Feedforward neural network¶

An artificial neural network whose within-evaluation signals move from input to output through an acyclic directed graph.

Version: v1 · 2026-09-28 · History
Domain-specific #: 9423
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Subdomain: Machine Learning → Computer Science & Software Engineering
Aliases: Feed-forward neural network, FFNN

Core Idea¶

A feedforward neural network is a parameterized artificial neural network whose signal graph is directed and acyclic for one evaluation. An input representation passes through weighted computational units and optional nonlinear transformations to an output; connections may be layered, convolutional, or skip paths as long as none sends a later signal back into an earlier state. The defining contrast is a recurrent network, whose reusable state carries feedback or history into subsequent computation.

Feedforward does not name one training algorithm. Backpropagation can calculate gradients through an acyclic graph, but changing weights across training steps is not an inference-time feedback edge; recurrent models can also be trained through unrolled computations. A simple linear single-layer network may satisfy the structural test, while deeper nonlinear networks have different expressive power. Recurrence changes the reusable signal architecture, not the mathematical possibility of differentiating it. LeNet-5 illustrates an attested convolutional feedforward application to document recognition.

Structural Signature¶

Sig role-phrases:

Input representation — Supplies a fixed observation vector, image, or tensor entering one evaluation. It is constitutive. Counterfactual: Without a defined input, there is no directed computation to evaluate.
Weighted computational units — Transform upstream values through parameterized aggregation and possible nonlinearities. It is constitutive. Counterfactual: A bare graph of labels without transforming units is not this computational network.
Acyclic signal graph — Orders connections so each within-evaluation value depends only on earlier nodes. It is constitutive. Counterfactual: A signal edge returning to an earlier state produces a recurrent computation.
Output mapping — Produces a result from the composed forward functions under stated task meaning. It is constitutive. Counterfactual: An incomplete internal layer without an output is not the whole input-output model.
Learning and evaluation boundary — Separates how parameters were fitted and validated from whether the inference architecture is feedforward. It is boundary. Counterfactual: A backpropagation update is not a recurrent inference edge, and fit alone does not show generalization.

What It Is Not¶

Not a recurrent network. A later state returning to earlier computation violates the within-evaluation acyclic condition.
Not backpropagation itself. Gradient direction in training differs from forward signal direction in inference.
Not necessarily fully connected. Convolutional and skip-connection designs may remain acyclic.
Not proof of generalization. A trained feedforward mapping still needs task-specific evaluation.
Closest near-miss. A recurrent neural network is the closest neighbor: its hidden state feeds forward in time but also creates a directed state-dependence cycle when viewed as the reusable architecture.

Scope of Application¶

Function approximation. Represent static mappings from typed inputs to outputs.
Image and document recognition. Use acyclic learned feature stages for visual classification.
Architecture comparison. Distinguish feedforward, convolutional, skip, and recurrent signal paths.
Training analysis. Separate backward derivative computation from the forward inference graph.

Clarity¶

Inspect the connection graph used for one input-to-output evaluation. An x→hidden→output chain qualifies, and a skip path can still qualify if no cycle appears. The nearest excluded case feeds a later state back to earlier computation. Backpropagation during learning runs gradient information in a reverse calculation but does not make the inference graph recurrent. Training fit and document-recognition accuracy are separate empirical questions.

Manages Complexity¶

The acyclic graph organizes many parameterized unit operations into a composed map that can be evaluated in dependency order. This makes forward inference and gradient accounting tractable, but hides data, optimization, and validation assumptions under an architecture label. Calling a network feedforward says how signals are wired, not that it learned a good function.

Abstract Reasoning¶

Name the input, output, computational units, and weighted connections.
Draw the within-evaluation direction of every signal dependency.
Check that a topological ordering exists and no later state feeds an earlier one.
Classify convolutions or skip paths by cycle structure rather than visual layout.
Assess training and task performance separately from the structural classification.

Knowledge Transfer¶

The acyclic input-to-output criterion transfers across tabular MLPs, convolutional models, and other finite directed neural graphs. LeNet-5's image preprocessing, learned parameters, and recognition results do not transfer to an arbitrary feedforward net. A recurrent network unrolled for a finite time produces an acyclic computation graph for that particular unrolling, but the reusable architecture retains state feedback and is not thereby reclassified.

Examples¶

Canonical¶

Consider an input x mapped to a hidden value h=σ(W1x+b1), then to y=W2h+b2. Within one evaluation every edge runs x→h→y; no output is fed back into h or x. This worked network is feedforward whether its parameters were fit by gradient descent or another method. A skip connection from x to y would remain feedforward if it introduces no directed cycle.

Mapped back: Input representation → x; Weighted computational units → W1,b1,σ and W2,b2; Acyclic signal graph → x→h→y with no return edge; Output mapping → y as task result; Learning and evaluation boundary → fitting method not part of the cycle test.

Applied / In Practice¶

LeCun and coauthors' published LeNet-5 document-recognition work maps digit images through convolution/subsampling and later classification stages to character outputs. The signal passes through a directed sequence of learned transformations; convolution does not make the network recurrent. The paper demonstrates a specific trained visual-recognition use, not a guarantee that all feedforward networks recognize documents or generalize without test data.

Mapped back: Input representation → digit/document image; Weighted computational units → learned convolution and later classifier stages; Acyclic signal graph → ordered image-to-feature-to-class path; Output mapping → character/digit recognition scores; Learning and evaluation boundary → published task evaluation, not universal model performance.

Structural Tensions¶

T1 — Expressive Composed Mapping versus No Persistent Feedback State. Depth and nonlinearity permit rich static functions while leaving temporal recurrence outside the architecture.

Diagnostic: Does the task need history carried across evaluations?

T2 — Forward Evaluation versus Backward Training Gradient. Gradients may propagate backward through the graph during learning without creating a backward signal edge in the deployed forward computation.

Diagnostic: Is a training derivative being mistaken for inference recurrence?

Structural–Framed Character¶

The skeleton is acyclic composition of parameterized computational transformations from input toward output. A feedforward neural network has no feedback cycle in its within-evaluation signal graph, whether or not it has been trained. It is an approved unparented root pending reconciliation with the live ANN node, which currently requires fitted parameters.

Evaluative weight: Architectural class does not imply performance on a task or trained weights.

Human-practice-bound: Designers choose units, layers, activations, and intended inputs/outputs.

Institutional origin: Machine-learning terminology separates network architecture from optimization and validation.

Vocabulary travels: “Feedforward” in control systems may describe a different mechanism.

Import versus recognize: Acyclic graph reasoning transfers, but a spreadsheet DAG lacks neural units and their signal operations.

Its character: An artificial neural architecture class, not a prime for all directed acyclic computation.

Structural Core vs. Domain Accent¶

Skeletal core. Directed acyclic transformations can compose a mapping from input to output.

Domain-bound accent. In this class the nodes and connections form an artificial neural computation with weighted or parameterized units. Training may later set parameters but is not required for architectural identity.

Why not prime. A recurrent architecture retains feedback even if one finite execution is unrolled into a DAG; an ordinary dependency graph is not thereby neural. The existing ANN parent cannot currently be asserted without its fitted-parameter condition.

This entry under conditions is a kind of Machine-Learning Model.

Related — artificial neural network. Feedforward describes an acyclic neural architecture; a fitted network is one realization, but the architecture can be specified before its parameters are trained.
Related — backpropagation. Reverse-mode gradients can train feedforward parameters, but are not a feedback edge in inference.

Relationships to Other Abstractions¶

Current abstraction Feedforward neural network Domain-specific

Parents (1) — more general patterns this builds on

Feedforward neural network is a kind of, conditional Machine-Learning Model Domain-specific

Supports fitted feedforward network models, not the bare architecture alone.

Condition / exception Supports fitted feedforward network models, not the bare architecture alone.

Children (1) — more specific cases that build on this

Convolutional neural network Domain-specific is a kind of Feedforward neural network

A convolutional neural network is a feedforward neural network specialized by learned convolutional filters.

Hierarchy path (1) — routes to 1 parentless root

Feedforward neural network → Machine-Learning Model

Neighborhood in Abstraction Space¶

Feedforward neural network sits in a crowded region of the domain-specific corpus (33^rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Operators, Functions & Data Abstractions (11 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Recurrent neural network. Tell: Does a state feed into earlier or later evaluations through a feedback dependency?
Gradient backpropagation. Tell: Is this a training derivative rather than a forward signal path?
Convolutional neural network. Tell: Are convolutional stages acyclic in the particular architecture?
Any directed graph. Tell: Are there weighted artificial neural units and an input-output computation?

References¶

Goodfellow, Bengio, and Courville, Deep Learning, chapter 6, online author text: https://www.deeplearningbook.org/contents/mlp.html
LeCun, Bottou, Bengio, and Haffner, Gradient-Based Learning Applied to Document Recognition, author publication record: https://bottou.org/papers/lecun-98h
Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Feedforward_neural_network (revision 1371072101).
Preserved source candidate: http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf
Preserved source candidate: https://web.archive.org/web/20160414055503/http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf
Preserved source candidate: https://apps.dtic.mil/dtic/tr/fulltext/u2/a164453.pdf
Preserved source candidate: https://web.archive.org/web/20221013070443/https://apps.dtic.mil/dtic/tr/fulltext/u2/a164453.pdf
Preserved source candidate: https://archive.org/details/historyofstatist00stig
Preserved source candidate: https://doi.org/10.1007/BF02478259
Preserved source candidate: https://direct.mit.edu/books/book/4886/Talking-NetsAn-Oral-History-of-Neural-Networks
Preserved source candidate: https://people.idsia.ch/~juergen/who-invented-backpropagation.html