Gold Pruning Trajectories

• Gold pruning trajectories are optimal, data-driven sequences that dictate the retention or removal of model components at each stage.
• They are derived using global optimization and reference processes, ensuring formal, reproducible roadmaps for efficient resource allocation.
• Applications include MoE pruning, TableQA, dynamic data selection, vision-language modeling, and graph-based SLAM, achieving significant performance gains.

A gold pruning trajectory is an optimal, data-driven sequence or path through decision space that determines which elements (experts, samples, tokens, rows/columns, graph nodes, etc.) should be retained or removed at each stage of a multi-step modeling process. Gold pruning trajectories are typically derived through global optimization, mechanical execution of reference procedures, or complexity-adaptive policies, rather than by static, local, or heuristic strategies. They provide formal, reproducible, and often provably minimal “road maps” for resource allocation, correctness, and efficiency in model pruning across diverse domains. This concept is instantiated in recent works on Mixture-of-Experts (MoE) pruning, table reasoning, lifelong SLAM, vision-language modeling, and data selection in deep learning, each leveraging a trajectory-based formalism tailored to its structural and algorithmic constraints.

1. Gold Pruning Trajectories: Definitions and Formalism

Gold pruning trajectory refers to the optimal sequence of retention/removal choices within a structured, multi-step system driven by well-defined reference signals. In MoE pruning, the gold trajectory minimizes a holistic cost through the computation graph; in TableQA, it emerges from clause-wise execution of a reference SQL; in data pruning, it is the subset progression that maximizes performance given a dynamic model state. The gold trajectory is typically formalized with respect to target objectives (e.g., minimal loss, maximal recall of critical elements, or adherence to budgets) and obtained by solving global or dynamic programming problems, simulating gold-standard processes, or analytically adapting policy parameterizations.

This gold-standard designation implies that, under the model’s cost function and data distribution, the trajectory embodies provably optimal or reference-aligned pruning—enabling precise benchmarking and process supervision (Yang et al., 20 Dec 2025, Guo et al., 7 Jan 2026, Kurz et al., 2021, Wang et al., 28 Sep 2025, Raju et al., 2021).

2. Methodologies for Gold Pruning Trajectory Derivation

MoE Expert Pruning

In MoE architectures, the gold pruning trajectory is computed as the globally cost-minimizing path through a layered, directed acyclic graph (DAG), where each node corresponds to an expert in a layer and each edge is weighted by a combined cost of local statistics: reconstruction error ($L_{\mathrm{rec}}$), average routing probability ($p$), and activation strength ($a$). The scalar edge cost is

$$w_{i,j \rightarrow i+1,k} = \alpha \cdot L_{\mathrm{rec}}(i,j) - \beta \cdot \log p_{i,j} - \gamma \cdot a_{i,j}$$

where $\alpha, \beta, \gamma > 0$ are hyperparameters. The optimal trajectory $p^*$ is computed via forward dynamic programming and corresponds to the minimal composite cost path from input to output layer (Yang et al., 20 Dec 2025).

Table Pruning in TableQA

In TableQA, the gold pruning trajectory is defined as the sequence of intermediate sub-tables produced by sequentially applying the clauses of a known-correct (gold) SQL query to the original table. This yields an unambiguous, mechanistically verified sequence $(T_0, T_1^+, \dots, T_n^+)$, where each $T_t^+$ preserves all answer-critical cells up to that point. This trajectory provides stepwise, clause-aligned supervision for model learning and supports parallel search during inference (Guo et al., 7 Jan 2026).

Data Pruning in Deep Learning

Dynamic data pruning frameworks characterize pruning as a trajectory through the space of sample subsets, with selections adapting to the evolving model state. Instead of fixed, static scoring, the system interleaves re-scoring and selection, forming a temporal trajectory $X_p^0, X_p^1, \dots, X_p^{M-1}$ of kept subsets. The gold path, in principle, would maximize downstream accuracy or efficiency under a time or resource constraint, potentially found by planning in the space of pruning sequences via bandit or reinforcement learning (Raju et al., 2021).

Vision-LLM Token Pruning

In large vision-LLMs, gold pruning trajectories are complexity-adaptive, varying per-sample according to measured mutual information between vision and language tokens. AutoPrune computes a task- and input-specific logistic retention curve:

$$f_q(x) = \frac{N_{\mathrm{init}}}{1 + \exp(k_q (x - x_0^q))}$$

with $k_q, x_0^q$ parameterized linearly by the sample’s mutual information, and then rescales the resulting per-layer schedule to enforce a global budget. Discretization yields the per-layer quota of tokens to retain, forming the gold pruning trajectory tailored to each query’s complexity (Wang et al., 28 Sep 2025).

Graph Pruning in Lifelong SLAM

In lifelong SLAM, gold trajectory pruning is achieved by iteratively removing graph nodes (poses) with the highest scale-invariant density, ensuring spatial uniformity and bounded map size. The pruning trajectory is the prioritized sequence of node removals dictated by the local geometric density metric, subject to constraints on accuracy and coverage (Kurz et al., 2021).

3. Supervisory and Optimization Roles

Gold pruning trajectories serve as the foundation for supervising data-driven pruners and verifiers. In TableQA, they provide progression and correction tuples for pruner supervision and recall-biased F-score signals for verifiers, enabling stepwise alignment and error correction:

• Progression: training on $(Q, T_0, T_{t-1}^+ \rightarrow T_t^+)$
• Correction: training on negative variants $(Q, T_0, T_{t-1}^- \rightarrow T_t^+)$
• Verifier: regression to $S(T_t)$ (recall-biased F-score vs. $T_n^+$)

In MoE, aggregating gold paths from a sample set yields a non-uniform, globally consistent expert-retention mask, eliminating the need for uniform pruning ratios. In dynamic data pruning, the trajectory supports analysis of "always", "never", and "sometimes" samples, providing structure for both empirical evaluation and future policy optimization (Yang et al., 20 Dec 2025, Guo et al., 7 Jan 2026, Raju et al., 2021).

4. Empirical Performance Impact and Trade-offs

Experiments across modalities demonstrate that gold pruning trajectories provide robust performance improvements:

• MoE Pathfinder achieves higher compression rates and accuracy compared with local or uniform expert pruning across standard LLM tasks (Yang et al., 20 Dec 2025).
• TabTrim surpasses critique-based and sequential pruning frameworks by large margins on TableQA benchmarks (up to 6.8% improvement on "Hard" categories in TableBench), confirming the advantage of trajectory supervision and parallel search (Guo et al., 7 Jan 2026).
• AutoPrune delivers superior efficiency and accuracy trade-offs in vision-LLMs, retaining over 96% of full accuracy at aggressive token budgets across multiple datasets (Wang et al., 28 Sep 2025).
• In lifelong SLAM, prioritized SID-based trajectory pruning yields up to 40x speedup while incurring mean map errors increases of only a few centimeters (Kurz et al., 2021).
• Dynamic data pruning cuts training time by 2x with minimal accuracy loss, outperforming static selection at higher prune rates (Raju et al., 2021).

These results corroborate that gold trajectory approaches better preserve critical paths or data, adapt to heterogeneity, and avoid irreversible early pruning errors common to myopic or purely sequential baselines.

5. Theoretical Guarantees and Robustness

Gold pruning trajectories inherit strong guarantees from their global or reference-aligned construction:

• Trajectory-based inference as shortest-path optimization in MoE ensures that all kept experts are globally important for the modeled task, not just for local per-layer criteria (Yang et al., 20 Dec 2025).
• Gold trajectory supervision in TableQA eliminates the possibility of answer-critical cell loss at any step, since every pruning action is grounded in the executable semantics of the gold SQL (Guo et al., 7 Jan 2026).
• In dynamic data or sample pruning, the avoidance of static, one-shot deletion allows recovery from misclassification of “sometimes” samples and supports robust exploration via bandit/RL policies (Raju et al., 2021).
• In geometric graph pruning, iterative removal and robust marginalization yield bounded spatial error despite dramatic reduction in pose graph size and complexity (Kurz et al., 2021).

These frameworks typically feature adaptivity (to inputs, tasks, or model state), parallel exploration (inference-time beam search), and explicit global constraint satisfaction (budgeted FLOPs, non-uniform expert retention, map sparsity).

6. Distinction from Heuristic and Sequential Pruning

Gold pruning trajectories are distinguished from heuristic, fixed-schedule, or purely sequential strategies by three salient features:

• Global optimality: Decisions are planned at a trajectory or path level, not greedily or layerwise, ensuring consistency and completeness.
• Reference-alignment: They encode ground-truth or gold reference information (e.g., compositional SQL execution, model complexity measurements), sidestepping the unreliability of self-critique or executor-only signals.
• Process supervision: The gold trajectory offers explicit, actionable supervision at each pruning step, enabling off-trajectory correction, loss-aware verification, and sophisticated search during inference (Yang et al., 20 Dec 2025, Guo et al., 7 Jan 2026, Wang et al., 28 Sep 2025).

Sequential or heuristic approaches, in contrast, lack unambiguous guidance throughout the process, are prone to error propagation, and typically apply inflexible retention ratios or criteria that ignore structural or distributional heterogeneity.

7. Perspectives and Future Directions

Recent research foregrounds the utility of gold pruning trajectories for interpretability, adaptation, and empirical performance; yet, their construction may depend on availability of reference processes (e.g., gold SQL, model measurements) or tractable optimization structures. There is ongoing investigation into meta-optimization over pruning trajectories, such as using imitation or inverse reinforcement learning to approach the gold path in highly dynamic, non-stationary settings (e.g., dynamic data pruning) (Raju et al., 2021). A plausible implication is that as model architectures become more modular and data distributions more heterogeneous, trajectory-driven pruning policies—automatically adapting at both global and instance levels—will become central to efficient, scalable model deployment.

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References:

• MoE Pathfinder: Trajectory-driven Expert Pruning (Yang et al., 20 Dec 2025)
• Rethinking Table Pruning in TableQA: From Sequential Revisions to Gold Trajectory-Supervised Parallel Search (Guo et al., 7 Jan 2026)
• Geometry-based Graph Pruning for Lifelong SLAM (Kurz et al., 2021)
• AutoPrune: Each Complexity Deserves a Pruning Policy (Wang et al., 28 Sep 2025)
• Accelerating Deep Learning with Dynamic Data Pruning (Raju et al., 2021)