TractOracle: Oracle-Guided Frameworks

• TractOracle is a suite of computational frameworks that employs transformer-based oracles to guide RL tractography and automata-theoretic query evaluation.
• Its methodologies fuse anatomical priors with Markov Decision Process modeling and complexity-theoretic classification to optimize decision-making.
• Iterative reward training and diverse algorithmic variants consistently enhance plausible streamline generation while mitigating reward model drift.

TractOracle encompasses a family of computational frameworks and methodologies integrating oracle-based evaluation and guidance mechanisms into automated reasoning, tractography, or query evaluation processes. The most prominent instantiations of TractOracle center on RL-based tractography in diffusion MRI, the complexity-theoretic classification of regular trail queries in graph databases, and neuro-symbolic test oracle synthesis in program analysis. Each instantiation exploits an “oracle”—typically a transformer-based model or algorithmic criteria trained to encapsulate anatomical, logical, or axiomatic priors—to enforce validity and optimize decision-making beyond local signal or naïve heuristics.

1. RL-Based Tractography: Anatomically-Informed Oracles

TractOracle-RL formulates white-matter tract reconstruction as a Markov Decision Process (MDP) where the agent sequentially propagates from seed points, guided by local fiber orientation and an oracle-derived reward. The state representation $s_t$ comprises the local fiber-orientation distribution function (fODF) (either patches of spherical harmonics coefficients or 3D-convolved local tensors) concatenated with the previous $100$ tracking directions. Action $a_t \in \mathbb{R}^3$ is a unit-norm direction sampled from a parameterized stochastic policy $\pi_\theta(s_t)$, advancing a fixed step. The transition model deterministically increments position: $p_{t+1} = p_t + \Delta a_t$, and re-extracts the contextual state.

The reward function merges a local tracking term and a global anatomical term inferred by the oracle network $\Omega_\psi$:

$r_t = |\langle a_t, v_{\max}(p_t) \rangle| \cdot \langle a_t, a_{t-1} \rangle + \alpha \, \mathds{1}_{\Omega_\psi(P_{0..t}) \ge 0.5 \wedge (t=T)}$

where $v_{\max}(p_t)$ is the peak fODF direction at location $p_t$, and $\mathds{1}$ triggers the terminal anatomical reward based on oracle plausibility. Empirically, setting $\alpha=10$ achieves a balance between local and global terms (Levesque et al., 15 Jul 2025, Théberge et al., 26 Mar 2024).

2. Oracle Network Construction and Operation

The TractOracle anatomical oracle, $\Omega_\psi$, is instantiated as a compact transformer ($4 \times 4$ attention blocks, $\sim550$K parameters), ingesting resampled streamline segments (typically $32$–$128$ points, direction vectors) prepended with a learnable “CLS” token. The CLS final embedding passes through a linear-sigmoid head, outputting a plausibility score in $[0,1]$. The oracle is trained via mean-squared error against curated silver-standard positive/negative labels, sourced from pipelines such as PFT, Tractometer, RecobundlesX, extractor_flow, and Verifyber. Augmentation includes random flips, cropping, and noise (Levesque et al., 15 Jul 2025, Théberge et al., 26 Mar 2024).

Early stopping utilizes $\Omega_\psi$ at each trajectory extension. When $t > T_{\text{min}}$ and $\Omega_\psi(P_{0..t}) < 0.5$ (with $T_{\text{min}} = 20$), tracking aborts. Additional termination criteria include white-matter occupancy decline and excessive stepwise angular deviation.

3. Iterative Reward Training: Oracle–Policy Co-Evolution

Iterative Reward Training (IRT) extends the RL protocol by cyclically updating both the agent policy $\pi_\theta$ and the oracle $\Omega_\psi$ to mitigate reward model drift and improve anatomical alignment. Initially, $\Omega_\psi$ is trained on classical streamline tracks. In each IRT iteration, $\pi_\theta$ is trained with the current oracle, generates new candidate streamlines, which are labeled as plausible/implausible via bundle filtering methods, and appended to the training data. The oracle is then fine-tuned on the expanded mixed-agent classical-positive dataset. Loss is:

$$L_{\text{oracle}}(\psi) = \mathbb{E}_{(P, y)} \left[(\Omega_\psi(P) - y)^2\right]$$

IRT consistently boosts plausible streamline counts by up to $50\%$ and prevents reward hacking phenomena over extended training (Levesque et al., 15 Jul 2025).

4. Algorithmic Variants and Extensions

Several policy optimization frameworks are embedded within TractOracle-RL:

• SAC-1K/SAC-3K: Soft Actor-Critic trained for $1000$ or $3000$ episodes.
• DroQ-1K: SAC augmented with Dropout Q-functions and increased update-to-data ratio (UTD $=5$).
• CrossQ-3K/CrossQ-AE: Cross-critic architecture with BatchNorm across concatenated state-action pairs, optionally replacing fODF context with 3D-Conv autoencoder latent embedding.
• IRT Variants: SAC-IRT and CrossQ-IRT are trained within the IRT loop, ensuring oracle adaptation to policy-induced distributions.

Extended RL training up to $3000$ episodes, as well as the use of richer state context (autoencoder latents), showed marginal further improvements which were offset by computational cost (Levesque et al., 15 Jul 2025).

5. Quantitative Performance and Empirical Robustness

TractOracle-based tractography and classification achieve substantial advances in anatomical validity and reduction of false positives across both synthetic (ISMRM2015 phantom, Tractometer metrics) and in vivo datasets (BIL&GIN, TractoInferno, HCP105, Penthera 3T):

Metric	TractOracle(-RL)	Track-to-Learn	sd_stream/iFOD2/PTT
VC (%)	88	66	–
IC (%)	12	34	44
NC (%)	0.73	2.85	–
F1 (%)	~57	~57	–
Plausible (in vivo)	3–20× higher	–	–

Accuracy, sensitivity, and F1-score for streamline classification reach $97\%$, $98\%$, and $96\%$, respectively, on ISMRM2015 (Théberge et al., 26 Mar 2024). IRT-trained oracle-guided RL agents generalize robustly across datasets, showing no indication of reward hacking after thousands of episodes. Cross-dataset transfer recovers $2$–$7$ times more plausible streamlines than non-oracle baselines. Oracle inference speed is optimized at $32$ streamline points with no loss of classification performance.

6. Theoretical Oracle: Regular Trail Query Trichotomy

In automata-theoretic settings, “TractOracle” denotes a decision procedure for the tractability of regular trail queries (RTQ) over edge-labeled graphs (Martens et al., 2019). For a fixed regular expression $r$ (language $L$), the RTQ decision problem is classified as:

• AC⁰: $L$ finite.
• NL-complete: $L \in \mathrm{Ttract}$, satisfying left-synchronized containment and power abbreviation properties, verified in NL for DFAs.
• NP-complete: otherwise.

$\mathrm{Ttract}$ includes all regular languages for which enumeration of trails (non-repeating edge paths) admitting $L$-labeled sequences is feasible in nondeterministic logarithmic space. DFA-based recognition exploits counter-automata and product-NFA reachability checks. The notion extends closure properties and links to FO²[<] logical fragments. This theoretical result yields a “TractOracle” tool blueprint that guarantees tractability status and evaluation protocol for regular path queries in database systems.

7. Future Directions and Limitations

Proposed expansions for TractOracle frameworks include:

• Training larger oracle models on ensembles of anatomical filtering methods to capture richer priors (Levesque et al., 15 Jul 2025).
• Integrating global context into policy state for improved tract navigation in complex anatomical regions.
• Validating in cases of pathological anatomy (e.g., tumors, multiple sclerosis).
• Enhancing interpretability via attention visualization for clinical and neuroimaging deployment.
• Extending oracle-based reward paradigms (both empirical and theoretical) to bundle-specific, multi-class, and autonomous self-critique frameworks.

Observed limitations include decreased spatial overlap in synthetic tractography compared to non-oracle RL, terminal-only oracle reward in most policies (which may restrict feedback granularity), and computational overhead for autoencoder states. For automata-theoretic oracles, recognition complexity is bounded by NL/PSPACE for DFA/NFA input and expressivity by the characteristics of $\mathrm{Ttract}$.

TractOracle systems unify oracle-based validation with policy-driven optimality, facilitating high-fidelity tractography, tractable query processing, and axiomatic assertion synthesis in diverse computational domains.