The study, published in Results in Engineering by Kazuki Kaneko and Zongze Li, addresses a fundamental blind spot in digital manufacturing. Computer-aided manufacturing (CAM) software can simulate geometry and generate tool paths from a CAD model, but it cannot simulate what happens inside the machine’s controller. The G-code is filtered by the CNC interpolator, feedforward controllers and feedback control loops before it ever reaches the servomotors, and these proprietary algorithms are closely guarded black boxes maintained by machine tool builders. Physical modeling of this chain is extraordinarily difficult precisely because the control algorithms are secret and the dynamics are deeply nonlinear. The result is that manufacturers often discover machining errors only after cutting — or resort to time-consuming air runs in which the machine executes the program without a workpiece just to observe its behavior.

The authors reframed the problem as one of sequence translation. From a data-processing perspective, G-code execution is a stream of discrete commands fed row by row into a black-box system that emits corresponding sequences of tool-path and cycle time errors. Predicting those errors for a given program is therefore fundamentally a sequence-to-sequence problem — exactly the kind of task at which Transformers excel. Unlike recurrent networks or long short-term memory (LSTM) models, which process sequences step by step, a Transformer uses multi-head self-attention to derive global relational weights across all positions simultaneously. This allows it to capture long-range temporal dependencies, such as how a sharp corner several blocks ahead causes the servo system to decelerate and how a large acceleration from a previous segment continues to influence subsequent commands as the transient response gradually decays.

The researchers drew a striking analogy between the Transformer’s internal machinery and the physics of a CNC controller. In their framing, the query represents the motion state of the current G-code command, while the keys and values carry error features of the surrounding tool path; scaled dot-product attention then assigns weights to nearby and distant blocks, mirroring the feedforward and feedback structure of a real servo loop. Position-wise feedforward networks introduce the nonlinear modeling capacity needed to emulate local servo behaviors such as PID control and friction, while residual connections — which pass inputs directly forward — resemble a closed-loop feedback system that focuses on predicting small dynamic deviations rather than reconstructing the entire tool path. Layer normalization, meanwhile, stabilizes the wildly different physical scales of position increments and feed rates, functioning much like a gain stabilizer in a servo drive.

Training such a model requires data that spans the machine’s full dynamic repertoire, so the team avoided reliance on specific workpiece geometries, which would limit generalization. Instead, they semi-randomly generated ten sets of training G-code combining local blending segments, where the path passes directly through control points, and global blending segments, where B-spline interpolation smooths the trajectory at constant feed rate. Displacements and feed rates were drawn randomly from defined ranges, producing tool paths with varied travel ranges and frequent direction changes. Each program was then executed on a real three-axis ROBODRILL machine equipped with a Fanuc Series 31i controller, and actual tool-path data were captured at a sampling frequency of 1 kHz using Fanuc’s SERVO Guide monitoring software. The training targets were thus experimentally measured servo responses rather than virtual simulations, grounding the digital twin in physical reality.

The model itself is an encoder-only Transformer with a model dimension of 512, eight layers and four attention heads, trained for 2000 epochs on a workstation with an RTX 4090 GPU. Input sequences consisted of nominal positional increments along the three feed axes plus the commanded feed rate, segmented into windows of 32 control points using a causal sliding window. The output comprised the three-dimensional tool-path error and the cumulative cycle time error at each point. Notably, the authors found that longer input sequences converged more slowly without improving final accuracy — a result that aligns neatly with servo physics, since the transient influence of any single command naturally fades over time. When compared against a Bi-LSTM model of equal dimensions trained on identical data, the Transformer converged in roughly 500 epochs, three times faster than its recurrent rival.

Validation was carried out on six G-code programs derived from two physical specimens: a 25-millimeter-radius hemispherical part machined along morphing spiral and bidirectional paths, and a complex artifact geometry, each run at nominal feed rates of 1000 and 3000 millimeters per minute. The results were decisive. Both models avoided large systematic bias, with mean prediction deviations generally within ±1 micrometer or millisecond, but the Transformer’s uncertainty bands were roughly 1.5 to 2 times tighter than the Bi-LSTM’s across all error components — and in some conditions nearly four times tighter. Its error distributions clustered markedly more sharply around zero, and while the Bi-LSTM’s cycle time root-mean-square error ballooned to about 8 milliseconds on the most demanding program against a mean error of 2.5 milliseconds, the Transformer suppressed such outliers, keeping RMSE close to MAE.

The comparison also revealed how differently the two architectures degrade under stress. Higher feed rates inherently reduce the accuracy of the controller’s feedforward and feedback loops, and the Bi-LSTM’s errors doubled or even tripled when the feed rate rose from 1000 to 3000 millimeters per minute. The Transformer, by contrast, showed far more graceful degradation, keeping mean errors below 2 micrometers or milliseconds even on the most challenging high-speed program. The authors attribute the residual errors that remain — small but nonzero — to highly random mechanical nonlinearities such as micro-friction variations and backlash during axis reversals, along with the quantization limits of encoder feedback at the 1 kHz sampling rate.

Perhaps the most industrially compelling result is speed. Predicting errors for an entire validation program took the Transformer less than 3.5 seconds, regardless of program complexity, whereas air-running the same programs on the machine took anywhere from roughly 38 to 202 seconds. Because prediction time depends only on G-code length, the trained model can instantly screen massive production programs offline, eliminating the need for preliminary air runs and sharpening both production scheduling and machining efficiency. The approach does not generalize across machines — each machine tool has unique controller and mechanical characteristics — but the authors emphasize that adapting to a new machine requires only executing the training G-codes, acquiring a fresh dataset and retraining, after which the model serves as a customized digital surrogate for that specific machine.

The work points toward a future in which every machine tool carries its own learned digital twin, capable of vetting programs before metal is ever cut. The team’s next steps include extending the model to account for cutting force-induced deflections of tool and workpiece, which superimpose on servo tracking errors in real machining; probing how specific G-code features such as control point density affect prediction performance; scaling the sequence-to-sequence methodology to five-axis simultaneous machining; and developing real-time servo signal acquisition for online error prediction during actual cutting. They also plan to build open-architecture experimental CNC systems, since proprietary commercial controllers block the integration of theoretical control equations needed for hybrid physical-digital modeling. If those ambitions pan out, the humble G-code file may one day arrive at the shop floor already annotated with a complete forecast of its own imperfections.

Subject of Research: Transformer-based deep learning prediction of tool-path and cycle time errors in CNC machining from G-code

Article Title: Prediction of tool-path and cycle time errors of CNC machining using a transformer-based deep learning model

Article References: Kaneko, K., & Li, Z. (2026). Prediction of tool-path and cycle time errors of CNC machining using a transformer-based deep learning model. Results in Engineering, 32, Article 112872. https://doi.org/10.1016/j.rineng.2026.112872

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.112872

Keywords: CNC machining, Transformer model, deep learning, digital twin, tool-path error, cycle time prediction, G-code, servo dynamics, Bi-LSTM comparison, precision manufacturing, sequence-to-sequence learning, machine tools