FASTER: Accelerating Algorithms & Inference

• FASTER is a suite of techniques that optimize core computational primitives through structure-exploiting algorithms and innovative data decomposition strategies.
• Its applications span convex optimization, real-time robotics planning, numerical linear algebra, and quantum simulation, demonstrating measurable speedups and efficiency gains.
• By leveraging methodologies such as recursive low-rank updates, mixed-integer programming, and focal token selection, FASTER frameworks deliver significant latency reductions with minimal loss in fidelity.

FASTER encompasses a diverse set of algorithmic advances and system designs aimed at reducing computational complexity, improving inference or training latency, and accelerating numerical or optimization operations in scientific computing and machine learning. Methods and frameworks carrying the FASTER name span convex optimization, trajectory planning, 3D detection, integer multiplication, neural modeling, quantum sampling, approximations of special numbers, and high-efficiency video classification. The core theme uniting these contributions is the technical optimization of core primitives—often through structure-exploiting algorithms, novel data structures, or domain decomposition—to yield significant speedups over conventional approaches, often with minimal loss in fidelity or generality.

1. Acceleration in Convex Optimization and Dynamic Matrix Problems

One prominent strand of the FASTER literature targets linear algebraic primitives within convex optimization, specifically the dynamic maintenance of matrix inverses and its application to general linear programming (LP). Standard LP interior-point methods require repeated updates and inversions of large matrices, with naive algorithms incurring $O(n^\omega)$ time per update, where $\omega$ is the exponent of matrix multiplication.

The FASTER framework for this task exploits the Woodbury-Morrison identity recursively to maintain the inverse of an $n \times n$ matrix under a sequence of low-rank updates. By organizing updates into $K$ hierarchical epochs—with each level handling only updates up to a budgeted rank threshold—and combining this with left-sided sketching (random projections) and right-sided sparsification of query vectors, the framework achieves amortized sub-$O(n^2)$ update and query costs. Specifically, for matrices with slowly changing right-hand sides and update sequences of bounded low-rank, per-iteration costs exhibit exponents depending on the structure parameters ($\omega$, $\alpha$):

$$O^*\left(n^{2 + \max\left\{\frac{1}{18},\omega-2,\frac{1-\alpha}{2}\right\}}\right),$$

where $O^*$ hides polylogarithmic factors. For conjectured values $\omega \approx 2$, $\omega$0, the overall LP solver runtime reduces to $\omega$1, a notable improvement over previous exponent barriers, thus pushing the envelope for practical large-scale dense LP solvers (Jiang et al., 2020).

2. Real-Time and Safety-Critical Robotics: FASTER in Planning and Action

The FASTER approach has been influential in robotics, especially for trajectory planning and control in dynamic or partially observed environments.

Trajectory Planning for UAVs

The “FASTER” planner for UAV operations in unknown environments introduces a mixed-integer quadratic programming (MIQP) formulation that balances agile, high-speed trajectory generation with guaranteed collision avoidance. Unlike prior schemes that restrict optimization to known free space (yielding slow, conservative motion), FASTER allows planning in both known-free and unknown spaces, but always ensures a safe, dynamically feasible “back-up” trajectory in the current known space. At every replanning step, it runs coupled MIQPs to compute a whole trajectory (potentially transiting unknown) and a safe trajectory (entirely within the free-known set). Warm-started interval allocation heuristics enable rapid solver convergence (<32 ms for typical scenarios), and the method consistently achieves higher speed (up to 3.6 m/s) and lower completion time (up to 63% reduction) compared to state-of-the-art alternatives (Tordesillas et al., 2019).

Low-Latency Vision-Language-Action (VLA) Control

Recent work on FASTER for real-time VLA models in robotics introduces formal reaction time analysis and direct algorithmic interventions at the inference layer. The “Fast Action Sampling for ImmediaTE Reaction” (FASTER) framework analytically characterizes reaction time as a function of both time-to-first-action (TTFA) and chunk execution horizon, showing that naive fixed-step denoising schedules become the primary bottleneck. The core solution is a horizon-aware, per-index adaptive schedule that departs from constant-step denoising: immediate actions are compressed into a single inference step by setting their “hit time” so they are decoded first and streamed as soon as available, while future actions can be resolved in subsequent steps. Experimentally, this yields 10x reduction in reaction latency for the critical first action, tightens the uniform reaction time bound, and enables high-speed real-world tasks (e.g., table tennis) on edge GPUs, advancing practical deployability of generalist robot policies (Lu et al., 19 Mar 2026).

3. Structural Pruning and Compression for Efficient Machine Learning

FASTER frameworks also encompass substantial contributions to the design of high-throughput machine learning models, especially in multimodal and sequential domains.

Autoregressive Vision-Language-Action Models

FASTerVQ and FASTerVLA introduce a unified framework that combines a transformer-based residual vector quantizer for action sequences with a block-wise, coarse-to-fine autoregressive policy, capped by a lightweight action expert module. Actions are tokenized as “single-channel images” for spatial and temporal context preservation and compressed using residual vector quantization over multiple codebooks. The resulting VQ codes are then consumed by an autoregressive model with hierarchical decoding and block-wise parallelism, dramatically reducing inference depth and latency (e.g., 112 ms for full RL-chunk decoding). The system achieves >10× compression and near-lossless reconstruction fidelity, with observed generalization to new tasks and embodiments, and yields state-of-the-art efficiency and accuracy across standard robot learning benchmarks (Liu et al., 4 Dec 2025).

Scalable 3D Object Detection in Long-Range Fusion

The FASTer (Focal Token Acquiring-and-Scaling Transformer) architecture for temporal 3D object detection in autonomous driving dynamically selects a compact, information-rich set of “focal tokens” per LiDAR frame, scoring and scaling points for geometric context relevance. These tokens undergo hierarchical groupwise transformer-based fusion, ensuring both local-detail preservation and global context propagation across up to 64 frames. This yields a 10–20× computational reduction relative to naive temporal transformers and achieves superior detection accuracy (e.g., L2 mAP of 66.73% with latency of 45 ms/sweep) compared to state-of-the-art multi-frame detectors (Dang et al., 28 Feb 2025).

4. Classical Algorithmic Speedups in Numerical Linear Algebra and Quantum Simulation

FASTER paradigms also extend to classic algorithmics, most notably in integer multiplication and quantum algorithm simulation.

Integer Multiplication via Preprocessed NTT

A new number-theoretic transform (NTT) design achieves per-multiplication cost of

$\omega$2

with $\omega$3 lookup table preprocessing, beating the $\omega$4 barrier of straightforward FFT-based multiplication. This is achieved by massive table-lookup at the smallest DFT (or NTT) recursion levels, exploiting CRT digit decomposition and precomputed transform maps for small block sizes. While achieving the theoretical minimum $\omega$5 for integer multiplication remains conjectural and depends on further breakthroughs in table construction, the FASTER NTT implementation provides concrete exponential speedup factors over previous schemes in practice at large sizes (Groff, 2019).

Fast Classical Boson Sampling

In quantum computing simulation, the “Faster classical Boson Sampling” algorithm reduces the sampling complexity for $\omega$6 photons in $\omega$7 modes from the prior $\omega$8 per sample to an average-case $\omega$9 when $n \times n$0, by exploiting low-rank structure and incremental permanents via generalised Gray-code orderings. This narrows the practical gap between classical and photonic quantum simulators, and pushes the threshold for quantum supremacy higher (requiring larger $n \times n$1 before quantum sampling is unequivocally faster than any classical algorithm) (Clifford et al., 2020).

5. Approximation, Acceleration, and Efficient Learning

Fast Approximation Sequences

In pure mathematics, FASTER methodology can refer to systematically accelerated convergence for number-theoretic constants. Using multiple-correction sequences—compound rational function corrections to classical recurrence or series expansions—approximations for the Euler-Mascheroni constant $n \times n$2 and the Landau constant $n \times n$3 attain exponential convergence rates (e.g., error $n \times n$4 at the third step), thus outperforming traditional single-correction and continued-fraction schemes (Cao et al., 2014).

Efficient Model Training and Inference

Analyses of faster alternatives to deep learning in text mining show that clustering input embeddings and training local, per-cluster SVMs (with hyperparameters optimized via differential evolution) can lead to overall training speedup by factors of 500–900× over CNNs, with F1 score performance within 2% of the state-of-the-art. These results advocate for measuring sophisticated models against local, simple baselines, especially when resources or reproducibility are concerns (Majumder et al., 2018).

In video classification, the FASTER framework (Feature Aggregation for Spatio-TEmporal Redundancy) employs a mixture-of-experts approach, extracting features from a small number of “expensive” clips via high-capacity networks, many “cheap” clips via lightweight models, and then fusing their representations with a specialized recurrent architecture (FAST-GRU). This approach consistently achieves state-of-the-art accuracy at roughly an order of magnitude lower computational cost versus uniform processing (Zhu et al., 2019).

6. Cross-Domain Patterns and Theoretical Insights

Despite differing domains, FASTER approaches share several recurring algorithmic motifs:

• Recursive, multi-level or hierarchical data decomposition
• Low-rank, sparse, or focal selection to reduce computational blow-up
• Strategic use of sketching, quantization, or codebook compression
• Tight complexity analysis balancing worst-case and average-case costs
• Fusion of structural domain knowledge (e.g., known-free/unknown sets in planning, redundancy in sequence modeling) with standard deep or convex optimization primitives

These principles serve both to guide future designs seeking speedups in new areas and to identify where further theoretical gains (e.g., pushing integer multiplication to true $n \times n$5) may be unlocked by extending or combining such techniques.

7. Summary Table: Representative FASTER Approaches

Area	Key Technique/Framework	Exemplary Speedup/Impact
LP and dynamic matrix inverse	Recursive low-rank updates, sketching	Exponent shaved from $n \times n$6 to $n \times n$7 (Jiang et al., 2020)
UAV trajectory planning	MIQP with safety-in-unknowns, backup trajectory	63% faster completion, real-hardware validation (Tordesillas et al., 2019)
3D object detection	Focal token selection, grouped transformer fusion	+1.5% L2 mAP, 10–20× FLOP reduction (Dang et al., 28 Feb 2025)
Integer multiplication	Preprocessing-based fast NTT	from $n \times n$8 to $n \times n$9 (Groff, 2019)
VLA/robot action models	Tokenization + blockwise AR decoding	Halved latency, >10× compression, SOTA accuracy (Liu et al., 4 Dec 2025)
Video classification	Mixed-complexity feature fusion (FASTER, FAST-GRU)	$K$0× less FLOPs, same accuracy (Zhu et al., 2019)
Quantum simulation	Low-rank permanents, Gray-code order	$K$1 per sample (Clifford et al., 2020)
Constant approximation	Multiple-correction method	$K$2 to $K$3 (γ) (Cao et al., 2014)
Text mining/classification	Clustering+local SVM	$K$4× faster training (Majumder et al., 2018)

Each instance illustrates how FASTER methodologies provide both practical and theoretical speedups while shaping contemporary best practices in their respective fields.