Pull: A Cross-Disciplinary Operation

• Pull is a cross-disciplinary concept defining operations that move states, signals, or objects toward a target configuration across various domains.
• In neural implicit geometry, pull functions as a differentiable projection operator that refines point positions using predicted signed distance gradients.
• In computation, robotics, and physics, pull facilitates demand-driven control, mechanical separation, and directional information transfer via precise protocols and physical forces.

“Pull” is not a single technical object but a family of domain-specific constructs that recur across geometry processing, distributed systems, robotics, acoustics, collider physics, materials science, and software engineering. Across these literatures, the term consistently denotes an operation or process that draws a state, signal, object, or workload toward a target configuration: a query point toward an implicit surface, retrieval toward an adversarial document, a particle toward an acoustic source, an object toward a robot hand, or jobs toward idle servers. In some fields, “pull” names a mathematically explicit operator; in others, it denotes a protocol, an instability regime, or a workflow abstraction. The resulting concept is therefore best understood as a cross-disciplinary technical term whose precise meaning depends on the governing state space, interaction law, and performance criterion (Ma et al., 2020, Stolyar, 2014).

1. Pull as a projection operator in implicit geometry

In neural implicit surface reconstruction, “pull” denotes a differentiable geometric projection defined on a query point $q \in \mathbb{R}^3$ and a neural function intended to represent a signed distance field (SDF). In Neural-Pull, the network predicts both a scalar signed distance $f(c,q)$ and, via automatic differentiation, its gradient $\nabla f(c,q)$. The pull operation is then defined as

$$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$

so that the query point is moved along the estimated unit gradient direction by a stride equal to the predicted signed distance (Ma et al., 2020).

This definition encodes the characteristic local property of an ideal SDF: moving a point by $-f(q)\nabla f(q)$ lands on the zero level set. Neural-Pull uses that property as supervision without ground-truth signed distances. Query points are sampled around a point cloud $P=\{p_j\}_{j=1}^J$, pulled once, and the pulled points are forced to coincide with nearest points on the cloud through the loss

$$d(\{t_i\}, \{t_i^\star\}) = \sum_{i=1}^I \| t_i - t_i^\star \|_2^2.$$

The operation is differentiable, so training updates both the scalar field and its gradient field simultaneously (Ma et al., 2020).

In this usage, “pull” is neither metaphorical nor iterative in the training objective; it is a specific one-step projection-like map used to learn SDFs directly from raw point clouds. The paper further argues, through Theorem 1 and the condition

$f(p - N \Delta t) = - f(p + N \Delta t),$

that minimizing the pull-based loss can converge to a signed distance function rather than merely an unsigned distance field (Ma et al., 2020).

2. Pull as demand-driven control in computation and routing

In distributed and streaming systems, “pull” denotes control initiated by demand rather than supply. Two distinct literatures instantiate this idea with different technical formalisms.

In pull-streams, “pull” names a JavaScript demand-driven functional design pattern in which downstream explicitly requests the next item from upstream. The protocol is callback-based: downstream issues requests such as ask[\bar x_i], abort[\bar x_i], or error[err,\bar x_i], and upstream responds with \bar x_i := v_i, \bar x_i := done, or \bar x_i := err. The paper formalizes valid histories through normal and early-terminated event sequences and characterizes correctness by single assignment, in-order answers, and disciplined termination behavior (Lavoie et al., 2018).

This formalization shows that pull-streams are a form of declarative concurrent programming. The stream is modeled as a sequence of single-assignment variables $\bar x_i$, and the protocol language specifies partial orders of request and answer events. Here, “pull” means that the consumer controls the pace of computation; data are produced only in response to explicit downstream demand (Lavoie et al., 2018).

In large-scale heterogeneous service systems, PULL is instead a routing algorithm for many-server queues. Each idle server sends a pull-message to a router; an arriving customer is assigned according to a randomly chosen pull-message if any are available, or to a random server otherwise. In the many-server regime with $N_j=\beta_j n$, $f(c,q)$0, and sub-critical load

$f(c,q)$1

the steady-state occupancy converges to a fluid equilibrium $f(c,q)$2 characterized by

$f(c,q)$3

with $f(c,q)$4 and $f(c,q)$5 for $f(c,q)$6 (Stolyar, 2014).

In this queueing usage, “pull” denotes idle capacity advertising itself to the router. A plausible implication is that the term retains its demand-driven character: work is drawn toward available service rather than pushed blindly into the system (Stolyar, 2014).

3. Pull as mechanical separation, adhesion, and instability

In mechanics and materials, “pull” often appears in the compound forms “pull-off” and “pull-in,” which refer to opposite physical transitions.

For adhesive contacts, pull-off is the maximum tensile force needed to separate contacting bodies. In viscoelastic Hertzian adhesive contact, the pull-off force is defined as

$f(c,q)$7

during unloading of a rigid sphere from a viscoelastic substrate. The work to pull-off is

$f(c,q)$8

and the paper introduces a physics-augmented machine learning framework that uses the XPB analytical prediction of $f(c,q)$9 as an additional feature to predict $\nabla f(c,q)$0 and $\nabla f(c,q)$1. For $\nabla f(c,q)$2, the best pure ML model is XGBoost with MSE $\nabla f(c,q)$3, $\nabla f(c,q)$4, while the best PA-ML model is Random Forest with MSE $\nabla f(c,q)$5, $\nabla f(c,q)$6 (Maghami et al., 16 May 2025).

In fiber adhesion, pull-off denotes the final stage of a two-sided peeling process. Numerical simulations of two adhesive elastic fibers show three phases—initiation, peeling, and final pull-off—and reveal that the location of the maximum force depends on the interaction law. For electrostatic attraction, the maximum force occurs in the pull-off phase; for van der Waals adhesion, it occurs in the initiation phase (Grill et al., 2019).

By contrast, in dielectric elastomers, pull-in is an electromechanical instability associated with catastrophic thinning. The free energy is written as

$\nabla f(c,q)$7

and stability requires the Hessian $\nabla f(c,q)$8 of $\nabla f(c,q)$9 with respect to $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$0 to remain positive definite. Under voltage control and equi-biaxial free expansion, the pull-in criterion becomes

$$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$1

whereas under charge control, the corresponding criterion has no real root, so pull-in is suppressed in the neo-Hookean ideal dielectric model (Su et al., 2020).

These uses show that mechanical “pull” can refer either to the force needed to separate an adhered configuration or to the loading path that destabilizes a compliant one. The common structure is a threshold phenomenon governed by force balance and energy curvature (Maghami et al., 16 May 2025, Su et al., 2020).

4. Pull as manipulation and transport in robotics and acoustics

In robotics, “pulling” names a nonprehensile manipulation mode in which a robot maintains contact with an object and transports it toward itself without force-closure grasping. Geometry-aware Dexterous Pushing and Pulling (GD2P) formulates the problem as synthesis of pre-contact hand poses $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$2 conditioned on object geometry and desired motion direction $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$3. Candidate poses are generated by minimizing

$$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$4

where

$$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$5

A diffusion model conditioned on a 4096-dimensional Basis Point Set representation then predicts viable poses, and ranking at test time uses

$$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$6

In real-world Direction 2 experiments, which correspond to pulling toward the robot, GD2P achieves $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$7 All Avg., compared with $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$8 for GD2P w/o ranking, $$t_i = q_i - f(c, q_i) \cdot \frac{\nabla f(c, q_i)}{\|\nabla f(c, q_i)\|_2},$$9 for Nearest Neighbor, and $-f(q)\nabla f(q)$0 for Pre-Trained Grasp Pose (Li et al., 22 Sep 2025).

In topological acoustics, pulling refers to a negative radiation force exerted on a particle by chiral surface waves. A pair of one-way surface modes supported at the interface between two phononic crystals with opposite spinning-cylinder rotations is used so that a particle scatters the excited mode B into mode D with a larger Bloch wave vector. The time-averaged force is computed from the acoustic stress tensor, and the longitudinal force component is

$-f(q)\nabla f(q)$1

Averaged over one lattice period, the longitudinal force is always negative for the tested particle sizes and materials, enabling robust pulling along flexible trajectories protected against backscattering by the chiral surface modes (Wang et al., 2020).

In both fields, “pull” is directional transport under contact-mediated or wave-mediated constraints. This suggests a common operational meaning: the system is engineered so that forward dynamics of the medium induce backward motion of the target object (Li et al., 22 Sep 2025, Wang et al., 2020).

5. Pull as information flow, retrieval redirection, and software contribution

In information systems, “pull” frequently denotes a directional transfer of content, whether benign or adversarial.

In RAG-Pull, the retriever in a code-oriented retrieval-augmented generation pipeline is “pulled” toward attacker-controlled snippets through invisible Unicode perturbations inserted into the query, the corpus target, or both. Retrieval is formalized as

$-f(q)\nabla f(q)$2

and the core attack objective is

$-f(q)\nabla f(q)$3

Combined query-and-target perturbations yield 100% retrieval for $-f(q)\nabla f(q)$4 on Python Alpaca and Java VFD, and query perturbation in Java VFD causes FindSecBugs-detected vulnerabilities to jump by $-f(q)\nabla f(q)$5 (LOW), $-f(q)\nabla f(q)$6 (MEDIUM), and $-f(q)\nabla f(q)$7 (HIGH) versus vanilla LLM (Stambolic et al., 13 Oct 2025).

In software engineering, a pull request is a contribution proposal in pull-based development, where maintainers are asked to “pull” changes from an external branch or fork into the main repository. An empirical study of ansible, rails, and kubernetes shows that contributors with more prior pull requests generally have higher acceptance rates, and that rejected or long-open pull requests are associated with fewer future contributions. For example, the probability of contributing again after an accepted pull request is $-f(q)\nabla f(q)$8 in ansible, $-f(q)\nabla f(q)$9 in rails, and $P=\{p_j\}_{j=1}^J$0 in kubernetes, compared with $P=\{p_j\}_{j=1}^J$1, $P=\{p_j\}_{j=1}^J$2, and $P=\{p_j\}_{j=1}^J$3 after rejection (Legay et al., 2018).

These usages are institutionally different but structurally related. In both, “pull” denotes a mediated transfer controlled by a receiving system: a retriever ranking attacker-chosen documents, or maintainers integrating outside code. A plausible implication is that “pull” in information systems often marks the receiver’s selection mechanism rather than the sender’s transmission mechanism (Stambolic et al., 13 Oct 2025, Legay et al., 2018).

6. Pull in statistical physics and collider observables

In statistical physics, pulling is an external mechanical field applied to a polymer tethered to an adsorbing surface. In a partially directed walk model, the force components are

$P=\{p_j\}_{j=1}^J$4

with corresponding fugacities

$P=\{p_j\}_{j=1}^J$5

The paper derives exact generating functions and phase diagrams, showing adsorbed and desorbed phases separated by a phase transition. Purely lateral pulling shifts the thermal transition, while any non-zero vertical component makes the transition first-order. In 2D, there is a critical angle

$P=\{p_j\}_{j=1}^J$6

below which sufficiently strong pulling induces adsorption no matter how large the temperature (Osborn et al., 2010).

In collider physics, “pull” refers to a jet substructure observable sensitive to color flow. The original pull vector is

$P=\{p_j\}_{j=1}^J$7

while the modified $P=\{p_j\}_{j=1}^J$8 version is

$P=\{p_j\}_{j=1}^J$9

The pull angle probes whether radiation is concentrated between two jets, but it is not infrared and collinear safe; it is only Sudakov safe after resummation. Later work introduces IRC-safe projections

$$d(\{t_i\}, \{t_i^\star\}) = \sum_{i=1}^I \| t_i - t_i^\star \|_2^2.$$0

and asymmetry distributions as safe analogues of the pull angle (Larkoski et al., 2019, Larkoski et al., 2019).

A related calculation for non-singlet jet pairs derives the leading-order pull distribution in $$d(\{t_i\}, \{t_i^\star\}) = \sum_{i=1}^I \| t_i - t_i^\star \|_2^2.$$1 and gives a universal high-boost, small-$$d(\{t_i\}, \{t_i^\star\}) = \sum_{i=1}^I \| t_i - t_i^\star \|_2^2.$$2 formula

$$d(\{t_i\}, \{t_i^\star\}) = \sum_{i=1}^I \| t_i - t_i^\star \|_2^2.$$3

showing explicitly how the observable depends on the color representation of the jet pair (Bao et al., 2019).

Here, “pull” again names a directional bias induced by an interaction field: in polymers, a force field; in jets, the soft-radiation pattern determined by color dipoles. The conceptual parallel is not asserted in the papers, but it is a natural cross-domain reading of the term (Osborn et al., 2010, Bao et al., 2019).