AutochaosNet: Hyperparameter-Free NL Classifier

• AutochaosNet is a hyperparameter-free variant of Neurochaos Learning that replaces tunable chaotic maps with a universal orbit from the Champernowne constant.
• It computes neural traces through min-max normalization and DSM iterations, extracting trace mean (and optionally firing rate) for direct cosine-based classification.
• Empirical results on benchmark datasets show competitive classification performance with substantially reduced computational time compared to ChaosNet.

Searching arXiv for the cited AutochaosNet paper and closely related Neurochaos Learning work. AutochaosNet is a hyperparameter-free variant of the Neurochaos Learning (NL) classification framework that uses chaotic dynamics for feature extraction while eliminating both training and parameter optimization. Proposed in “Hyperparameter-Free Neurochaos Learning Algorithm for Classification,” it replaces the tunable chaotic-map configuration used in ChaosNet with a universal chaotic sequence derived from the Champernowne constant under the Decimal Shift Map (DSM), and it evaluates classification by class mean vectors and cosine similarity rather than by an iteratively trained parametric model (Henry et al., 2 Aug 2025).

1. Position within Neurochaos Learning

AutochaosNet is best understood as a simplified member of the Neurochaos Learning family. In the terminology used by the paper, NL is the broader brain-inspired framework in which chaotic trajectories, described as “neural traces,” are used for feature extraction. ChaosNet is an earlier NL architecture that uses the Skew Tent Map and typically extracts four features per input dimension—Firing Time, Firing Rate, Energy, and Entropy—thereby transforming an $n$-dimensional input into a $4n$-dimensional representation. AutochaosNet preserves the NL premise that chaotic dynamics can produce discriminative features, but it removes the need to tune the chaotic-map initial condition, skew value, and noise threshold, and it reduces the extracted representation to either one or two features per original attribute (Henry et al., 2 Aug 2025).

The paper identifies two principal motivations for this redesign. First, standard NL and ChaosNet pipelines require multiple hyperparameters, which makes deployment computationally expensive and operationally inconvenient. Second, ChaosNet computes four chaotic features per input sample, whereas AutochaosNet is intended to obtain similar classification performance with fewer extracted quantities and without iterative training. In this sense, AutochaosNet is not a separate learning paradigm; it is a parameter-free NL classifier intended as a simpler substitute for ChaosNet-style pipelines (Henry et al., 2 Aug 2025).

2. Universal orbit and firing-time construction

The central methodological innovation is the replacement of tunable chaotic initialization by a universal orbit derived from the Champernowne constant. The paper uses the truncated constant

$C = 0.1234567891011\ldots 498499$

as the starting point of the DSM orbit. Its theoretical justification is a lemma concerning the occurrence of finite digit strings in the decimal expansion of the Champernowne constant. Writing

$$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$

and

$c_N = 0.1234567891011\ldots (N-2)(N-1),$

where $N=a_1a_2\ldots a_d$, $d\ge 2$, the paper states that the number of digits after the decimal point in $c_N$ is

$dN-(10+10^2+\ldots+10^{d-1})-1.$

Equivalently, the number $N$ occurs in the decimal expansion of $4n$0 after

$4n$1

digits from the decimal point (Henry et al., 2 Aug 2025).

AutochaosNet uses this lemma to define a stimulus-dependent firing-time bound. If an input feature takes the normalized form

$4n$2

the method extracts the first three decimal places,

$4n$3

and defines the firing-time upper bound

$4n$4

that is,

$4n$5

The paper states that $4n$6 serves as an upper bound for the firing time. This is the mechanism by which AutochaosNet removes the noise-threshold hyperparameter: the stopping criterion is no longer based on proximity to a tuned threshold but is determined directly from the input stimulus through the universal-orbit construction (Henry et al., 2 Aug 2025).

3. Feature transformation and classification rule

The algorithm begins with min-max normalization. For a dataset of size $4n$7, with entries $4n$8, the normalized value is

$4n$9

For each normalized feature, the method computes a firing-time bound $C = 0.1234567891011\ldots 498499$0 from the Champernowne-based rule and generates a neural trace

$C = 0.1234567891011\ldots 498499$1

where $C = 0.1234567891011\ldots 498499$2 is the truncated Champernowne constant and $C = 0.1234567891011\ldots 498499$3 denotes the DSM iteration (Henry et al., 2 Aug 2025).

Two simplified variants are defined. TM AutochaosNet computes only the mean of the neural trace,

$C = 0.1234567891011\ldots 498499$4

so the transformed dataset remains $C = 0.1234567891011\ldots 498499$5-dimensional. TM-FR AutochaosNet computes both the trace mean and the firing rate, where firing rate is defined as the fraction of time the neural trace exceeds $C = 0.1234567891011\ldots 498499$6:

$C = 0.1234567891011\ldots 498499$7

TM-FR AutochaosNet therefore produces a $C = 0.1234567891011\ldots 498499$8-dimensional representation (Henry et al., 2 Aug 2025).

After feature extraction, classification proceeds through class mean vectors and cosine similarity. For a transformed test instance $C = 0.1234567891011\ldots 498499$9 and class mean vector $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$0, the similarity is

$$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$1

The paper describes prediction as comparison against class mean vectors under this cosine-based criterion. Because no weights are learned by gradient descent or iterative fitting, the method has no training stage in the usual parametric sense; class representatives are computed directly from the transformed data (Henry et al., 2 Aug 2025).

4. AutochaosNet variants

The two variants differ only in the number of extracted chaotic descriptors and the dimension of the transformed representation.

Variant	Extracted features	Output dimension
TM AutochaosNet	Trace Mean	$$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$2
TM-FR AutochaosNet	Trace Mean + Firing Rate	$$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$3

TM AutochaosNet is the most reduced formulation, retaining only the mean of the neural trace. TM-FR AutochaosNet adds firing rate while remaining hyperparameter-free. Both variants are contrasted with ChaosNet, which uses four chaotic features and three hyperparameters. This reduction in representational complexity is one of the paper’s explicit design goals: to retain the chaos-based feature-extraction principle while lowering computational burden and removing manual parameter selection (Henry et al., 2 Aug 2025).

5. Empirical evaluation

The reported experiments use 10 benchmark datasets: Iris, Haberman’s Survival, Seeds, Statlog (Heart), Ionosphere, Bank Note Authentication, Breast Cancer Wisconsin, Wine, Palmer Penguins, and Sonar. The primary evaluation metric is F1 score. For computational cost, the paper reports mean elapsed time over 50 iterations together with the standard deviation of elapsed time. ChaosNet is used as the baseline (Henry et al., 2 Aug 2025).

The quantitative picture is mixed but favorable to AutochaosNet in the sense emphasized by the paper. On Iris, ChaosNet remains stronger, with F1 scores of $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$4 versus $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$5 for TM-FR AutochaosNet and $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$6 for TM AutochaosNet. On Haberman, the values are $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$7 for ChaosNet, $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$8 for TM-FR, and $$c=0.1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,11\ldots N(N+1)(N+2)\ldots$$9 for TM. On several datasets, however, AutochaosNet is reported to exceed ChaosNet: on Seeds, TM-FR and TM both reach $c_N = 0.1234567891011\ldots (N-2)(N-1),$0 versus $c_N = 0.1234567891011\ldots (N-2)(N-1),$1 for ChaosNet; on Statlog, TM-FR and TM both reach $c_N = 0.1234567891011\ldots (N-2)(N-1),$2 versus $c_N = 0.1234567891011\ldots (N-2)(N-1),$3; and on Sonar, TM-FR reaches $c_N = 0.1234567891011\ldots (N-2)(N-1),$4, TM reaches $c_N = 0.1234567891011\ldots (N-2)(N-1),$5, and ChaosNet reaches $c_N = 0.1234567891011\ldots (N-2)(N-1),$6. On Palmer Penguins, the scores are $c_N = 0.1234567891011\ldots (N-2)(N-1),$7 for TM-FR, $c_N = 0.1234567891011\ldots (N-2)(N-1),$8 for TM, and $c_N = 0.1234567891011\ldots (N-2)(N-1),$9 for ChaosNet. The paper therefore characterizes the overall outcome as competitive performance, with superiority on some datasets despite the reduced complexity (Henry et al., 2 Aug 2025).

The timing results are much more decisive. For Iris, the reported mean elapsed times are $N=a_1a_2\ldots a_d$0 s for TM-FR AutochaosNet, $N=a_1a_2\ldots a_d$1 s for TM AutochaosNet, and $N=a_1a_2\ldots a_d$2 s for ChaosNet. For Seeds, the corresponding values are $N=a_1a_2\ldots a_d$3 s, $N=a_1a_2\ldots a_d$4 s, and $N=a_1a_2\ldots a_d$5 s. For Statlog, they are $N=a_1a_2\ldots a_d$6 s, $N=a_1a_2\ldots a_d$7 s, and $N=a_1a_2\ldots a_d$8 s. For Sonar, they are $N=a_1a_2\ldots a_d$9 s, $d\ge 2$0 s, and $d\ge 2$1 s. These measurements support the paper’s main computational claim: AutochaosNet substantially reduces elapsed time by removing hyperparameter tuning, reducing the number of chaotic features, and using direct similarity-based classification (Henry et al., 2 Aug 2025).

6. Interpretation, limitations, and terminological scope

The paper presents AutochaosNet as a hyperparameter-free, no-training NL classifier with competitive or superior classification performance and markedly lower computational effort. Its practical advantages, as stated in the paper, are the absence of hyperparameter tuning, the absence of iterative training of model weights, the simplicity of the classification pipeline, and the resulting efficiency and scalability. The same source also states that AutochaosNet exhibits excellent generalisation capabilities and frames it as a deployable simplification of ChaosNet rather than as a replacement of chaos-based learning by conventional optimization (Henry et al., 2 Aug 2025).

Several limitations are also explicit or implicit in the reported formulation. The use of the first three decimal places to construct the firing-time bound is identified as arbitrary. The method depends on a particular universal orbit and on a truncated version of the Champernowne constant. Its performance is competitive but not uniformly superior to ChaosNet; on datasets such as Iris, Breast Cancer Wisconsin, Wine, and Palmer Penguins, the baseline remains stronger. The cosine-similarity rule is simple and may not capture complex class boundaries. The future-work direction proposed by the paper is to identify universal orbits under other chaotic maps and incorporate them into the NL framework while preserving the parameter-free character of the method (Henry et al., 2 Aug 2025).

A useful terminological distinction follows from later literature. “AutochaosNet” is a literal algorithmic name only in the 2025 classification paper (Henry et al., 2 Aug 2025). Other works use the phrase only in an analogical or “-style” sense: adaptive networks with slow self-generated chaos and recurrent adaptive chaotic clustering (Sales et al., 2024), auto-differentiated tangent-map chaos indicators for dynamic aperture optimization (Qiang et al., 29 Oct 2025), automated chaos scoring for pedestrian trajectories with supervised learning (Shahrier et al., 28 Nov 2025), and chaos in autobidding systems (Anagnostides et al., 9 Feb 2026). This suggests a broader informal usage of the term around automated chaos extraction, quantification, or exploitation, but the specific technical meaning of AutochaosNet remains the hyperparameter-free Neurochaos Learning classifier based on a universal DSM orbit derived from the Champernowne constant (Henry et al., 2 Aug 2025).