Multi-agent systems built on large language models (LLMs) require many coordination choices that are difficult to fix a priori: which skill protocol to invoke, which agent role should perform a subtask, which model to bind to each role, how roles should interact, when to use retrieval or verification, and when to omit a step entirely. These choices interact with task regime and operational constraints, so static pipelines and one-off model comparisons provide only a limited view of the design space. This paper introduces AgensFlow, an open-source framework that treats multi-agent coordination as an online policy-learning problem under partial observability. The framework makes coordination decisions observable and learnable from repeated trajectories, rather than treating skill, role, model, topology, and evaluation choices as fixed pipeline design. AgensFlow is evaluated on two corpora: distributed-systems incident tasks and security-advisory tasks. The evaluation shows three main results: learned routing reaches a higher-quality operating point than a fixed pipeline baseline on coordination-heavy classes; skip:X isolates topology compression as a meaningful part of the substrate; and warm-started policy graphs can reduce exploration cost while preserving plateau quality. Overall, the results support that learned, auditable routing can improve coordination-heavy multi-agent workflows over static wiring.

Trajectory is betting the rapid iteration cycle that supercharged vibe-coding can help all kinds of companies build AI products that learn continuously. Trajectory founders, Ronak Malde (left), Michael Elabd(center), and Arjun Karanam (right). A group of AI researchers who previously worked at Google DeepMind, Apple, OpenAI, and Meta Superintelligence Labs announced on Wednesday they're launching a new startup called Trajectory, which aims to help companies regularly improve their AI products by training on real-world user interactions. Trajectory wants to build a platform for AI that can learn continuously, a capability that researchers have long held up as a major barrier to further AI progress. OpenAI, Google, and Anthropic have found success training increasingly capable versions of AI models, especially for domains such as coding, math, and science.

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a move that remains on the learned data manifold and, paired with a Metropolis-Hastings correction, samples from energy-modified targets. For synthetic languages, we show that minimal U-turn dynamics undergoes an ergodicity-breaking phase transition driven by fragmentation of the data manifold; ergodicity is restored at larger U-turn magnitude. In the non-ergodic regime, low-level features relax faster than high-level ones, an ordering that inverts only at sufficiently large U-turn magnitude. We test these predictions on natural language and natural images. In both modalities, minimal U-turns relax slowly, especially for high-level features approximated by deep representations in CNNs or LLMs. The layer-ordering inversion appears only at large noise when mixing is efficient -- signatures consistent with strongly constrained, weakly mixing local dynamics. We discuss the implications of these results for sampling with diffusion models.

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's dynamics. Recently, score-based diffusion models have learned global diffusion priors that effectively model (stochastic) dynamics, revealing strong potential for data assimilation. In this paper, we investigate how information from noisy observations can be incorporated to enable continuous correction and refinement of the predicted system state when using a diffusion prior. Motivated by particle filtering methods, we represent the posterior distribution using a set of particles. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. Nevertheless, such guidance does not guarantee sampling from the true posterior. We therefore employ a Sequential Monte Carlo approach over the diffusion trajectory, viewed as a path measure, to reweight and resample particles, thereby correcting the generation process and ensuring convergence toward the desired posterior distribution. This leads to an unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.

We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems, where the process rapidly mixes within basins while transitions between basins occur rarely on the timescale of interest, or even when the state space is reducible. Existing approaches typically rely on spatial discretization or spectral analysis of estimated transition operators, which can become unreliable in high dimensional settings or when the underlying basin geometry is highly nonlinear. We propose a discriminative approach to basin identification based on marginal trajectory distribution comparison. We prove a simple risk separation result: if two initial states belong to the same basin, the Bayes-optimal classifier distinguishing their marginal trajectory distributions achieves risk close to 1/2, whereas if they lie in distinct basins, the optimal risk is close to zero. This observation reduces basin detection to a two-sample discrimination problem between marginal trajectory distributions. Motivated by this principle, we develop a neural algorithm that receives a set of candidate basin representatives and iteratively merges them by estimating classification risk with a neural network that approximates the Bayes classifier. We evaluate the method on various metastable systems. These include synthetic systems constructed by embedding low-dimensional dynamics into high dimensional noisy ambient spaces. In these settings, standard spectral and clustering-based methods often fail, while our approach accurately recovers the underlying basin structure. These results display a shortcoming of existing methods and highlight trajectory discrimination as an effective tool for identifying dynamical basins in high dimensional stochastic systems.

We study inference-time alignment for diffusion-based generative models, aiming to steer a base model toward high-reward outputs without updating its weights. Recent Sequential Monte Carlo (SMC)-based steering methods approximate reward-tilted target distributions in a principled way, but their proposals remain largely tied to the base sampler. Since reward information is mainly used after propagation through particle reweighting and resampling, these methods can require large particle budgets and suffer from weight degeneracy and high-variance estimates. One way to reduce variance and improve particle efficiency is to iteratively learn twisting functions that provide look-ahead guidance, as in twisted SMC. However, existing learnable twisting methods are developed mainly for classical sequential inference and can be unstable when applied to diffusion-based alignment with high-dimensional state spaces and terminal, noisy, or black-box rewards. We propose Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC), a trust-region framework for learning twisting functions in SMC-based inference-time alignment. Each iteration computes an exact KL-constrained update in path space, which admits a closed-form solution by tempered importance reweighting, and projects this target back to the parameterized twisted family by weighted maximum likelihood. Theoretically, we formalize the value-function interpretation of the optimal twisting function and show that it yields a zero-variance sampler. We prove that the trust-region update follows an escort path toward the target distribution, that the weighted maximum-likelihood update is a forward-KL projection, and that the path reduces residual importance-weight variance. Empirically, TRI-TSMC improves primary alignment objectives on discrete diffusion text generation and text-to-image generation under matched inference-time budgets.

This paper proposes StrTransformer, a source-wise structured Transformer framework for blind source recovery and branch-wise latent modeling. Instead of using an encoder to infer latent variables, StrTransformer directly optimizes the latent source matrix together with an observation-space mixer and source-wise structural Transformer branches. The mixer enforces reconstruction consistency, while each Transformer branch imposes a differentiable structural constraint on one latent source trajectory. Specifically, each source is converted into multi-scale patch tokens, randomly masked, processed by a locality-biased Transformer, and evaluated through a masked patch reconstruction energy. This energy acts as an implicit source-wise structural prior. To encourage different latent branches to specialize into different temporal regimes, StrTransformer further introduces an ordered multi-scale controller that learns branch-specific patch-scale weights, ordered scale centers, and locality attention slopes. The resulting objective combines observation reconstruction, source-wise structural regularization, and modular auxiliary penalties for separation and scale specialization. We analyze the decoupling and coupling structure of the objective, the regularized exact-reconstruction fiber, and the reduction of permutation symmetry induced by ordered branch descriptors. A controlled case study shows that the learned branches converge to distinct temporal-scale structures and recover source-aligned latent trajectories under post-hoc evaluation.

Deep learning is increasingly viewed as a dynamical process in parameter space, yet many existing theories still treat training as a closed optimization system. This view is limited for real-world AI, where models operate under uncertainty, resource constraints, distribution shift, downstream decision risks, and human feedback. We propose Human-Centered Learning Mechanics (HCLM), a dynamical and information-theoretic framework for open and controlled learning systems. The central idea is that entropy regularization is useful only when the chosen entropy surrogate generates a non-degenerate information force along the optimization trajectory. Otherwise, entropy terms may produce weak, unstable, or misaligned gradients, causing the dynamics to collapse toward ordinary loss minimization. We introduce the notion of effective entropy and study tractable geometric entropy surrogates, including variance-based and log-determinant covariance proxies. The paper makes three contributions. First, it formalizes entropy regularization through effective information force and characterizes degenerate entropy regimes. Second, it derives convergence, entropy-flow, Wasserstein-gradient-flow, and noisy-representation generalization results under explicit assumptions. Third, it offers a conditional dynamical interpretation of scaling-law-like behavior as a balance between information injection, entropy dissipation, and residual risk, without claiming an unconditional derivation of empirical neural scaling laws. Controlled representation-learning experiments support the hypothesis that geometric entropy surrogates, especially log-determinant covariance entropy, induce stronger and more stable information forces than softmax-normalized entropy.

Agentic text-simulation systems write in sequence, with each item becoming possible context for later steps. That makes uncertainty path-dependent: an early ambiguity can affect later outputs. This paper studies this problem with HawkesLLM, a framework that separates temporal influence modeling from text generation. We represent the cascade as a network whose nodes are text-generating agents. A multivariate Hawkes process models how these nodes activate over time and which earlier node outputs should influence later prompts. A language model then writes each new event from the compact memory selected by this temporal model. We evaluate the framework on a held-out Global Database of Events, Language, and Tone (GDELT) news-cascade case study. The diagnostics track semantic alignment with local held-out references and separate local drift from global drift. In this setting, HawkesLLM improves late-stage semantic alignment under a compact prompt-memory budget.

Language models trained on observed sequences are often described as learning the conditional distribution of the next token given previous tokens. This description is only conditionally correct. A model trained on realized token trajectories does not observe full conditional laws; it receives sampled continuations. Moreover, real language generation is conditioned not only on previous words but also on non-textual circumstances: facts, events, intentions, goals, beliefs, social context, and task-specific constraints. This paper distinguishes three objects that are often conflated: the full conditional language process conditioned on latent circumstances, the marginal text-only process obtained by integrating those circumstances out, and the model-induced distribution learned from finite observed corpora. The paper argues that interpreting model training as estimating the marginal text-only law requires strong assumptions of stationarity, representativeness, and ergodicity, assumptions that are standard in statistical estimation but problematic when applied to heterogeneous language corpora. Even if these assumptions hold, the marginal text-only law is useful only when the observed prefix is an approximately sufficient statistic for the latent circumstances relevant to continuation. In information-theoretic terms, usefulness requires that the residual conditional mutual information between the next token and the omitted circumstances, given the observed text, be small. The paper then extends this argument to heterogeneous training corpora. Finally, the paper interprets Retrieval Augmented Generation (RAG) and tool use as conditional sufficiency devices.