty estimates. Because these attractors often lie in high-reward regions, latent rollouts systematically overestimate predicted rewards. Our findings highlight key limitations of epistemic uncertainty estimation in latent dynamics models and motivate more critical evaluation of this method.

Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent \emph{monostability trap}: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the \textbf{Hysteresis Graph ODE (HGODE)}, which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.

We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes, eight GABAergic interneuron classes), forty-seven compartments, multi-rule plasticity (recurrent Hebb, BCM anti-saturation, mossy-fiber short-term, endocannabinoid iLTD, burst-gated Hebb), and a bimodal cholinergic encoding/consolidation cycle. Evaluated on pattern completion across auto-associative, associative, and temporal regimes, and on a controlled inhibitory-proportion manipulation at $N{=}256$, the full architecture exhibits \emph{three qualitative signatures absent from a minimal Hopfield baseline}: (i)~multi-attractor cross-seed behaviour at $K{=}5$ with biologically realistic inhibitory proportions, where two of five seeds converge to positive attractors with margin ${+}0.10{-}0.22$ (Cohen's $d{=}0.71$, one-sided $p{=}0.08$); (ii)~target-selective associative recall in paired $(A, B)$ memory at $K{\geq}5$, where the full model retrieves $B$ from a partial cue of $A$ while the minimal model echoes $A$ (Pearson margin $Δ{=}{+}0.163$ at $K{=}5$); (iii)~reduced cross-seed variance of the full model below the minimal baseline under clean upstream, with ratios $1.0{-}3.0$. These three signatures are architecture-specific: they appear consistently across independent regimes and are absent from the minimal control.

Constitution-conditioned post-training can be analysed as a structured perturbation of a model's learned representational geometry. We introduce ATLAS, a geometry-first program that traces constitution-induced hidden-state structure across charts, models, and substrates. Instead of treating the relevant unit as a single behaviour, neuron, vector, or patch, ATLAS tests a local chart whose tangent structure, occupancy distribution, and behavioural coupling can be measured under system change. On Gemma, the anchored source-local chart captures 310 / 320 reviewed source rows and all 84 / 84 reviewed score-flip rows, but compact exact-patch sufficiency does not close, so the exportable unit is the broader source-defined family. Freezing that family, we re-identify a target-local realisation in an unadapted Phi model, where the fully adjudicated confirmatory contrast separates with AUC 0.984 and mean gap 5.50. In held-out ALM8 mouse frontal-cortex perturbation data, the same source-defined family receives support across 5/5 folds, with mean held-out AUC 0.72 and mean fold gap 4.50. A multiple-choice analysis provides the main boundary: nearby target-local signals can appear without source-faithful closure. The resulting correspondence is not coordinate identity, site identity, or a target-side mediation theorem. It is geometric recurrence under redistribution: written constitutions can induce recoverable latent geometry whose organisation remains detectable across model and substrate changes while its local coordinates, occupancy, and behavioural expression shift.

Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To address this question, we introduce adaptive time scales through a leak term in recurrent neural networks (RNNs), forming leaky RNNs discretized from the continuous attractors of firing rate models. Our results demonstrate that leaky RNNs substantially enhance the emergence of well-defined and highly regular hexagonal firing patterns. Compared with vanilla RNNs lacking a leak term, the trained leaky RNNs produce more accurate position estimates while generating reliable grid-cell-like representations. Furthermore, under identical noise conditions, leaky RNNs consistently exhibit more stable dynamics and better-defined grid structures. The learned dynamics also give rise to stable torus attractors with a clear central hole, supporting robust and regular grid-like activity. Overall, the dynamic leak acts as a low-pass filtering mechanism that protects recurrent neural circuitry from noise, stabilizes network dynamics, and improves path-integration accuracy in recurrent neural networks.

We present causal evidence that hallucination in autoregressive language models is an early trajectory commitment governed by asymmetric attractor dynamics. Using same-prompt bifurcation, in which we repeatedly sample identical inputs to observe spontaneous divergence, we isolate trajectory dynamics from prompt-level confounds. On Qwen2.5-1.5B across 61 prompts spanning six categories, 27 prompts (44.3%) bifurcate with factual and hallucinated trajectories diverging at the first generated token (KL = 0 at step 0, KL > 1.0 at step 1). Activation patching across 28 layers reveals a pronounced causal asymmetry: injecting a hallucinated activation into a correct trajectory corrupts output in 87.5% of trials (layer 20), while the reverse recovers only 33.3% (layer 24); both exceed the 10.4% baseline (p = 0.025) and 12.5% random-patch control. Window patching shows correction requires sustained multi-step intervention, whereas corruption needs only a single perturbation. Probing the prompt encoding itself, step-0 residual states predict per-prompt hallucination rate at Pearson r = 0.776 at layer 15 (p < 0.001 against a 1000-permutation null); unsupervised clustering identifies five regime-like groups (eta^2 = 0.55) whose saddle-adjacent cluster concentrates 12 of the 13 bifurcating false-premise prompts, indicating that the basin structure is organized around regime commitments fixed at prompt encoding. These findings characterize hallucination as a locally stable attractor basin: entry is probabilistic and rapid, exit demands coordinated intervention across layers and steps, and the relevant basins are selected by clusterable regimes already discernible at step 0.

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the \textit{Spectral Sensitivity Theorem}, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment. We validate this theory by analyzing the eigenspectra of activation graphs in Whisper models (Tiny to Large-v3-Turbo) under adversarial stress. Our results confirm the theoretical prediction: intermediate models exhibit \textit{Structural Disintegration} (Regime I), characterized by a $13.4\%$ collapse in Cross-Attention rank. Conversely, large models enter a \textit{Compression-Seeking Attractor} state (Regime II), where Self-Attention actively compresses rank ($-2.34\%$) and hardens the spectral slope, decoupling the model from acoustic evidence.

Existing data poisoning attacks on retrieval-augmented generation (RAG) systems scale poorly because they require costly optimization of poisoned documents for each target phrase. We introduce Eyes-on-Me, a modular attack that decomposes an adversarial document into reusable Attention Attractors and Focus Regions. Attractors are optimized to direct attention to the Focus Region. Attackers can then insert semantic baits for the retriever or malicious instructions for the generator, adapting to new targets at near zero cost. This is achieved by steering a small subset of attention heads that we empirically identify as strongly correlated with attack success. Across 18 end-to-end RAG settings (3 datasets $\times$ 2 retrievers $\times$ 3 generators), Eyes-on-Me raises average attack success rates from 21.9 to 57.8 (+35.9 points, 2.6$\times$ over prior work). A single optimized attractor transfers to unseen black box retrievers and generators without retraining. Our findings establish a scalable paradigm for RAG data poisoning and show that modular, reusable components pose a practical threat to modern AI systems. They also contribute to interpretability research by revealing a strong link between attention concentration and model outputs.