From Propagator to Oscillator: The Dual Role of Symmetric Differential Equations in Neural Systems

Kun Jiang

REVIEW 5 major objections 4 minor 6 references

From Propagator to Oscillator: The Dual Role of Symmetric Differential Equations in Neural Systems

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that a single symmetric differential-equation neuron model can act as both a signal propagator and a self-oscillating signal generator, with mode selection controlled by parameters, connectivity structure, or external…

desk verdict The model and simulations are worthy of a second look, but the paper's claimed proof of a propagator/oscillator dichotomy replaces Lyapunov stability with recurrence and never proves the uniqueness it relies on. read the letter →

arxiv 2507.22916 v1 pith:Q7LNWKKK submitted 2025-07-20 cs.NE cs.AI

Kun Jiang This is my paper

classification cs.NEcs.AI MSC 34D2034C1537C7592B20

keywords symmetricdifferentialequationsneuronmodelstabilityanalysisfunctionaldualitysignalgeneratorpropagationon-roadenergyoscillationsuppression

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that one symmetric differential-equation model of a neuron can do two jobs: faithfully propagate input signals and autonomously generate rhythmic output. The model is a small set of cyclically coupled equations in which each element is excited by its predecessor, decays on its own, and is inhibited by a more distant element. The paper argues that every bounded trajectory of this system either converges to the unique positive fixed point (the propagation regime) or keeps returning to a neighborhood of that point, producing self-sustained oscillations (the generation regime). It supports this with a stability proof built from positivity, a Lyapunov function, Brouwer's fixed-point theorem, and a homotopy argument, plus simulations in which lowering the damping parameter $K_2$ or lengthening the inhibitory loop switches the system from propagator to oscillator. If true, the framework gives a unified, analytically tractable substrate for neuromorphic circuits that need both signal relay and rhythm generation.

What carries the argument

The load-bearing object is the rotationally symmetric differential equation $dE_i/dt = k_{1i}E_{i-1} - k_{2i}E_i - k_{3i}E_i E_{i-2}$ with cyclic indices, a five-element (or $n$-element) system containing one generative linear loop, one self-decay term, and one inhibitory quadratic loop. Its two-cycle feedback structure is what lets the same equations support both settling and oscillation. The supporting machinery is the proof chain---positivity, the Lyapunov function $V(t)=\sum_i E_i$ for boundedness, Brouwer's fixed-point theorem for existence, and a homotopy-interpolation argument for uniqueness---together with the on-road energy $R(D)=\sum_i k_{3i}D_i D_{i-2}$, which monitors the deviation $D(t)=E(t)-B$ to distinguish convergence from ongoing oscillation.

What would settle it

Randomly sample positive parameters satisfying $K_1 > K_2$ in the five-variable system and search for two distinct positive fixed points; finding one refutes the uniqueness claim. Alternatively, simulate the eight-variable model with small $K_2$ and a large initial kick and check whether the trajectory stays bounded but never revisits a fixed neighborhood of the fixed point, which would contradict the claimed dichotomy.

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Extended reading notes

Core claim

The central claim is that the symmetric differential system of Equation (3.4) has exactly two possible long-term behaviors for bounded positive trajectories: asymptotic convergence to the unique positive fixed point, or Lyapunov-stable recurrent motion around it. The author proves that the state space stays in the positive orthant, constructs a Lyapunov function $V(t)=\sum_i E_i$ to show boundedness, invokes Brouwer's fixed-point theorem to guarantee a fixed point, and attempts to show uniqueness by a monotone homotopy from two uniform-parameter extremes. Trajectories that do not terminate at the fixed point are argued to revisit its neighborhood infinitely often, ruling out escape; this recurrent behavior is identified with sustained oscillations. Numerically, the paper exhibits both regimes for a five-element system and an eight-element system, and introduces on-road energy as a global observable that declines when the system is settling and stays positive or fluctuating when it oscillates.

Load-bearing premise

The proof of a unique rest state for every allowed choice of parameters depends on an unshown claim that one can move smoothly between two special parameter sets without ever passing through a case where the rest state duplicates.

Editorial extensions

If this is right

With $K_2$ large, the model transmits a signal and returns to its fixed point; with $K_2$ small, the same equations enter sustained oscillation, so one unit can be reconfigured between relay and rhythm-generator roles.
Changing only the inhibitory-loop offset in an eight-element system, from $-2$ to $-3$, switches the unit into oscillation even with identical parameters, giving a structural as well as a parametric control knob.
On-road energy trends downward while individual components still oscillate, so it offers an early, global indicator of impending convergence in simulation and potentially in hardware monitoring.
Injecting an external signal of sufficient strength drives either kind of oscillator to a new stable fixed point, allowing artificial central pattern generators to be switched on and off.
Because the $n$-element generalization retains the same cyclic symmetry, the analytical results for five elements are claimed to carry over to larger symmetric networks.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the dichotomy is genuine, this is a rare polynomial system whose global behavior is fully classified; closing the homotopy gap by actually proving that no fixed-point duplication occurs along the interpolation would turn the uniqueness step into a theorem rather than an assertion.
The on-road energy $R(D)$ could be tested as a control Lyapunov function: if one can steer $R$ downward by feedback, it would provide a practical stabilization law for neuromorphic oscillators, a direction the paper does not pursue.
The cyclic symmetry invites an equivariant-dynamics lens: symmetry-breaking bifurcations could yield multiple coexisting rhythms or traveling waves in coupled copies, which the paper's uniqueness result rules out only for the single unit.
External suppression with a constant input suggests a natural next test: periodic or noisy inputs may entrain the oscillation to a driving rhythm, connecting the model to central pattern generator entrainment experiments.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is a decent engineering-oriented study of a symmetric five-variable neuron model, but the central theoretical claims don't hold up. The takeaway: the duality is plausible and the simulations look real, but the proof of the dichotomy is not there—recurrence is not Lyapunov stability, and uniqueness is asserted along a homotopy path that is never justified.

What is actually new: the model itself, used in prior work as a signal propagator, is shown here to also produce sustained oscillations via two mechanisms—parameter adjustment (K2) and structural changes in the inhibitory loop. That dual use of the same framework is useful, and the on-road energy metric, though simple, is a practical diagnostic for spotting convergence in simulations. The simulation setups are described with enough parameter detail to be reproducible.

What the paper does well: the simulations are clearly presented, the parameter choices are explicit, and the biological parallel (propagator vs pacemaker) is intuitively reasonable. The citation pattern is fine, with self-citations to the author's earlier papers that are on point.

The soft spots are serious. Step 4 of Section 3.3 attempts to prove uniqueness by interpolating between symmetrized extremes, but the "properly chosen sequence" that keeps the fixed point unique is never given, and monotonicity of fixed points under arbitrary parameter changes is not established. More importantly, Step 5 claims that a bounded trajectory that keeps returning to a neighborhood of the fixed point is Lyapunov stable. That is not what Lyapunov stability means. Recurrent behavior around an equilibrium does not imply that nearby initial conditions stay close; a limit cycle around an unstable fixed point is the standard counterexample. The paper's central dichotomy—asymptotic stability vs Lyapunov stability—is therefore unsupported, even if uniqueness were granted. The on-road energy is defined relative to the fixed point B, so if you don't know B, you can't compute it; and as a predictor of convergence it partly restates the deviation definition. These are load-bearing flaws, not minor ones.

Who this is for: neuromorphic engineers who want a compact oscillator/propagator model. They can still get value from the empirical findings. The paper does not deserve acceptance as is, but it does deserve a serious referee who can push the author to either repair the proofs or reframe the claims as numerical observations.

Recommendation: send it to review, expecting major revision. If the proofs can't be fixed, the paper should be reframed as a simulation study.

Referee Report

5 major / 4 minor

Summary. The paper studies a five-variable (and, in Section 4.2, eight-variable) dynamical system built from 'symmetric differential equations' derived from a Wuxing-inspired cyclic interaction structure. The central theoretical claim, stated in the abstract and Section 3.3, is that the system has a unique positive fixed point and that every bounded trajectory either converges to that fixed point (asymptotic stability, identified with signal propagation) or repeatedly returns to a neighborhood of it (labeled 'Lyapunov stability', identified with sustained oscillation). The paper further introduces an 'on-road energy' R(D), defined from the deviation from the fixed point, as a diagnostic for convergence versus oscillation, and presents simulations showing mode switching by changing the K2 parameter or the connection topology, as well as suppression of oscillations by external inputs.

Significance. If the theorem were correctly proved, the model would offer a compact single framework for both reliable signal propagation and autonomous rhythm generation, which would be of interest for neuromorphic engineering. The simulation results in Sections 4.1, 4.2 and 4.4 are suggestive: they show parameter-dependent and structure-dependent transitions between convergent and oscillatory behavior, and the idea of a structural offset controlling oscillation is interesting. However, the theoretical core of the paper, which is its main claimed contribution, is not sound. The uniqueness proof is asserted rather than demonstrated, the stability labels are not justified by the arguments given, and the on-road energy is defined in terms of the very fixed point whose attainment it is supposed to predict. Because the manuscript's central claims rest on these gaps, the paper in its current form does not support its conclusions.

major comments (5)

[Section 3.3, Step 4] The uniqueness proof is not a proof. Equation (3.17) is introduced as an approximation of the fixed point, and the text then asserts that 'a properly chosen sequence of parameter adjustments ensures that the fixed point remains unique throughout the transformation path' (text after Eq. (3.27)). No such sequence is constructed, no argument is given that the monotonicity is preserved for all intermediate parameter sets, and no bifurcation analysis is provided. Since Step 5's Case 2 contradiction relies on the uniqueness of the fixed point, this is a load-bearing gap: if uniqueness can fail, the claimed dichotomy collapses.
[Section 3.3, Step 5] The inference from trajectory behavior to stability is invalid in both directions. The text states that if a trajectory terminates at the fixed point, the omega-limit set is a singleton, 'indicating that the system is asymptotically stable.' Convergence of one trajectory does not imply asymptotic stability of the equilibrium, which requires all sufficiently nearby trajectories to converge. Similarly, the statement that a non-convergent trajectory 'returns to a neighborhood of the fixed point infinitely often' is concluded to imply Lyapunov stability. Recurrence is not Lyapunov stability: a limit cycle surrounding an unstable equilibrium is recurrent and bounded, yet the equilibrium is not Lyapunov stable and nearby trajectories can separate over time. Thus the central dichotomy between asymptotic stability and Lyapunov stability is not established.
[Section 3.3, Step 3] The Brouwer fixed-point argument is incomplete. The proof requires a compact convex forward-invariant set Omega on which T(x)=x+epsilon f(x) maps Omega into itself. The preceding Lyapunov argument only suggests boundedness of individual trajectories; it does not construct a convex invariant region. For a point on the boundary of Omega, taking epsilon small does not prevent x+epsilon f(x) from leaving Omega if f(x) points outward. Hence the existence of a fixed point is not rigorously established by the argument as written.
[Section 3.3, Step 2] The boundedness claim based on the Lyapunov function V(t)=sum E_i is not demonstrated. Equations (3.7)-(3.10) yield dV/dt = L(E_i) - Q(E_i), and the text asserts that for sufficiently large E_i the quadratic terms dominate. This is not generally true: if one component is large while its multiplicative partners in Q are bounded, Q grows only linearly in that component, and since L contains positive linear terms under K1>K2, dV/dt need not become negative. Boundedness may be provable by other means, but the stated argument is insufficient.
[Section 4.3, Eq. (4.8)] The 'on-road energy' R(D) is defined using the deviation D(t)=E(t)-B, where B is the system's fixed point. Computing R(D) therefore requires knowledge of the very fixed point whose attainment the metric is claimed to predict. If B is taken from the simulation or from an approximate formula, the statement that R(D) decays to zero in the convergent case is essentially a restatement of E(t) approaching B, rather than an independent predictive quantity. The claimed 'fast and effective indicator' status is thus not supported and inherits the unproved uniqueness of B.

minor comments (4)

[Equations (3.4), (3.24)-(3.27)] The notation in these equations is badly garbled in the typeset text; the indices and the offsets of the generative and suppressive loops are not legible. The paper should be edited so that the equations are readable.
[Section 3.3, Step 4] The symbols B_max and B_min are used without specifying whether they are vectors or scalar bounds, and the inequality B_min < B < B_max in Eq. (3.26) is not justified quantitatively, especially since B is a 5-dimensional vector.
[Figures 3 and 5] The use of a logarithmic scale in Figures 3d and 5d is mentioned in the text but not labeled on the axes; please add explicit axis labels or captions.
[Section 1] The phrase 'rigorously prove' in the introduction overstates what is actually shown; the conclusion in Section 3.3 should be aligned with the weaker statements that the arguments support.

Circularity Check

3 steps flagged · score 6.0 of 10

The 'proof' of functional duality is partly circular: uniqueness is assumed along an interpolation path, recurrence is renamed Lyapunov stability, and on-road energy is the deviation variable relabeled.

self definitional [Section 3.3, Step 4 (Equations (3.24)-(3.30) and following paragraph)]
"According to the previous monotonicity results, when the parameters K1, K2 and K3 change monotonically, the corresponding fixed point B also changes monotonically. Although this monotonicity is conditional, a properly chosen sequence of parameter adjustments ensures that the fixed point remains unique throughout the transformation path. ... By carefully regulating the full set of parameters in K1, K2 and K3, we guarantee that the fixed point evolves in a strictly monotonic manner along the transition path."

The uniqueness proof for Equation (3.4) is carried out by interpolation between two systems whose fixed points are unique, and the key step is the assertion that a 'properly chosen sequence' of parameter adjustments keeps the fixed point unique and monotone along the entire path. That is exactly the property to be established for each interpolated system; no sequence is exhibited and no argument excluding the birth of additional fixed points is given. The conclusion that uniqueness is 'preserved throughout' restates the assumption used to select the path, so uniqueness of the target fixed point is never independently proved.
renaming known result [Section 3.3, Step 5, final paragraph]
"On the other hand, if the trajectory does not terminate at the fixed point but revisits its neighborhood infinitely often, the system is Lyapunov stable."

The only antecedent derived for a non-terminating trajectory is that it 'will return to a neighborhood of the fixed point infinitely often.' Lyapunov stability is then attached to that recurrent behavior by fiat, without verifying the standard definition: for every neighborhood of the equilibrium there is a neighborhood of initial conditions whose forward orbits stay inside it. Recurrence of a single orbit does not imply Lyapunov stability (a limit cycle around an unstable equilibrium is a counterexample), and convergence of one trajectory to the fixed point does not imply asymptotic stability of the fixed point. The claimed dichotomy therefore reduces to 'converge or be recurrent,' with the second case renamed 'Lyapunov stable' rather than derived.

1 more flagged steps

self definitional [Section 4.3, Equations (4.3)-(4.8)]
"we decompose the system's state variable E(t) as follows: E(t)=B+D(t) ... Based on Equation (4.7), we define the on-road energy, denoted as R(D)... The central idea is: if the on-road energy monotonically decays to zero over time, it indicates efficient energy dissipation within the system, ultimately stabilizing at the lowest-energy fixed point. Conversely, if the on-road energy maintains a nonzero level or exhibits persistent fluctuations, it implies ... sustained oscillations."

R(D) is defined in Equation (4.8) as a quadratic function of D(t)=E(t)-B, the deviation from the fixed point. Therefore 'on-road energy decays to zero' is, up to the continuity of that quadratic form, the statement that E(t) approaches B, and 'persistent fluctuations' restates that D(t) does not converge to zero. The claimed power to 'predict' convergence or oscillation is not an independent dynamical observable; it is the deviation variable repackaged. Any such metric will trivially vanish at the fixed point by construction, so the monitoring claim is definitional rather than a derived prediction.

full rationale

Section 3.3's central theorem is not self-contained. Step 4 proves uniqueness of the positive fixed point only by assuming uniqueness along a monotone interpolation path ('a properly chosen sequence ... ensures that the fixed point remains unique'), which is precisely the conclusion needed for each interpolated system. Step 5 then converts the non-convergent case into 'Lyapunov stability' by terminology rather than by checking the standard definition; recurrence of a single orbit is not Lyapunov stability, and convergence of one orbit is not asymptotic stability. The on-road energy of Section 4.3 is defined as a function of D=E-B, so its decay is the convergence criterion restated. These are definitional reductions of the paper's 'rigorous' claims. However, the paper does not rest its model on a self-citation chain: [21-23] are background for the propagator role, while the oscillatory mode is directly exhibited in the simulations of Sections 4.1, 4.2, and 4.4. The mode-switching phenomenology is thus not circular, even though the theoretical labeling and uniqueness proof are. Score 6 reflects partial circularity: the central dichotomy and the monitoring metric reduce by construction, while the empirical simulations retain independent content.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The model itself is a cyclic predator-prey system with damping, so the main mathematical ingredients are standard. The paper adds hand-picked parameter values to produce the two regimes, an unproven uniqueness assumption, and a diagnostic metric that depends on knowing the fixed point in advance.

free parameters (2)

K2 decay coefficient (mode switch) = 0.5 (stable), 0.16 (oscillatory)
K2 is varied to demonstrate convergence versus oscillation; no theoretical critical value is derived, the values are hand-picked to produce the two regimes.
External suppression input amplitude = 0.5-1.5 for model 3d, 0.5-1.0 for model 5d
The amplitudes that fail or succeed in quenching oscillations are chosen empirically; no threshold is predicted.

assumptions (5)

domain assumption K1 > K2 for all components
Section 2 imposes this to guarantee a positive fixed point; no biological justification is given.
ad hoc to paper Equation (3.17) accurately approximates the true fixed point of Equation (3.4)
Step 4 uses this approximation to argue monotone dependence of the true fixed point, but no error bound is provided.
ad hoc to paper Monotone parameter interpolation preserves uniqueness of the fixed point
Step 4 relies on this to claim no bifurcations along the transformation path, but no proof is given that sequential parameter adjustment avoids bifurcations.
standard math Brouwer fixed-point theorem
Invoked in Step 3 to establish existence of a fixed point in a compact convex region.
standard math Lyapunov's second method
Invoked in Step 2 for boundedness; the constructed Lyapunov function is used informally.

invented entities (1)

On-road energy R(D)
purpose: A real-time scalar diagnostic to distinguish convergent from oscillatory regimes during simulations.
It is defined as a weighted sum of products of deviations from the fixed point; its behavior simply mirrors the deviation dynamics, so it offers no falsifiable handle outside the model. It also requires the fixed point B, which is only known exactly in symmetric cases.

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Cite this review

Pith. "Pith review of From Propagator to Oscillator: The Dual Role of Symmetric Differential Equations in Neural Systems." pith.science (2026). https://pith.science/paper/Q7LNWKKK

@misc{pith2026250722916,
  author       = {Pith},
  title        = {Pith review of: From Propagator to Oscillator: The Dual Role of Symmetric Differential Equations in Neural Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q7LNWKKK}},
  note         = {Machine review of arXiv:2507.22916}
}

read the original abstract

In our previous work, we proposed a novel neuron model based on symmetric differential equations and demonstrated its potential as an efficient signal propagator. Building upon that foundation, the present study delves deeper into the intrinsic dynamics and functional diversity of this model. By systematically exploring the parameter space and employing a range of mathematical analysis tools, we theoretically reveal the system 's core property of functional duality. Specifically, the model exhibits two distinct trajectory behaviors: one is asymptotically stable, corresponding to a reliable signal propagator; the other is Lyapunov stable, characterized by sustained self-excited oscillations, functioning as a signal generator. To enable effective monitoring and prediction of system states during simulations, we introduce a novel intermediate-state metric termed on-road energy. Simulation results confirm that transitions between the two functional modes can be induced through parameter adjustments or modifications to the connection structure. Moreover, we show that oscillations can be effectively suppressed by introducing external signals. These findings draw a compelling parallel to the dual roles of biological neurons in both information transmission and rhythm generation, thereby establishing a solid theoretical basis and a clear functional roadmap for the broader application of this model in neuromorphic engineering.

Figures

Figures reproduced from arXiv: 2507.22916 by the authors.

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Reference graph

Works this paper leans on

6 extracted references · 5 canonical work pages

[1]

Introduction Artificial Neural Networks (ANNs), particularly deep learning systems, have achieved remarkable breakthroughs in recent years across a wide range of fields including image recognition, language understanding, control, and de cision-making[1-3]. However, these successes largely rely on massive computational resources and high energy consumptio...

work page
[2]

However, classical mode ls such as the Hodgkin-Huxley (HH) system[12], despite their biological fidelity, are often too complex to be deployed at scale

Symmetric differential equations and parameter choices In the field of computational neuroscience, differential equations have long served as a foundational tool for modeling the dynamical behavior of neural systems. However, classical mode ls such as the Hodgkin-Huxley (HH) system[12], despite their biological fidelity, are often too complex to be deploy...

work page
[3]

Fixed points provide an intuitive geometric interpretation of equilibrium or steady-state solutions of differential equations

System analysis 3.1 Static Analysis In dynamical systems, fixed point theory serves as one of the most f undamental approaches for analyzing system properties. Fixed points provide an intuitive geometric interpretation of equilibrium or steady-state solutions of differential equations. For a given differential equation, a fixed point corresponds to a stat...

work page
[4]

On -road Energy

System Functionality and Simulation In Chapter 3, we conducted a rigorous mathematical analysis d emonstrating that the proposed symmetric differential equation system possesses a functional duality: depending on specific parameter settings and system states, its trajectories may either asymptotically stabilize at a fixed point or exhibit sustained oscill...

work page
[5]

We proved that the system's state space is bounded, and that its trajectories either converge to a unique positive fixed point or recurrently return to its neighborhood

Conclusion In this work, we have systematically investigated th e dynamic characteristics of a symmetric differential equation-based neural model. We proved that the system's state space is bounded, and that its trajectories either converge to a unique positive fixed point or recurrently return to its neighborhood. This property reveals the model’s potent...

arXiv 2015
[2025]

A Neural Network Training Method Based on Neuron Connection Coefficient Adjustments

17(7): p. 1129 [23]. Jiang, K., A Neural Network Training Method Based on Neuron Connection Coefficient Adjustments. arXiv preprint arXiv:2502.10414, 2025. https://doi.org/10.48550/arXiv.2502.10414 [24]. Sussillo, D. and O. Barak, Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural computation, 2013. 25(3)...

work page Pith review arXiv doi:10.48550/arxiv.2502.10414 2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Introduction Artificial Neural Networks (ANNs), particularly deep learning systems, have achieved remarkable breakthroughs in recent years across a wide range of fields including image recognition, language understanding, control, and de cision-making[1-3]. However, these successes largely rely on massive computational resources and high energy consumptio...

work page

[2] [2]

However, classical mode ls such as the Hodgkin-Huxley (HH) system[12], despite their biological fidelity, are often too complex to be deployed at scale

Symmetric differential equations and parameter choices In the field of computational neuroscience, differential equations have long served as a foundational tool for modeling the dynamical behavior of neural systems. However, classical mode ls such as the Hodgkin-Huxley (HH) system[12], despite their biological fidelity, are often too complex to be deploy...

work page

[3] [3]

Fixed points provide an intuitive geometric interpretation of equilibrium or steady-state solutions of differential equations

System analysis 3.1 Static Analysis In dynamical systems, fixed point theory serves as one of the most f undamental approaches for analyzing system properties. Fixed points provide an intuitive geometric interpretation of equilibrium or steady-state solutions of differential equations. For a given differential equation, a fixed point corresponds to a stat...

work page

[4] [4]

On -road Energy

System Functionality and Simulation In Chapter 3, we conducted a rigorous mathematical analysis d emonstrating that the proposed symmetric differential equation system possesses a functional duality: depending on specific parameter settings and system states, its trajectories may either asymptotically stabilize at a fixed point or exhibit sustained oscill...

work page

[5] [5]

We proved that the system's state space is bounded, and that its trajectories either converge to a unique positive fixed point or recurrently return to its neighborhood

Conclusion In this work, we have systematically investigated th e dynamic characteristics of a symmetric differential equation-based neural model. We proved that the system's state space is bounded, and that its trajectories either converge to a unique positive fixed point or recurrently return to its neighborhood. This property reveals the model’s potent...

arXiv 2015

[6] [2025]

A Neural Network Training Method Based on Neuron Connection Coefficient Adjustments

17(7): p. 1129 [23]. Jiang, K., A Neural Network Training Method Based on Neuron Connection Coefficient Adjustments. arXiv preprint arXiv:2502.10414, 2025. https://doi.org/10.48550/arXiv.2502.10414 [24]. Sussillo, D. and O. Barak, Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural computation, 2013. 25(3)...

work page Pith review arXiv doi:10.48550/arxiv.2502.10414 2025